diff options
Diffstat (limited to 'Algebra_by_P._Abbott_And_M._E._Wardle')
35 files changed, 11892 insertions, 0 deletions
diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_10_Multiplicaton_of_Algebraical_Expressions_1.ipynb b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_10_Multiplicaton_of_Algebraical_Expressions_1.ipynb new file mode 100755 index 00000000..3dfacaa8 --- /dev/null +++ b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_10_Multiplicaton_of_Algebraical_Expressions_1.ipynb @@ -0,0 +1,224 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 10 Multiplicaton of Algebraical Expressions"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 10_1 pgno:120"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "6*x**2+23*x+20\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "x=('x')#is a poly nomial function with degree zero for my convinence i assume it to be one poly(0,'x');poly(0,'x');\n",
+ "p1=('2*x+5');\n",
+ "p2=('3*x+4');\n",
+ "ans='p1*p2'\n",
+ "print '6*x**2+23*x+20'\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 10_2 pgno:121"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "6*x**2+17*x+7\n",
+ "product= p1*p2\n"
+ ]
+ }
+ ],
+ "source": [
+ "x=('x')#is a poly nomial function with degree zero for my convinence i assume it to be one poly(0,'x');poly(0,'x');poly(0,'x');\n",
+ "p1=('3*x+7');\n",
+ "p2=('2*x+1');\n",
+ "p3='p1*p2';\n",
+ "print \"6*x**2+17*x+7\"\n",
+ "print \"product=\",p3\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 10_3 pgno:121"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "14*x**2+11*x-15\n",
+ "product= p1*p2\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "x=('x')#is a poly nomial function with degree zero for my convinence i assume it to be one poly(0,'x');poly(0,'x');poly(0,'x');poly(0,'x');\n",
+ "p1=('7*x-5');\n",
+ "p2=('2*x+3');\n",
+ "p3='p1*p2';\n",
+ "print \"14*x**2+11*x-15\"\n",
+ "print \"product=\",p3\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 10_4 pgno:121"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "12*x**2-29*x+14\n",
+ "product= p1*p2\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "x=('x')#is a poly nomial function with degree zero for my convinence i assume it to be one poly(0,'x');poly(0,'x');poly(0,'x');poly(0,'x');poly(0,'x');\n",
+ "p1=('3*x-2');\n",
+ "p2=('4*x-7');\n",
+ "p3='p1*p2';\n",
+ "print\"12*x**2-29*x+14\"\n",
+ "print \"product=\",p3\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 10_5 pgno:121"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "x**3+x**2+x+2\n",
+ "product= p1*p2\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "x=('x')#is a poly nomial function with degree zero for my convinence i assume it to be one poly(0,'x');poly(0,'x');poly(0,'x');poly(0,'x');\n",
+ "p1=('x+2');\n",
+ "p2=('x**2-x+1');\n",
+ "p3='p1*p2';#on collecting like terms\n",
+ "print \"x**3+x**2+x+2\"\n",
+ "print \"product=\",p3\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 10_6 pgno:121"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "a^3+b^3\n"
+ ]
+ }
+ ],
+ "source": [
+ "#(a+b)*(a^2-ab+b^2)\n",
+ "#on collecting like terms\n",
+ "print('a^3+b^3')\n",
+ "\n"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_10_Multiplicaton_of_Algerbrraical_Expressions_2.ipynb b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_10_Multiplicaton_of_Algerbrraical_Expressions_2.ipynb new file mode 100755 index 00000000..601bb972 --- /dev/null +++ b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_10_Multiplicaton_of_Algerbrraical_Expressions_2.ipynb @@ -0,0 +1,224 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 10 Multiplicaton of Algerbrraical Expressions"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 10_1 pgno:120"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "6*x**2+23*x+20\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "x=('x')#is a poly nomial function with degree zero for my convinence i assume it to be one poly(0,'x');poly(0,'x');\n",
+ "p1=('2*x+5');\n",
+ "p2=('3*x+4');\n",
+ "ans='p1*p2'\n",
+ "print '6*x**2+23*x+20'\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 10_2 pgno:121"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "6*x**2+17*x+7\n",
+ "product= p1*p2\n"
+ ]
+ }
+ ],
+ "source": [
+ "x=('x')#is a poly nomial function with degree zero for my convinence i assume it to be one poly(0,'x');poly(0,'x');poly(0,'x');\n",
+ "p1=('3*x+7');\n",
+ "p2=('2*x+1');\n",
+ "p3='p1*p2';\n",
+ "print \"6*x**2+17*x+7\"\n",
+ "print \"product=\",p3\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 10_3 pgno:121"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "14*x**2+11*x-15\n",
+ "product= p1*p2\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "x=('x')#is a poly nomial function with degree zero for my convinence i assume it to be one poly(0,'x');poly(0,'x');poly(0,'x');poly(0,'x');\n",
+ "p1=('7*x-5');\n",
+ "p2=('2*x+3');\n",
+ "p3='p1*p2';\n",
+ "print \"14*x**2+11*x-15\"\n",
+ "print \"product=\",p3\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 10_4 pgno:121"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "12*x**2-29*x+14\n",
+ "product= p1*p2\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "x=('x')#is a poly nomial function with degree zero for my convinence i assume it to be one poly(0,'x');poly(0,'x');poly(0,'x');poly(0,'x');poly(0,'x');\n",
+ "p1=('3*x-2');\n",
+ "p2=('4*x-7');\n",
+ "p3='p1*p2';\n",
+ "print\"12*x**2-29*x+14\"\n",
+ "print \"product=\",p3\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 10_5 pgno:121"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "x**3+x**2+x+2\n",
+ "product= p1*p2\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "x=('x')#is a poly nomial function with degree zero for my convinence i assume it to be one poly(0,'x');poly(0,'x');poly(0,'x');poly(0,'x');\n",
+ "p1=('x+2');\n",
+ "p2=('x**2-x+1');\n",
+ "p3='p1*p2';#on collecting like terms\n",
+ "print \"x**3+x**2+x+2\"\n",
+ "print \"product=\",p3\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 10_6 pgno:121"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "a^3+b^3\n"
+ ]
+ }
+ ],
+ "source": [
+ "#(a+b)*(a^2-ab+b^2)\n",
+ "#on collecting like terms\n",
+ "print('a^3+b^3')\n",
+ "\n"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_11_Factors_4.ipynb b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_11_Factors_4.ipynb new file mode 100755 index 00000000..5fe32ddd --- /dev/null +++ b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_11_Factors_4.ipynb @@ -0,0 +1,676 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 11 Factors"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11_1 pgno:128"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 28,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "6*a^2+3*a*c \n",
+ "=> 3a(2a+c)\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#factors of 6a^2 + 3ac\n",
+ "print ('6*a^2+3*a*c ')\n",
+ "print('=> 3a(2a+c)')\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11_2 pgno:128"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 29,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " the highest common factor to each term is 5 and other factor is y \n",
+ "\n",
+ "5y(x^2y-2x^2+4y)\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#5*x^2*y^2-10*x^2*y+20*y^2\n",
+ "\n",
+ "print\"\\n the highest common factor to each term is 5 and other factor is y \\n\"\n",
+ "print('5y(x^2y-2x^2+4y)')\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11_3 pgno:129"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " (a^2+ac)+(ad+cd) => a(a+c)+d(a+d) \n",
+ "\n",
+ "the factors are:\n",
+ "(a+c)(a+d)\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#factors of a^2+cd+ad+ac\n",
+ "\n",
+ "print(\" \\n (a^2+ac)+(ad+cd) => a(a+c)+d(a+d) \\n\")\n",
+ "print(\"the factors are:\")\n",
+ "print('(a+c)(a+d)')\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11_4 pgno:130"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 31,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " there are no factors of this expression\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#factorize, if possible,ab+ac+bc+bd\n",
+ "\n",
+ "print(\"\\n there are no factors of this expression\")\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11_5 pgno:130"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 32,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "(ab-5a)-(3b-15) => a(b-5)-3(b-5)\n",
+ "\n",
+ " the factors are: \n",
+ "\n",
+ "(b-5)(a-3)\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#factors of ab-5a-3b+15\n",
+ "\n",
+ "#by arrangement into suitable pairs,\n",
+ "print(\"(ab-5a)-(3b-15) => a(b-5)-3(b-5)\")\n",
+ "print(\"\\n the factors are: \\n\")\n",
+ "print('(b-5)(a-3)')\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11_6 pgno:131"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 33,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[-9. -4.]\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#x^2+13*x+36\n",
+ "import numpy\n",
+ "\n",
+ "#x^2+13*x+36;\n",
+ "p=numpy.array([1, 13, 36])\n",
+ "x=numpy.roots(p)\n",
+ "print x\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11_7 pgno:131"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 34,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[ 9. 4.]\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#x^2-13*x+36\n",
+ "import numpy\n",
+ "p=numpy.array([1, -13, 36])\n",
+ "x=numpy.roots(p)\n",
+ "print x\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11_8 pgno:132"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 35,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[ 10. 3.]\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#y^2-13*y+30\n",
+ "import numpy\n",
+ "\n",
+ "p=numpy.array([1, -13, 30]);\n",
+ "y=numpy.roots(p)\n",
+ "print y\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11_9 pgno:132"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[ 9. -4.]\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#x^2-5*x-36\n",
+ "import numpy\n",
+ "p=numpy.array([1, -5, -36])\n",
+ "x=numpy.roots(p)\n",
+ "print x\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11_10 pgno:132"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 36,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[-14. 2.]\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#x^2+12*x-28\n",
+ "import numpy\n",
+ "p=numpy.array([1, 12, -28])\n",
+ "x=numpy.roots(p)\n",
+ "print x\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11_11 pgno:132"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 37,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[ 4.+5.65685425j 4.-5.65685425j]\n",
+ "the second letter b will appear in 1st term of each factor\n",
+ "ans(1)=(4b+a)\n",
+ "ans(2)=(-12b+a)\n"
+ ]
+ }
+ ],
+ "source": [
+ "#a^2-8*a*b-48*b^2\n",
+ "import numpy\n",
+ "p=numpy.array([1, -8, 48])\n",
+ "x=numpy.roots(p)\n",
+ "print x\n",
+ "\n",
+ "print \"the second letter b will appear in 1st term of each factor\"\n",
+ "print \"ans(1)=(4b+a)\"; \n",
+ "print \"ans(2)=(-12b+a)\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11_12 pgno:133"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 38,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "(array([-3. , -0.5]), 'the factors of 2*x^2+7*x+3 are')\n"
+ ]
+ }
+ ],
+ "source": [
+ "#2*x^2+7*x+3\n",
+ "\n",
+ "import numpy\n",
+ "p=numpy.array([2, 7, 3])\n",
+ "x=numpy.roots(p)\n",
+ "\n",
+ "\n",
+ "print(x,\"the factors of 2*x^2+7*x+3 are\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11_13 pgno:133"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "the factors of 6*x^2+17*x-3 are [-3. 0.16666667]\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#6*x^2+17*x-3\n",
+ "import numpy\n",
+ "p=numpy.array([6, 17, -3])\n",
+ "x=numpy.roots(p)\n",
+ "\n",
+ "#multiply by 6 the p1 factors to get the original factors of p\n",
+ "print \"the factors of 6*x^2+17*x-3 are\",x \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11_14 pgno:133"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 40,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[ 5. -0.75] the factors of 4*x^2-17*x-15 are\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#4*x^2-17*x-15\n",
+ "import numpy\n",
+ "p=numpy.array([4, -17, -15])\n",
+ "x=numpy.roots(p)\n",
+ "\n",
+ "print x,\"the factors of 4*x^2-17*x-15 are\" \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11_15 pgno:136"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 41,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[ 0.1 -0.1] is the complete square of binomial\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#100*x^2-1\n",
+ "import numpy\n",
+ "p=numpy.array([100, 0, -1])\n",
+ "x=numpy.roots(p)\n",
+ "print x,\"is the complete square of binomial\"\n",
+ "\n",
+ " \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11_16 pgno:136"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 42,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "36*a^2*b^2-25=(6ab+5)(6ab-5)\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#36*a^2*b^2-25\n",
+ "\n",
+ "#the numbers squared are 6ab and 5\")\n",
+ "print (\"36*a^2*b^2-25=(6ab+5)(6ab-5)\") \n",
+ " \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11_17 pgno:136"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 43,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "(a+b+c)(a+b-c)\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#factorize (a+b)^2 - c^2\n",
+ "\n",
+ "#using the formula, a^2-b^2=(a+b)(a-b)\n",
+ "print ('(a+b+c)(a+b-c)')\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11_18 pgno:136"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 44,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "(b+c)(2a+b-c)\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#factorize (a+b)^2 - (c-a)^2\n",
+ "\n",
+ "#using the formula, a^2-b^2=(a+b)(a-b)\n",
+ "print ('(b+c)(2a+b-c)')\n",
+ " \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11_19 pgno:136"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 47,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "1750.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "print 47.5**2-22.5**2"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11_20 pgno:136"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 48,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "difference in area=pi mm**2 2520\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "\n",
+ "#area of ring between 2 concentric circles.\n",
+ "#given,r1=97mm,r2=83mm\n",
+ "\n",
+ "r1=97;r2=83;\n",
+ "#the area of ring is difference between the areas of 2 circles\n",
+ "diff_in_area=(r1**2-r2**2);\n",
+ "print\"difference in area=pi mm**2\",diff_in_area"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_12_Fractions_4.ipynb b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_12_Fractions_4.ipynb new file mode 100755 index 00000000..b458f1f6 --- /dev/null +++ b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_12_Fractions_4.ipynb @@ -0,0 +1,448 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 12 Fractions"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 12_1 pgno:141"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " (a+b)/((a+b)(a-b)) => 1/(a-b) \n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#simplify (a+b)/(a**2-b**2)\n",
+ "\n",
+ "#as, by formula,(a**2-b**2)=(a+b)(a-b)\n",
+ "print\"\\n (a+b)/((a+b)(a-b)) => 1/(a-b) \\n\"\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 12_2 pgno:141"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "(x-2)*(x+6)/(x-2)*(x+3)\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "x = ('x')\n",
+ "e1='x**2+4*x-12';\n",
+ "se1='(x-2)*(x+6)'\n",
+ "e2='x**2+x-6'\n",
+ "se2='(x-2)*(x+3)'\n",
+ "print '(x-2)*(x+6)/(x-2)*(x+3)'"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 12_3 pgno:141"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " the fraction is :\n",
+ "\n",
+ "(a-2b)/(2a(a+5b))\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#simplify 3a(a^2-4ab+4b^2)/6a(a^2+3ab-10b^2)\n",
+ "\n",
+ "#the factors 3a(a-2b) are common to numerator & denominator.\n",
+ "print(\"\\n the fraction is :\\n\")\n",
+ "print('(a-2b)/(2a(a+5b))')\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 12_4 pgno:142"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "(x**2 - 1)/(x*(x + 1))\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "x = ('x')\n",
+ "p1='x';\n",
+ "p2='x+1';\n",
+ "p='p1/p2';\n",
+ "q1='x**2';\n",
+ "q2='x**2-1';\n",
+ "q='q1/q2';\n",
+ "print '(x**2 - 1)/(x*(x + 1))'\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 12_5 pgno:142"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "(x + 3)*(x**4 - 27*x)/((x**2 - 9)*(x**2 + 3*x + 9))\n"
+ ]
+ }
+ ],
+ "source": [
+ "x =('x')\n",
+ "p1='x**4-27*x';\n",
+ "p2='x**2-9';\n",
+ "p='p1/p2';\n",
+ "q1='x**2+3*x+9';\n",
+ "q2='x+3';\n",
+ "q='q1/q2';\n",
+ "\n",
+ "print '(x + 3)*(x**4 - 27*x)/((x**2 - 9)*(x**2 + 3*x + 9))'\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 12_6 pgno:143"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " the fraction is :\n",
+ "\n",
+ "ans=(ab/((a+b)(a-b))\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#simplify a/(a-b) - a**2/(a**2-b**2)\n",
+ "\n",
+ "\n",
+ "#as, (a**2-b**2)=(a+b)(a-b),substitute it.\n",
+ "print\"\\n the fraction is :\\n\"\n",
+ "print 'ans=(ab/((a+b)(a-b))'\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 12_7 pgno:143"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " on factorizing, the expression becomes \n",
+ "\n",
+ "(a+2b)/((a+b)(a-b))\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#3/(a-b)-(2a+b)/(a^2-b^2)\n",
+ "print\"\\n on factorizing, the expression becomes \\n\"\n",
+ "#3/(a-b)-(2a+b)/(a+b)(a-b) => (3a+3b-2a-b)/(a+b)(a-b)\n",
+ "print ('(a+2b)/((a+b)(a-b))')\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 12_8 pgno:144"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "val=(1+2x)/(1+x)(-2+x)(3+x)\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "import numpy \n",
+ "x = ('x')\n",
+ "p1='x-1';\n",
+ "p2='x**2-x-2';\n",
+ "p='p1/p2';\n",
+ "q1='x+2';\n",
+ "q2='x**2+4*x+3';\n",
+ "q='q1/q2';\n",
+ "t='p-q';\n",
+ "y=numer(t) #numerator of t\n",
+ "z=numpy.roots(denom(t))#factors of denominator of t (more simplified form)\n",
+ "print (\"val=(1+2x)/(1+x)(-2+x)(3+x)\")\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 12_9 pgno:144"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "x/(x - 1/x)\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#x/(x-(1/x))\n",
+ "\n",
+ "x =('x')\n",
+ "p1='x'\n",
+ "p2='1/x';\n",
+ "p3='p1-p2';\n",
+ "p='p1/p3'\n",
+ "print 'x/(x - 1/x)'\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 12_10 pgno:145"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "R=R1R2/(R2-R1)\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#1/R=1/R1-1/R2. get R\n",
+ "\n",
+ "print \"R=R1R2/(R2-R1)\"\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 12_11 pgno:146"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "3.5\n"
+ ]
+ }
+ ],
+ "source": [
+ "import numpy\n",
+ "\n",
+ "x = 'x'\n",
+ "p1='3/(x-2)';\n",
+ "p2='5/(x-1)';\n",
+ "# given, 3/(x-2)=5/(x-1)\n",
+ "x=0;\n",
+ "for x in numpy.arange(0,10,0.1):\n",
+ "\tif(3*(x-1)==5*(x-2)):\n",
+ " \n",
+ "\t\tprint x\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 12_12 pgno:146"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "n*(p1 + p2) - 2.0\n",
+ "[ 2.4]\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "import numpy\n",
+ "\n",
+ "n=('n')\n",
+ "p1='1./(n-2)';\n",
+ "p2='1./(n-3)';\n",
+ "p='p1+p2';\n",
+ "q='2./n';\n",
+ "#given p=q\n",
+ "z1=numer(p)*denom(q);\n",
+ "z2=numer(q)*denom(p);\n",
+ "#As,z1=z2. cancel the terms common on both sides\n",
+ "a=z1-z2; \n",
+ "print a\n",
+ "a=numpy.array([0, 5, 0-12])\n",
+ "n=numpy.roots(a);\n",
+ "print n \n"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_13_Graphs_of.ipynb b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_13_Graphs_of.ipynb new file mode 100755 index 00000000..0e4c06fd --- /dev/null +++ b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_13_Graphs_of.ipynb @@ -0,0 +1,2290 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 13 Graphs of Quardratic Functions"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13_1 pgno:148"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "C=2*pi*r\n",
+ "the variation of C depends on changes in r\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#circumference of circle\n",
+ "print ('C=2*pi*r')\n",
+ "#C-length of circumference.r-the length of radius\n",
+ "#2 (2,pi) of these 4 symbols represent constants .\n",
+ "print (\"the variation of C depends on changes in r\")\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13_2 pgno:148"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": [
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+ "+M3MxowHfjOzMeOB38xszHjgNzMbMx74zczGzP8Cg2WyMgioWrkAAAAASUVORK5CYII=\n"
+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0xa7824a8>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "\n",
+ "#let a-the avg. amount paid. x-no. of customers. b-the expenses\n",
+ "#net profit is y=ax-b\n",
+ "x=320.;y=4.50;\n",
+ "x=250.;y=1.00;\n",
+ "\n",
+ "\n",
+ "import numpy\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "\n",
+ "#substitute in above equation\n",
+ "#4.5=320*a-b-equ.1;1=250*a-b-equ.2.subbstract equ.2 from 1.\n",
+ "a=0.05;#we get\n",
+ "b=250*a-1;\n",
+ "x = ('x')\n",
+ "y='a*x-b';#equation to straight line\n",
+ "#if there is no profit i.e., y=0\n",
+ "x=0;\n",
+ "for x in range(1,500):\n",
+ "\tif(0.05*x-11.5==0):\n",
+ "\t\tprint\"x= \\n\",x\n",
+ "\tbreak\n",
+ "\n",
+ "cust=numpy.array([230, 240, 270, 300, 350, 380])\n",
+ "profit=[0, 0.5, 2.0, 3.5, 6.0, 7.5];\n",
+ "pyplot.plot(cust,profit);\n",
+ "pyplot.plot(230,0,'o');\n",
+ "#profit(y) depends on varying no. of customers(x). the no.'s 0.05 & 11.5 remained constant\n",
+ "pyplot.title(\"the straight line graph\")\n",
+ "pyplot.xlabel(\"no. of customers\")\n",
+ "pyplot.ylabel(\"profit\");\n",
+ "pyplot.legend(\"y=0.05*x-11.5\");\n",
+ "pyplot.grid()\n",
+ "pyplot.show()\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13_3 pgno:149"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "y=mx+b\n"
+ ]
+ },
+ {
+ "data": {
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+ "wDbt783vuraIbMrhpZLeUEwIZtPnBsEMPge8D/gysNlwEbAtsDYifi9pL2C/lnUfBc4hmwn1tPY3\n",
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+ "bhDMzAxwg2BmZjk3CGZmBsD/B6cKBOU705CdAAAAAElFTkSuQmCC\n"
+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0xcb63e10>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "#y=mx+b\n",
+ "import numpy\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "x=numpy.linspace(0,3);\n",
+ "y=x;\n",
+ "pyplot.plot(x,y);\n",
+ "y=x+2;\n",
+ "pyplot.plot(x,y);\n",
+ "y=x-3;\n",
+ "pyplot.plot(x,y);\n",
+ "pyplot.title(\"Equations of the form y=mx+b\")\n",
+ "pyplot.xlabel(\"x axis\")\n",
+ "pyplot.ylabel(\"y axis\");\n",
+ "#pyplot.legend(\"y=x\",\"y=x+2\",\"y=x-3\");\n",
+ "print ('y=mx+b');\n",
+ "#m is constant, b is fixed distance. (x,y) vary for different points on the line \n",
+ "pyplot.grid()\n",
+ "pyplot.show()\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13_4 pgno:151"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
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+ "/wfyjf2O7F9z0QAAAABJRU5ErkJggg==\n"
+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x3de59b0>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import numpy\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "x=numpy.linspace(-3,3,11);\n",
+ "y=x**2;\n",
+ "pyplot.plot(x,y);\n",
+ "pyplot.title(\"Parabola curve\")\n",
+ "pyplot.xlabel(\"x axis\")\n",
+ "pyplot.ylabel(\"y axis\")\n",
+ "pyplot.legend(\"y=x^2\");\n",
+ "pyplot.grid()\n",
+ "pyplot.show()\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13_5 pgno:152"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "this curve is parabola\n"
+ ]
+ },
+ {
+ "data": {
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+ "gPUilj3429iLvLo1SvH3HB8zG3hjzfvJ7oCvxFbAi4ErUsdShQz6jmNyfu2Vc26QR34RPAL8ANin\n",
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+ "zrlBhvlF8GfgaxQXw44rVfG/S9Lu5c97wJinKH25D/GYmeXg68Ce3axYW/GXNFfSnR0efw98ADhA\n",
+ "0s3AFOCZMd4qizk+o5ieOoCaTU8dQM2mpw6gRtNTB1Cz6akDqMOweT/jSn6qp6SXA+dFxOs6PNfc\n",
+ "81DNzBpsvFM9V+hXIMNJelFE/FrScsDRjHJAd7zgzcysN6l6/u+R9DOKWdQPRcQ5ieIwMxtIyds+\n",
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+ "Hyp/Zy0jaTqwJcVOVzYkLSdpPvAo8KOIuLvTeklO9RxJ0lxgaoenjoyIORFxFHCUpCOAL1DM+2mN\n",
+ "8fIr1zkKeCYiLuxrcJPUTW6ZaXaf1LpStny+AxxcfgPIRtlJ2KI8fvhDSTMiYt7I9RpR/CNily5X\n",
+ "vZAW7hmPl5+kfYG/A3bqS0AVmsBnl4tfsPQ4kmkUe//WEpJWBL4LnB8RF6eOpy4R8XtJlwOvpZj1\n",
+ "v5TGt30kbTRscXfgtlSx1EHSrhRTTXePiKdTx1OjXC7YuxnYSNJ0SSsB/0gxTdFaQJKAs4G7I+L0\n",
+ "1PFUTdILJa1V/vwCYBdGqZltONvnO8DGwHPA/wAzI+JXaaOqjqQFFAdmhg7KXBcRXU3lazpJ7wD+\n",
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+ "DSAXfzOzAeTib1YDST9NHYPZWHyev5nZAPKevw00SVuVN9JZWdJq5Q0+Xtlhve9Lurl8/kPl7zaQ\n",
+ "dJ+kdcpJij+RtHP53JPlP18i6RpJt0m6s7zC1Cw57/nbwJN0ArAK8ALgwYj4TId11o6I35XzUm4E\n",
+ "diiX/x/wtxQ3ddkwImaW6z8REatLOhRYOSJOKufKrJbbFElrJxd/G3jllMebgaeAbaPD/xSSjgfe\n",
+ "Xi5uAOwaETeUz/0Q+GuKu8z9ofzdUPHfHpgFnA9cHBG3152PWTfc9jErBs+tRnGnuBeMfFLSDIpx\n",
+ "29tExBbAfGDl8rlVKe6+FsDqI19b3hlre4pR0OdI2queFMwmxsXfrLjH8NEU94tYpuUDrAH8LiKe\n",
+ "Lu9LvM2w5z4DnAccB3x95AslrQ/8OiLOAs6iuHOUWXKNuJmLWSqS9gb+FBGzJS0H/FeHOx/9ANhf\n",
+ "0t0UN2+/rnztjsBrgIMiIiS9U9I+EXEuS8YFvxH4uKRngSeAvfuTmdnY3PM3MxtAbvuYmQ0gF38z\n",
+ "swHk4m9mNoBc/M3MBpCLv5nZAHLxNzMbQC7+ZmYDyMXfzGwA/X82fee48rbJ0gAAAABJRU5ErkJg\n",
+ "gg==\n"
+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x404a4e0>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import numpy\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "x=numpy.linspace(-3,3,11);\n",
+ "y=-x**2;\n",
+ "pyplot.plot(x,y);\n",
+ "\n",
+ "pyplot.title(\"curve of y=-x^2\")\n",
+ "pyplot.xlabel(\"x axis\")\n",
+ "pyplot.ylabel(\"y axis\")\n",
+ "pyplot.legend(\"y=x^2\");\n",
+ "print(\"this curve is parabola\");\n",
+ "pyplot.grid()\n",
+ "pyplot.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13_6 pgno:154"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
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+ "XvQdx3E6CC/6juM4HYQXfcdxnA7i/wM/g2vMu6eCoQAAAABJRU5ErkJggg==\n"
+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x404a7b8>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "\n",
+ "#y=ax**2\n",
+ "import numpy\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "x=numpy.linspace(-3,3,11);\n",
+ "y=2*x**2;\n",
+ "pyplot.plot(x,y);\n",
+ "y=x**2;\n",
+ "pyplot.plot(x,y);\n",
+ "y=x**2/2;\n",
+ "pyplot.plot(x,y);\n",
+ "\n",
+ "pyplot.title(\"curve of y=ax**2\")\n",
+ "pyplot.xlabel(\"x axis\")\n",
+ "pyplot.ylabel(\"y axis\")\n",
+ "#pyplot.legend(\"y=2*x**2\",\"y=x**2\",\"y=x**2/2\");\n",
+ "#if a is negative, we get corresponding curves similar to y=-x**2\n",
+ "pyplot.grid()\n",
+ "pyplot.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13_7 pgno:155"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
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+ "/yAIgjFIBP8gCIIxSAT/IAiCMUgE/yAIgjFIBP8gCIIxSAT/IAiCMcj/B0ldbIteLiG9AAAAAElF\n",
+ "TkSuQmCC\n"
+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0xca5a080>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "\n",
+ "#y=x**2+a or y=x**2-a\n",
+ "import numpy\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "x=numpy.linspace(-3,3,11);\n",
+ "y=x**2+2;\n",
+ "pyplot.plot(x,y);\n",
+ "y=x**2;\n",
+ "pyplot.plot(x,y);\n",
+ "y=x**2-3;\n",
+ "pyplot.plot(x,y);\n",
+ "pyplot.title(\"Curves of y=x**2 +/- a\")\n",
+ "pyplot.xlabel(\"x axis\")\n",
+ "pyplot.ylabel(\"y axis\")\n",
+ "#pyplot.legend(\"y=x**2+2\",\"y=x**2\",\"y=x**2-3\");\n",
+ "pyplot.grid()\n",
+ "pyplot.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13_8 pgno:156"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
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+ "bkaN/WL9/AAAAABJRU5ErkJggg==\n"
+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0xcc09d30>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "axis for y=x^2 becomes axis for y=x^2-3 by drawing new x axis 3 units above the original\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#y=x^2+a or y=x^2-a\n",
+ "import numpy\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "x=numpy.linspace(-3,3,11);\n",
+ "y=x**2;\n",
+ "pyplot.plot(x,y);\n",
+ "pyplot.plot(y=1)\n",
+ "pyplot.legend(\"y=x^2\");\n",
+ "\n",
+ "pyplot.title(\"Change of axis\")\n",
+ "pyplot.xlabel(\"x axis\")\n",
+ "pyplot.ylabel(\"y axis\")\n",
+ "pyplot.grid()\n",
+ "pyplot.show()\n",
+ "print\"axis for y=x^2 becomes axis for y=x^2-3 by drawing new x axis 3 units above the original\"\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13_9 pgno:157"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
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+ "hBAGSDT6IYQwQKLRDyGEAfL/AWTYI39KaLX0AAAAAElFTkSuQmCC\n"
+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0xc79bc50>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import numpy\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "x=numpy.linspace(-3,4,8);\n",
+ "y=(x-1)**2;\n",
+ "pyplot.plot(x,y);\n",
+ "pyplot.legend(\"y=(x-1)^2\");\n",
+ "pyplot.title(\"Curve of y=(x-1)^2\")\n",
+ "pyplot.xlabel(\"x axis\")\n",
+ "pyplot.ylabel(\"y axis\")\n",
+ "pyplot.grid()\n",
+ "pyplot.show()\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13_10 pgno:158"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "At these points curve cuts the axis of x\n"
+ ]
+ },
+ {
+ "data": {
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+ "RU5ErkJggg==\n"
+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0xa5e79e8>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "\n",
+ "#129,130,131 examples\n",
+ "\n",
+ "\n",
+ "import numpy\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "x=numpy.linspace(-3,4,8);\n",
+ "y=(x-1)**2-4;\n",
+ "pyplot.plot(x,y);\n",
+ "pyplot.legend(\"y=(x-1)^2-4\");\n",
+ "pyplot.title(\"Graph of y=(x-1)^2-4\")\n",
+ "pyplot.xlabel(\"x axis\")\n",
+ "pyplot.ylabel(\"y axis\")\n",
+ "\n",
+ "\n",
+ "x =('x')\n",
+ "y='(x-1)**2-4';\n",
+ "\n",
+ "#131 concept\n",
+ "print ('At these points curve cuts the axis of x')\n",
+ "x=3\n",
+ "pyplot.grid()\n",
+ "pyplot.show()\t\n"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_13_Graphs_of_Quadratic_Functions_3.ipynb b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_13_Graphs_of_Quadratic_Functions_3.ipynb new file mode 100755 index 00000000..540e6bfe --- /dev/null +++ b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_13_Graphs_of_Quadratic_Functions_3.ipynb @@ -0,0 +1,2290 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 13 Graphs of Quadratic Functions"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13_1 pgno:148"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "C=2*pi*r\n",
+ "the variation of C depends on changes in r\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#circumference of circle\n",
+ "print ('C=2*pi*r')\n",
+ "#C-length of circumference.r-the length of radius\n",
+ "#2 (2,pi) of these 4 symbols represent constants .\n",
+ "print (\"the variation of C depends on changes in r\")\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13_2 pgno:148"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
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+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0xa7824a8>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "\n",
+ "#let a-the avg. amount paid. x-no. of customers. b-the expenses\n",
+ "#net profit is y=ax-b\n",
+ "x=320.;y=4.50;\n",
+ "x=250.;y=1.00;\n",
+ "\n",
+ "\n",
+ "import numpy\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "\n",
+ "#substitute in above equation\n",
+ "#4.5=320*a-b-equ.1;1=250*a-b-equ.2.subbstract equ.2 from 1.\n",
+ "a=0.05;#we get\n",
+ "b=250*a-1;\n",
+ "x = ('x')\n",
+ "y='a*x-b';#equation to straight line\n",
+ "#if there is no profit i.e., y=0\n",
+ "x=0;\n",
+ "for x in range(1,500):\n",
+ "\tif(0.05*x-11.5==0):\n",
+ "\t\tprint\"x= \\n\",x\n",
+ "\tbreak\n",
+ "\n",
+ "cust=numpy.array([230, 240, 270, 300, 350, 380])\n",
+ "profit=[0, 0.5, 2.0, 3.5, 6.0, 7.5];\n",
+ "pyplot.plot(cust,profit);\n",
+ "pyplot.plot(230,0,'o');\n",
+ "#profit(y) depends on varying no. of customers(x). the no.'s 0.05 & 11.5 remained constant\n",
+ "pyplot.title(\"the straight line graph\")\n",
+ "pyplot.xlabel(\"no. of customers\")\n",
+ "pyplot.ylabel(\"profit\");\n",
+ "pyplot.legend(\"y=0.05*x-11.5\");\n",
+ "pyplot.grid()\n",
+ "pyplot.show()\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13_3 pgno:149"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "y=mx+b\n"
+ ]
+ },
+ {
+ "data": {
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+ "wDbt783vuraIbMrhpZLeUEwIZtPnBsEMPge8D/gysNlwEbAtsDYifi9pL2C/lnUfBc4hmwn1tPY3\n",
+ "StoduCciTgdOJ7trl1kllT79tVmZJB0N/CEizs2nEb6yw12nLgaOkXQj2Y3ar8rfexDwHOC4iAhJ\n",
+ "r5L0xog4i413pXoB8A5JjwAPks9Nb1ZFziGYmRngISMzM8u5QTAzM8ANgpmZ5dwgmJkZ4AbBzMxy\n",
+ "bhDMzAxwg2BmZjk3CGZmBsD/B6cKBOU705CdAAAAAElFTkSuQmCC\n"
+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0xcb63e10>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "#y=mx+b\n",
+ "import numpy\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "x=numpy.linspace(0,3);\n",
+ "y=x;\n",
+ "pyplot.plot(x,y);\n",
+ "y=x+2;\n",
+ "pyplot.plot(x,y);\n",
+ "y=x-3;\n",
+ "pyplot.plot(x,y);\n",
+ "pyplot.title(\"Equations of the form y=mx+b\")\n",
+ "pyplot.xlabel(\"x axis\")\n",
+ "pyplot.ylabel(\"y axis\");\n",
+ "#pyplot.legend(\"y=x\",\"y=x+2\",\"y=x-3\");\n",
+ "print ('y=mx+b');\n",
+ "#m is constant, b is fixed distance. (x,y) vary for different points on the line \n",
+ "pyplot.grid()\n",
+ "pyplot.show()\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13_4 pgno:151"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
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+ "/wfyjf2O7F9z0QAAAABJRU5ErkJggg==\n"
+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x3de59b0>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import numpy\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "x=numpy.linspace(-3,3,11);\n",
+ "y=x**2;\n",
+ "pyplot.plot(x,y);\n",
+ "pyplot.title(\"Parabola curve\")\n",
+ "pyplot.xlabel(\"x axis\")\n",
+ "pyplot.ylabel(\"y axis\")\n",
+ "pyplot.legend(\"y=x^2\");\n",
+ "pyplot.grid()\n",
+ "pyplot.show()\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13_5 pgno:152"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "this curve is parabola\n"
+ ]
+ },
+ {
+ "data": {
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+ "Lu9LvM2w5z4DnAccB3x95AslrQ/8OiLOAs6iuHOUWXKNuJmLWSqS9gb+FBGzJS0H/FeHOx/9ANhf\n",
+ "0t0UN2+/rnztjsBrgIMiIiS9U9I+EXEuS8YFvxH4uKRngSeAvfuTmdnY3PM3MxtAbvuYmQ0gF38z\n",
+ "swHk4m9mNoBc/M3MBpCLv5nZAHLxNzMbQC7+ZmYDyMXfzGwA/X82fee48rbJ0gAAAABJRU5ErkJg\n",
+ "gg==\n"
+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x404a4e0>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import numpy\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "x=numpy.linspace(-3,3,11);\n",
+ "y=-x**2;\n",
+ "pyplot.plot(x,y);\n",
+ "\n",
+ "pyplot.title(\"curve of y=-x^2\")\n",
+ "pyplot.xlabel(\"x axis\")\n",
+ "pyplot.ylabel(\"y axis\")\n",
+ "pyplot.legend(\"y=x^2\");\n",
+ "print(\"this curve is parabola\");\n",
+ "pyplot.grid()\n",
+ "pyplot.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13_6 pgno:154"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
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+ "XvQdx3E6CC/6juM4HYQXfcdxnA7i/wM/g2vMu6eCoQAAAABJRU5ErkJggg==\n"
+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x404a7b8>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "\n",
+ "#y=ax**2\n",
+ "import numpy\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "x=numpy.linspace(-3,3,11);\n",
+ "y=2*x**2;\n",
+ "pyplot.plot(x,y);\n",
+ "y=x**2;\n",
+ "pyplot.plot(x,y);\n",
+ "y=x**2/2;\n",
+ "pyplot.plot(x,y);\n",
+ "\n",
+ "pyplot.title(\"curve of y=ax**2\")\n",
+ "pyplot.xlabel(\"x axis\")\n",
+ "pyplot.ylabel(\"y axis\")\n",
+ "#pyplot.legend(\"y=2*x**2\",\"y=x**2\",\"y=x**2/2\");\n",
+ "#if a is negative, we get corresponding curves similar to y=-x**2\n",
+ "pyplot.grid()\n",
+ "pyplot.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13_7 pgno:155"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
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+ "gbuBebP35id1XzPw1v6fzTpjrU9aCnqapJ2LcSEIhkcE/yBIPYa/SuoXMYvkAywEPGf7lawv8dot\n",
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+ "Prsh8EFgX9uW9AlJu9g+m97lgj8MHCTpdeAFYHJnPAuC2ROafxAEwRgkZJ8gCIIxSAT/IAiCMUgE\n",
+ "/yAIgjFIBP8gCIIxSAT/IAiCMUgE/yAIgjFIBP8gCIIxSAT/IAiCMcj/B0ldbIteLiG9AAAAAElF\n",
+ "TkSuQmCC\n"
+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0xca5a080>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "\n",
+ "#y=x**2+a or y=x**2-a\n",
+ "import numpy\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "x=numpy.linspace(-3,3,11);\n",
+ "y=x**2+2;\n",
+ "pyplot.plot(x,y);\n",
+ "y=x**2;\n",
+ "pyplot.plot(x,y);\n",
+ "y=x**2-3;\n",
+ "pyplot.plot(x,y);\n",
+ "pyplot.title(\"Curves of y=x**2 +/- a\")\n",
+ "pyplot.xlabel(\"x axis\")\n",
+ "pyplot.ylabel(\"y axis\")\n",
+ "#pyplot.legend(\"y=x**2+2\",\"y=x**2\",\"y=x**2-3\");\n",
+ "pyplot.grid()\n",
+ "pyplot.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13_8 pgno:156"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
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+ "bkaN/WL9/AAAAABJRU5ErkJggg==\n"
+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0xcc09d30>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "axis for y=x^2 becomes axis for y=x^2-3 by drawing new x axis 3 units above the original\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#y=x^2+a or y=x^2-a\n",
+ "import numpy\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "x=numpy.linspace(-3,3,11);\n",
+ "y=x**2;\n",
+ "pyplot.plot(x,y);\n",
+ "pyplot.plot(y=1)\n",
+ "pyplot.legend(\"y=x^2\");\n",
+ "\n",
+ "pyplot.title(\"Change of axis\")\n",
+ "pyplot.xlabel(\"x axis\")\n",
+ "pyplot.ylabel(\"y axis\")\n",
+ "pyplot.grid()\n",
+ "pyplot.show()\n",
+ "print\"axis for y=x^2 becomes axis for y=x^2-3 by drawing new x axis 3 units above the original\"\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13_9 pgno:157"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
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+ "bdcAvijpOeBJYMzxzUPopajphxDCAInyTgghDJBo9EMIYYBEox9CCAMkGv0QQhgg0eiHEMIAiUY/\n",
+ "hBAGSDT6IYQwQKLRDyGEAfL/AWTYI39KaLX0AAAAAElFTkSuQmCC\n"
+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0xc79bc50>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import numpy\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "x=numpy.linspace(-3,4,8);\n",
+ "y=(x-1)**2;\n",
+ "pyplot.plot(x,y);\n",
+ "pyplot.legend(\"y=(x-1)^2\");\n",
+ "pyplot.title(\"Curve of y=(x-1)^2\")\n",
+ "pyplot.xlabel(\"x axis\")\n",
+ "pyplot.ylabel(\"y axis\")\n",
+ "pyplot.grid()\n",
+ "pyplot.show()\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13_10 pgno:158"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "At these points curve cuts the axis of x\n"
+ ]
+ },
+ {
+ "data": {
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+ "7VdS22cJYO1SJnmTtBnwmO1pNHHhbC1u5mJ7wyZXPYMaHjmPll/SZKqvYuv3JFCLWnj/S/AI0Dgo\n",
+ "YEmqo//QI5LmAM4Ffmb7gtx5xsr2U5IuAt4LXJM5TjPWBDaXtAnVnefml3Sq7e2HWrkWR/4jkfSO\n",
+ "hsUtgGm5soyFpI2pvoZtkU4mlayEaThuA94haaKkOYEtgQszZ+obqibrOhG4x/ZRufO0StIikhZM\n",
+ "v89DNfNwETXH9tdtL2n7P4GtgKuGK/xQQPEHDkktiOlUN9XeK3OeVh1LdaL6ijT86ke5A7VC0kcl\n",
+ "PUQ1cuMiSZfkzjQS2y9TzY9zGdWIh7Nt35s3VfMknQncCCwj6SFJO+TO1KIPANtSjZKZln5KGr30\n",
+ "ZuCqVG9uAX5p+9eZM43ViC3QuMgrhBD6UAlH/iGEEDosin8IIfShKP4hhNCHoviHEEIfiuIfQgh9\n",
+ "KIp/CCH0oSj+IXSBpBtyZwhhJDHOP4QQ+lAc+Ye+Jul96UY7c0maN92AZLkh1jtf0m3p+c+mx5aS\n",
+ "dL+kN6WZIK+XtEF67tn0v2+WdF260vXOAueGD+NUHPmHvifpQKqJsOYBHrJ92BDrLGT7yTTfy2+B\n",
+ "tdPyTsCHgFuBt9neNa3/jO0JkvYC5rJ9cJr3Zt7SZrkM41MU/9D30iyUtwH/AtbwEP9RSDoA+Eha\n",
+ "XArY2PYt6bnLgKWBlWw/lx4bKP5rAScBPwMusH17t/+eEJoRbZ8QYBFgXqoJ+OYZ/GSaz319YPU0\n",
+ "z/t0YK703Bup5n03MGHwa9Odudaimmp6qqTtuvMnhNCaKP4hwE+A/ajuF/G6lg8wP/Ck7eclvZNq\n",
+ "htMBhwGnUd1b+vjBL5T0VuDvtk+gurXeKh3OHsKY1OJmLiHkIml74AXbZ0l6A3CjpEm2r2lY7VLg\n",
+ "c5LuAf4A3JReuw6wKrCHbUv6uKTP2D6FWdPprgt8RdJLwDPAsPOrh9BL0fMPIYQ+FG2fEELoQ1H8\n",
+ "QwihD0XxDyGEPhTFP4QQ+lAU/xBC6ENR/EMIoQ9F8Q8hhD4UxT+EEPrQ/wdFKj3tiwH1PwAAAABJ\n",
+ "RU5ErkJggg==\n"
+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0xa5e79e8>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "\n",
+ "#129,130,131 examples\n",
+ "\n",
+ "\n",
+ "import numpy\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "x=numpy.linspace(-3,4,8);\n",
+ "y=(x-1)**2-4;\n",
+ "pyplot.plot(x,y);\n",
+ "pyplot.legend(\"y=(x-1)^2-4\");\n",
+ "pyplot.title(\"Graph of y=(x-1)^2-4\")\n",
+ "pyplot.xlabel(\"x axis\")\n",
+ "pyplot.ylabel(\"y axis\")\n",
+ "\n",
+ "\n",
+ "x =('x')\n",
+ "y='(x-1)**2-4';\n",
+ "\n",
+ "#131 concept\n",
+ "print ('At these points curve cuts the axis of x')\n",
+ "x=3\n",
+ "pyplot.grid()\n",
+ "pyplot.show()\t\n"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_14_Quardartic_Equations_4.ipynb b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_14_Quardartic_Equations_4.ipynb new file mode 100755 index 00000000..49ce88cf --- /dev/null +++ b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_14_Quardartic_Equations_4.ipynb @@ -0,0 +1,505 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 14 Quardartic Equations"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 14_1 pgno:168"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "the solution is \n",
+ "\n",
+ "[ 1.61803399 -0.61803399]\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#x^2-x-1=0\n",
+ "import numpy\n",
+ "\n",
+ "x=('x')\n",
+ "y=numpy.array([1, -1, -1])# y=0\n",
+ "print\"the solution is \\n\"\n",
+ "\n",
+ "x=numpy.roots(y)\n",
+ "print x\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 14_2 pgno:168"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "the solution is \n",
+ "\n",
+ "[ 1.43425855 0.23240812]\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#3*x^2-5*x+1=0\n",
+ "import numpy\n",
+ "x=('x');\n",
+ "y=([3, -5, 1]);# y=0\n",
+ "print\"the solution is \\n\"\n",
+ "\n",
+ "x=numpy.roots(y)\n",
+ "\n",
+ "print x\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 14_3 pgno:168"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "the solution is \n",
+ "\n",
+ "[-6.74456265 4.74456265]\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "import numpy\n",
+ "x=('x')\n",
+ "p1='1/(x-1)';\n",
+ "p2='1/(x+2)';\n",
+ "y='p1-p2';\n",
+ "y1=1./16.;\n",
+ "a=numer(y)*denom(y1);\n",
+ "b=numer(y1)*denom(y);\n",
+ "r=a-b;\n",
+ "print\"the solution is \\n\"\n",
+ "x=numpy.roots([-1, -1, 8])\n",
+ "print 2*x"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 14_4 pgno:171"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "the solution is \n",
+ "\n",
+ "('x=,', array([ 5., -3.]))\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#x^2-2*x-15=0\n",
+ "\n",
+ "import numpy\n",
+ "x=('x');\n",
+ "y=([1, -2, -15]);# y=0\n",
+ "print\"the solution is \\n\"\n",
+ "print(\"x=,\",numpy.roots(y))\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 14_5 pgno:171"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "the solution is \n",
+ "\n",
+ "('x=, \\n', array([-1.33333333, 0.33333333]))\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#9*x*(x+1)=4\n",
+ "\n",
+ "import numpy\n",
+ "x=('x')\n",
+ "y=[9, 9, -4]#9*x*(x+1)-4; #y=0\n",
+ "print\"the solution is \\n\"\n",
+ "print(\"x=, \\n\",numpy.roots(y))\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 14_6 pgno:173"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "('\\t x= \\n \\n or ', 0.20000000000000001)\n",
+ "(' x=', -2.0)\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#5*x**2+9*x-2=0\n",
+ "\n",
+ "from numpy import sqrt\n",
+ "x=('x');\n",
+ "y='5*x**2+9*x-2';\n",
+ "a=5;b=9;c=-2;#from equation we get these values\n",
+ "#using the formula - solution of quadratic equation ax**2+bx+c=0\n",
+ "x=(-b+sqrt(b**2-4*a*c))/(2*a);\n",
+ "print(\"\\t x= \\n \\n or \",x)\n",
+ "x=(-b-sqrt(b**2-4*a*c))/(2*a);\n",
+ "print(\" x=\",x)\n",
+ "\n",
+ " \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 14_7 pgno:174"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "the solution is\n",
+ "5.21221445045\n",
+ "or \n",
+ "\n",
+ "0.288\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "from math import sqrt\n",
+ "\n",
+ "x=('x');\n",
+ "p1='1/(x-1)';\n",
+ "p2=2./3.;\n",
+ "p3='2/(x-3)';\n",
+ "p='(p1+p2-p3)';\n",
+ "p=3*numer(p);#As p=0 and to remove fractions, multiply by 3\n",
+ "a=2;b=-11;c=3;#from equation we get these values\n",
+ "#using the formula - solution of quadratic equation ax**2+bx+c=0\n",
+ "print(\"the solution is\")\n",
+ "\n",
+ "x=(-b+sqrt(b**2-4*a*c))/(2*a)\n",
+ "print x\n",
+ "print(\"or \\n\")\n",
+ "x=(-b-sqrt(b**2-4*a*c))/(2*a)\n",
+ "print round(x,3)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 14_8 pgno:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "('\\n the solution is t= or t=\\n', 30.422, 1.578)\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "\n",
+ "#given u=160,g=10,h=240\n",
+ "\n",
+ "from math import sqrt\n",
+ "#using the formulae \"h=u*t-(g*t**2)/2\"\n",
+ "u=160;\n",
+ "g=10;\n",
+ "h=240;\n",
+ "t=('t');\n",
+ "r='(240-u*t+(g*t**2)/2)'#u*t-(g*t**2)/2-h=0\n",
+ "a=5;b=-160;c=240;#from equation we get these values\n",
+ "#using the formulae - solution of quadratic equation ax**2+bx+c=0\n",
+ "t=(-b+sqrt(b**2-4*a*c))/(2*a);\n",
+ "t1=(-b-sqrt(b**2-4*a*c))/(2*a);\n",
+ "print(\"\\n the solution is t= or t=\\n\",round(t,3),round(t1,3))#the answer given in textbook is wrong\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 14_9 pgno:176"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "avg. speed for 1st journey is x=24km/h\n",
+ "('total_timefhours', 6)\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "import numpy\n",
+ "#let x km/hr is avg. speed for 1st journey\n",
+ "#as velocity=distance/time, time for 1st journey is 84/x hrs\n",
+ "#speed for return journey is 84/(x+4).from given data, this is <1/2 hr than the 1st time \n",
+ "x=('x');\n",
+ "#In algebraic form,(84/x)-(84/(x+4))=1/2\n",
+ "y='(84/x)-(84/(x+4))-1/2'; #y=0. so, numerator=0\n",
+ "x=numpy.roots([-1, -4, 8])\n",
+ "#x=roots(numer(y));\n",
+ "#velocity can't be in negatives.take +ve root\n",
+ "print(\"avg. speed for 1st journey is x=24km/h\")\n",
+ "distance=84;#given\n",
+ "velocity=24;#found\n",
+ "time=distance/velocity;#time for 1st journey\n",
+ "time1=distance/(velocity+4);#time for 2nd journey\n",
+ "print(\"total_timefhours\",time+time1)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 14_10 pgno:179"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "the solutions are: \n",
+ "\n",
+ "({-12/5: 1, 3: 1}, '1-x')\n"
+ ]
+ }
+ ],
+ "source": [
+ "#x+y=1, 38x^2-x*y+y^2=37\n",
+ "\n",
+ "x=('x');\n",
+ "y='1-x';\n",
+ "#substitute y=1-x in equ. 38x^2-x*y+y^2=37\n",
+ "Y='3*x**2-x*(1-x)+(1-x)**2-37';\n",
+ "x=roots(Y);\n",
+ "#y=1-x;\n",
+ "print('the solutions are: \\n')\n",
+ "print(x,y)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 14_11 pgno:180"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "the solutions are: \n",
+ "\n",
+ "('(x,y)=() \\n', {12: 1, 7: 1})\n",
+ "y=19-x\n"
+ ]
+ }
+ ],
+ "source": [
+ "#x+y=19, xy=84\n",
+ "\n",
+ "x=('x');\n",
+ "#substitute y=19-x in xy=84\n",
+ "Y='x*(19-x)-84';\n",
+ "x=roots(Y);\n",
+ "\n",
+ "print('the solutions are: \\n')\n",
+ "print(\"(x,y)=() \\n\",x)\n",
+ "print 'y=19-x'\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 14_12 pgno:181"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "the solutions of (x,y) are: \n",
+ "\n",
+ "[array([ -1.02144599e+01+0.j , 1.02144599e+01+0.j ,\n",
+ " 1.11022302e-16+3.91601715j, 1.11022302e-16-3.91601715j]), {}]\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#x**2+y**2=89, xy=40\n",
+ "\n",
+ "import numpy\n",
+ "x=('x');\n",
+ "#substitute y=40/x in x**2+y**2=89\n",
+ "Y='x**2+(40/x)**2-89';\n",
+ "x=numpy.roots([1, 0, -89, 0, -1600]);#Y=0, numerator=0\n",
+ "y=roots(89-x**2);\n",
+ "print('the solutions of (x,y) are: \\n')\n",
+ "print [x,y]\n",
+ "\n"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_16_Logarithms_4.ipynb b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_16_Logarithms_4.ipynb new file mode 100755 index 00000000..b50fdfd2 --- /dev/null +++ b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_16_Logarithms_4.ipynb @@ -0,0 +1,716 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 16 Logarithms"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16_1 pgno:196"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": [
+ "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEZCAYAAACaWyIJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
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+ "FooFuRRRQIqCPzWCDcSCSEsuiCggTeliAJEiQiABQVBCVXpvBvL8/pg5zM7h5Jzd1+y9v+/X67yy\n",
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+ "AJ+tWN4WuD9/PAF4BRhWsf5xYOwA77sa8AawRMVzU4EzKmK7fpC43l8ZO3Ar8IkGcvUw8KF+z70B\n",
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+ "QPUeOz1ncRtJLCExXuKbEncCNwGjySZwWSmCyRGcWlkEPNZ6wbkoOBcF56Jx7iNoEYmFyQ7ym1T8\n",
+ "jAJmA38APgfc4iEdzCw1Nw01gcQwYG1gLMVBfzTwD+DPFT93eux+M2sV9xG0ST5i52rMf9B/H/AU\n",
+ "8x/0b4vgbcNrm5m1igtBi+QDtm3C/Af+AG6hOOjfGsFTrdm/r5Hu41wUnIuCc1HwfQRNILEU2fj8\n",
+ "lQf95YDEGyJQAAAGUElEQVS/kB34Twf2BR7x5Zxm1i169owgH5d/A+Y/6I8kGx678tv+fR6zx8w6\n",
+ "gZuGBn0/hgPrMn8Tz3uB+8gO9n0H/tm+a9fMOlVHFQJJp5ONlvlERIweYH3dhSDvzB3J/Af9jYDH\n",
+ "Kb7l3wLcHsErdf0CbeT2z4JzUXAuCs5FodP6CM4AfgT8X6NvJPFOiqadscB/Af+mOOh/k6wz99lG\n",
+ "95XIGLI7js25qORcFJyLBiUpBBFxvaSRtb5OYhmySzUrv+0vCdxKdtA/GdgngkebFmx6y6YOoESc\n",
+ "i4JzUXAuGlTaq4YkFiWr9JXf9lcFZpId9M8nG43z776Cx8ysfqUtBMAzwD1kB/3rgO8Dd0XwRtKo\n",
+ "2m9k6gBKZGTqAEpkZOoASmRk6gA6XbKrhvKmoUsW1Fnc9oDMzLpAJ3UWD6osdxWbmfWCJMNQS/ol\n",
+ "8CdgbUkPS9ozRRxmZlbSG8rMzKx9kk5MI2mSpHsk3SfpsAVsc2K+/g5JG7U7xnYZKheSdslzcKek\n",
+ "GyRtkCLOdqjmc5Fvt4mkNyTt2M742qnKv5EJkm6XNFvSjDaH2DZV/I2sKOlySTPzXExJEGbLSTpd\n",
+ "0uOSZg2yTW3HzYhI8gMMB+4n6/EfQXZZ6H/222Y74NL88fuBm1LFW4JcbAoskz+e1Mu5qNjuGuC3\n",
+ "wMdTx53wc7EscBewar68Yuq4E+biGODbfXkAngYWSh17C3Ixnmy0hFkLWF/zcTPlGcFY4P6ImBMR\n",
+ "c4FzgB36bTMZmA4QETcDy0p6Z3vDbIshcxERN0bE8/nizWT3VHSjaj4XAPsD5wFPtjO4NqsmF58G\n",
+ "zo+IRwAioiXDoZdANbn4J7B0/nhp4OmI6LrLzSPiehh0pISaj5spC8EqwMMVy4/kzw21TTceAKvJ\n",
+ "RaW9gUtbGlE6Q+ZC0ipkB4GT8qe6taOrms/FWsDykv4g6VZJu7UtuvaqJhenAO+V9BhwB3Bgm2Ir\n",
+ "m5qPmykvH632j7f/paTd+Edf9e8kaSKwF/DB1oWTVDW5OAH4SkSEJPH2z0i3qCYXI8jm0NgSWBy4\n",
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+ "yDuITwEmRUSnDqI3lGpy8T7gnKwGsCKwraS5EXFxe0Jsm2py8TDwVES8Crwq6TpgQ7Ih1rtJNbn4\n",
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+ "+A2wa0TcnyDGdhkyFxHx7ohYMyLWJOsn2LcLiwBU9zdyEbCZpOGSFifrHLy7zXG2QzW5uAfYCiBv\n",
+ "E18H+EdboyyHmo+byc4IIuINSf8LXEF2RcBpEfFXSZ/L158cEZdK2k7S/cDLQFfeeFZNLoCvkU2b\n",
+ "eVL+TXhuRIxNFXOrVJmLnlDl38g9ki4nm1lvHnBKRHRdIajyczEVOEPSHWRfcg+NiGeSBd0i+Q25\n",
+ "mwMrSnoYOJqsibDu46ZvKDMz63FJbygzM7P0XAjMzHqcC4GZWY9zITAz63EuBGZmPc6FwMysx7kQ\n",
+ "mDWRpBtSx2BWK99HYGbW43xGYD0pn9TmDkmLSFoin8hkvQG2uyAf1XO2pM/kz60h6W+SVpA0TNL1\n",
+ "kvqGNngp//ddkq7LJ4yZJWmz9v6GZtXzGYH1LEnfABYFFgMejojjBthmuYh4VtJiwC3Ah/LlvYEP\n",
+ "A38G3h0R++bbvxgRS0n6ErBIREzNR0hdIiJeatfvZlYLFwLrWZJGkA1m9iqwaQzwxyDpGOBj+eIa\n",
+ "ZCO/3pyvuwIYBWwYES/nz/UVgvHA6cBZwIURcUerfx+zerlpyHrZisASwJJkZwXzkTSBbJz/cREx\n",
+ "hmx6xEXydYuTDe8bwFL9X5vPIjWebPjfaV08YYx1ARcC62UnA0cBZwNvaxYim+7w2Yh4TdK6wLiK\n",
+ "dccBZ5KN/HhK/xfmw4Y/GRGnAqeSzTFrVkopJ6YxS0bS7sDrEXGOpGHAnyRNiIgZFZtdDnxe0t3A\n",
+ "vcCN+Ws3J5sc54B8lrSPS9ojIqZTzAQ1EfiypLnAi+Tjw5uVkfsIzMx6nJuGzMx6nAuBmVmPcyEw\n",
+ "M+txLgRmZj3OhcDMrMe5EJiZ9TgXAjOzHudCYGbW4/4/e2Zr8lsWfTYAAAAASUVORK5CYII=\n"
+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x3edc080>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "4.78630092323 1.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "import numpy\n",
+ "import numpy\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "x=numpy.linspace(0,1,7);\n",
+ "y=10**x;\n",
+ "pyplot.plot(x,y);\n",
+ "pyplot.title(\" graph of y=10**x\")\n",
+ "pyplot.xlabel(\"x axis\")\n",
+ "pyplot.ylabel(\"y axis\");\n",
+ "pyplot.legend(\"y=10**x\");\n",
+ "\n",
+ "pyplot.grid()\n",
+ "pyplot.show()\n",
+ "\n",
+ "\n",
+ "\n",
+ "#ex1:1.8*2.6=? ,from graph\n",
+ "#1.8=10**0.26 \\n 2.6=10**0.42 \n",
+ "x=10**0.26;y=10**0.42;\n",
+ "#format(4)\n",
+ "ex1_ans=x*y#from the graph\n",
+ "\n",
+ "#ex2:9**(1/3)\n",
+ "#9=10**0.96\n",
+ "x=10**0.96;\n",
+ "#format(4)\n",
+ "ex2_ans=x**(1/3)#third law of indices\n",
+ "\n",
+ "print ex1_ans,ex2_ans\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16_2 pgno:198"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "1.74973631557 10 3.0 4.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "from math import log10\n",
+ "\n",
+ "\n",
+ "ans1=log10(56.2)\n",
+ "ans2=10\n",
+ "ans3=log10(1000)\n",
+ "ans4=log10(81)/log10(3)\n",
+ "\n",
+ "print ans1,ans2,ans3,ans4\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16_3 pgno:201"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "from anti-logarithm table,corresponding no. is 2352\n",
+ "235.2\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#no. whose logarithm is 2.3714\n",
+ "\n",
+ "mantissa=0.3714;\n",
+ "print(\"from anti-logarithm table,corresponding no. is 2352\")\n",
+ "# As,characteristic is 2,no. must lie between 100 & 1000.\\n \\n hence 3 significant figures in the intergral part\n",
+ "print 235.2\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16_4 pgno:203"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "253.7161\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#value of (57.86*4.385)\n",
+ "from math import log10\n",
+ "#log(p*q)=log(p)+log(q)\n",
+ "p=57.86;q=4.385;\n",
+ "logx=log10(p)+log10(q);\n",
+ "format(6)\n",
+ "x=10**logx\n",
+ "print x\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16_5 pgno:204"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "61.1\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#value of (5.672*18.94)/1.758\n",
+ "from math import log10\n",
+ "#log(p*q)=log(p)+log(q) , log(p/q)=log(p)-log(q)\n",
+ "p=5.672;q=18.94;r=1.758;\n",
+ "logx=log10(p)+log10(q)-log10(r);\n",
+ "\n",
+ "x=10**logx\n",
+ "print round(x,1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16_6 pgno:204"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 27,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "3.73\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#5th root of 721.8\n",
+ "from math import log10\n",
+ "#log(a)^n=n*log(a)\n",
+ "p=721.8;n=1./5.;\n",
+ "logx=n*log10(p);\n",
+ "#format(6)\n",
+ "x=10**logx\n",
+ "print round(x,3)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16_7 pgno:206"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 28,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "-0.4969 -1.4969 -2.4969\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#logs of 0.3185,0.03185,0.003185\n",
+ "from math import log10\n",
+ "x=0.3185;y=0.03185;z=0.003185;\n",
+ "logx=log10(0.3185)\n",
+ "logy=log10(0.03185)\n",
+ "logz=log10(0.003185)\n",
+ "\n",
+ "print round(logx,4),round(logy,4),round(logz,4)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16_8 pgno:206"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 29,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "from anti-logarithm table, corresponding no.is 3840 \n",
+ "0.00348\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#no. with logarithm -3.5416\n",
+ "\n",
+ "mantissa=0.5416;\n",
+ "print(\"from anti-logarithm table, corresponding no.is 3840 \")\n",
+ "#characteristic is -3.\\n \\n hence there will be 2 zeros after the decimal point\n",
+ "print 0.003480\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16_9 pgno:207"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "('sum=-', 2.3455)\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#sum of logarithms -1.6173,-2.3415,-1.6493,-0.7374\n",
+ "\n",
+ "x=.6173;y=.3415;z=.6493;a=0.7374;#mantissa's of all 4 logarithms\n",
+ "mantissa=x+y+z+a;\n",
+ "#2 which is carried forward from the addition of mantissa is +ve.\n",
+ "characteristic=-1-2-1-0+2;#characteristic part of all 4 logarithms\n",
+ "print(\"sum=-\",mantissa)\n",
+ "\n",
+ "\n",
+ "\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16_10 pgno:207"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 31,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "1.7712\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#logarithm : -1.6175-(-3.8463)\n",
+ "\n",
+ "mantissa=1.6175-0.8463;\n",
+ "#in borrowing to subtract 8 from 6, -1(characteristic) becomes -2 \n",
+ "characteristic=-2-(-3);\n",
+ "print mantissa+characteristic\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16_11 pgno:208"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 32,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "-4.6289\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#logarithm : multiply -2.8763 by 3\n",
+ "\n",
+ "num=2.8763;#given\n",
+ "mantissa=0.8763;\n",
+ "mul=mantissa*3;\n",
+ "#when mantissa is multiplied, 2 is carried forward. (-2)*3=-6. the characteristic becomes -6+2=-4\n",
+ "print -4.6289\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16_12 pgno:208"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 33,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "1.16406\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#logarithm: -1.8738*1.3\n",
+ "\n",
+ "#multiply mantissa & characteristic seperately and add results\n",
+ "x=0.8738*1.3;\n",
+ "y=-1*1.3;\n",
+ "#as y=-1.3 is -ve, change it to -2.7 to make mantissa +ve\n",
+ "y=-2.7;\n",
+ "mantissa_sum=0.13594+0.7; #of x & y\n",
+ "characteristic_sum=2-1;\n",
+ "print 2*characteristic_sum-mantissa_sum\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16_13 pgno:208"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 34,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "-2.4572\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#divide -5.3716 by 3\n",
+ "\n",
+ "#characteristic=-5=-6+1 or the log as -6+1.3716\n",
+ "characteristic=-6/3;\n",
+ "mantissa=1.3716/3;\n",
+ "print characteristic-mantissa\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16_14 pgno:211"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 35,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "3.912\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#log50 to the base e \n",
+ "from math import log\n",
+ "print round(log(50),3)#natural logarithm\n",
+ "# or, log50_base_e=log10(50)*2.3026\n"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_18_Variation_4.ipynb b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_18_Variation_4.ipynb new file mode 100755 index 00000000..fad192e8 --- /dev/null +++ b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_18_Variation_4.ipynb @@ -0,0 +1,461 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 18 Variation"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 18_1 pgno:225"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": [
+ "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEZCAYAAAB4hzlwAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
+ "AAALEgAACxIB0t1+/AAAH6dJREFUeJzt3XuUZFV59/HvrwVGuQ5oFhhQJm8EXRplBCUoKhNFRDEo\n",
+ "ZAEiMyCJEBkjiErAgQSQWQbkldeAETUyFxkG9DWC6CAMRBBU5CIMIhdFwigQQSJ3UGHgyR9nd1MU\n",
+ "fTnVXdX77KrfZ61Z03Xpql8XQ+0++3nOU4oIzMzMAIZyBzAzs+bwomBmZiO8KJiZ2QgvCmZmNsKL\n",
+ "gpmZjfCiYGZmI7woWN+RdJykM7v0WJtKulzSw5JO7sZjlq6br681jxcF6zlJ75N0laRHJd0r6ceS\n",
+ "DunhU3bz5JuDgd9GxIYRcUQXH7drJB0gaadRrj9W0pYtl7eW9C1Jv5X0O0kXStp6Ek/pk5v6mBcF\n",
+ "6ylJHwc+B5wEbBoRmwIfAnaUtM4Y3zPVf5ea4ve32hK4pYuP1zWSDpb03mcu6mBJ75H0SUlvStev\n",
+ "JeloSX8JbAScB2wNbApcDXxrjMeeJemOsZ66iz+GNYwXBesZSRsBxwOHRMQ3I+IxgIhYFRFzI+KJ\n",
+ "dL8lkk6XdIGkR4E5knaTdL2khyT9WtKxLY87S9LTkg6SdLek/06Lz7AA1pG0NG37/EzSduPkfKOk\n",
+ "ayQ9KOlqSW8YzgXsD/yjpEckvbXt+14v6R5JarluT0mrOnydtpd0paQH0s9ymqS1W7LdJ2mLdHkb\n",
+ "Sfen3/AXAS8DPgp8GngiIr4F/CvwTuB9wOnATyPiqoi4JiIWR8SDEbGGarF+uaSNO8lL9fo+X9I5\n",
+ "6fX9iaTXdPgY1lBeFKyX3gDMYIzfRtvsC5wQEesDPwQeBeZGxEbAbsAhkt7T9j1zqN4UdwGOlPS2\n",
+ "dL2A3YGzqX47Ph/4/GhPKmkTYAXVG+QmwCnACkkbR8QHgLOAkyJig4j4Xuv3RsQ1wO+Ad7RcPQ9Y\n",
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+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0xad571d0>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Hence, the law is\n",
+ "\n",
+ "or by solving by the method of Section 185\n",
+ "3*x**2-10\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#y=a*x**2+b\n",
+ "import numpy\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "import numpy\n",
+ "\n",
+ "x=numpy.array([0, 0.5, 1, 1.5, 2, 2.5]);\n",
+ "y=numpy.array([-10, -9.25, -7, -3.25, 2, 8.75]);\n",
+ "pyplot.plot(x**2,y);\n",
+ "pyplot.title(\"Graph of y=ax**2+b\")\n",
+ "pyplot.xlabel(\"x axis\")\n",
+ "pyplot.ylabel(\"y axis\");\n",
+ "\n",
+ "pyplot.grid()\n",
+ "pyplot.show()\n",
+ "\n",
+ "\n",
+ "#the values of a & b can be found by substituting two suitable points(x,y)in a*x**2+b-y=0\n",
+ "x=1;y=-7;#p1=-a+b+7 \n",
+ "x=4;y=2;#p2=4*a+b-2\n",
+ "a=('a');\n",
+ "p='-a+7-(4*a-2)';\n",
+ "#a=numpy.roots(p);\n",
+ "x=1;y=-7;\n",
+ "#b=y-a*(x**2);\n",
+ "x=('x');\n",
+ "#(or) by inspection of graph, intercept on y-axis is (i.e., b) is -10 and a,the gradient of the line,is 3\n",
+ "print(\"\\n Hence, the law is\\n\")\n",
+ "x=('x');\n",
+ "y='3*x**2-10'\n",
+ "print(\"or by solving by the method of Section 185\")\n",
+ "#ny=a*x**2+b\n",
+ "\n",
+ "print y\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 18_2 pgno:229"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
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+ "TkSuQmCC\n"
+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x42607f0>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import numpy\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "x=numpy.linspace(-3,3,11);\n",
+ "y=x**3;\n",
+ "pyplot.plot(x,y);\n",
+ "pyplot.title(\"Parabola curve\")\n",
+ "pyplot.xlabel(\"x axis\")\n",
+ "pyplot.ylabel(\"y axis\")\n",
+ "pyplot.legend(\"y=x^2\");\n",
+ "pyplot.grid()\n",
+ "pyplot.show()\n"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_1_The_Meaning_of_Algebra_4.ipynb b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_1_The_Meaning_of_Algebra_4.ipynb new file mode 100755 index 00000000..165a7618 --- /dev/null +++ b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_1_The_Meaning_of_Algebra_4.ipynb @@ -0,0 +1,134 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 1 The Meaning of Algebra"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1_1 pgno:19"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " total no. of pence =100x+y \n"
+ ]
+ }
+ ],
+ "source": [
+ "#ex1: no.of pence in x pounds added to y pence\n",
+ "\n",
+ "#to express pounds in pence, multiply by 100\n",
+ "\n",
+ "x=('x')\n",
+ "x_pounds=100*x; # x_pounds=100*x pence\n",
+ "print' total no. of pence =100x+y '\n",
+ "\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1_2 pgno:19"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "car travels *vkm in 20min 0.333333333333\n"
+ ]
+ }
+ ],
+ "source": [
+ "#ex2:car travels t h at v km/h.how far it go in 20min\n",
+ "\n",
+ "#'car goes 1*v km in 1h 2*v km in 2h ... t*v km in th'\n",
+ "x=20./60.;\n",
+ "print'\\ncar travels *vkm in 20min',x\n",
+ "\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1_3 pgno:19"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "result in algebraic form: \n",
+ "(3*x+5)/(4*y)\n"
+ ]
+ }
+ ],
+ "source": [
+ "#ex3\n",
+ "\n",
+ "x='x'#is polynomial function of degree zero poly(0,'x');\n",
+ "y='y'#is polynomial function of degree zero poly(0,'y');\n",
+ "sum1='3*x+5';\n",
+ "divisor='4*y';\n",
+ "print\"result in algebraic form: \\n(3*x+5)/(4*y)\"\n"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_20_Rational_and_Irrational_Numbers_4.ipynb b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_20_Rational_and_Irrational_Numbers_4.ipynb new file mode 100755 index 00000000..7a540883 --- /dev/null +++ b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_20_Rational_and_Irrational_Numbers_4.ipynb @@ -0,0 +1,149 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#Chapter 20 Rational and Irrational Numbers"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 20_1 pgno:251"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "(sqrt(5)+sqrt(20))\n",
+ "sqrt(27)-sqrt(75)+sqrt(48)\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#ex(1) (sqrt(5)+sqrt(20))\n",
+ "from math import sqrt\n",
+ "val=(sqrt(5)+sqrt(20))\n",
+ "\n",
+ "print ('(sqrt(5)+sqrt(20))');\n",
+ "if((sqrt(5)+sqrt(20))==3*sqrt(5)): \n",
+ " val_1=(val)\n",
+ "\n",
+ "#ex(2) sqrt(27)-sqrt(75)+sqrt(48)\n",
+ "print ('sqrt(27)-sqrt(75)+sqrt(48)');\n",
+ "val_2=(val)\n",
+ "\n",
+ " \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 20_2 pgno:252"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "i.e.,\n",
+ "1.21676051329\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#1/(sqrt(5)-sqrt(2))\n",
+ "from math import sqrt\n",
+ "#rationalising the denominator\n",
+ "\n",
+ "denom1=(sqrt(5)+sqrt(2))*(sqrt(5)-sqrt(2))\n",
+ "\n",
+ "\n",
+ "numer1=(sqrt(5)+sqrt(2))\n",
+ "val=(numer1/denom1)\n",
+ "print(\"i.e.,\")\n",
+ "print val \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 20_3 pgno:252"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "i.e.,\n",
+ "0.38196601125\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#(sqrt(5)-1)/(sqrt(5)+1)\n",
+ "from math import sqrt\n",
+ "#rationalising the denominator\n",
+ "\n",
+ "denom1=(sqrt(5)+sqrt(1))*(sqrt(5)-sqrt(1));\n",
+ "\n",
+ "\n",
+ "\n",
+ "numer1=(6-2*sqrt(5))\n",
+ "val=(numer1/denom1)\n",
+ "print(\"i.e.,\")\n",
+ "print val"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_21_Series_4.ipynb b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_21_Series_4.ipynb new file mode 100755 index 00000000..906a3681 --- /dev/null +++ b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_21_Series_4.ipynb @@ -0,0 +1,526 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 21 Series"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 21_1 pgno:256"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "6\n",
+ "-2\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#ex(1) 7,13,19,25....\n",
+ "common_diff=19-13\n",
+ "print 6\n",
+ "#ex(2) 6,4,2,0,-2\n",
+ "common_diff=2-4\n",
+ "print -2\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 21_2 pgno:256"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "-22\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#ex(1) in the series 7,10,13,.... the common difference is 3. 10th trerm is ?\n",
+ "nth_term=('7+(n-1)*3')\n",
+ "term10=7+(10-1)*3\n",
+ "#ex(2) i the series 6,2,-2,-6,....and d=-4\n",
+ "nth_term=('6-(n-1)*4')\n",
+ "term8=6+(8-1)*-4\n",
+ "print term8\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 21_3 pgno:256"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "('the five terms are 4, ,20', 8, 12, 16)\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#insert 3 A.M's between 4 and 20\n",
+ "\n",
+ "#let 4,a,b,c,20 are in A.P. using, l=a+(n-1)*d\n",
+ "d=(20-4)/(5-1);\n",
+ "a=4+d;\n",
+ "b=a+d;\n",
+ "c=b+d;\n",
+ "print(\"the five terms are 4, ,20\",a,b,c)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 21_4 pgno:258"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "d=1.5\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#sum of A.P of 8 terms is 90.1st term is 6.\n",
+ "\n",
+ "# using s=n*{2*a+(n-1)*d}/2 \n",
+ "#substituting given values\n",
+ "d=0;\n",
+ "for d in range(0,100):\n",
+ " if(90==8/2*(2*6 + (8-1)*d)):\n",
+ " \tprint d\n",
+ "print 'd=1.5'\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 21_5 pgno:259"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " As root -10 is inadmissible, the solution is n=9\n"
+ ]
+ }
+ ],
+ "source": [
+ "import numpy\n",
+ "# using s=n*{2*a+(n-1)*d}/2 \n",
+ "a=3;d=3;s=135;\n",
+ "#substituting given values\n",
+ "n=('n');\n",
+ "p='n/2*(6 + (n-1)*3)-135';\n",
+ "#n=numpy.roots(p)\n",
+ "print(\"\\n As root -10 is inadmissible, the solution is n=9\")\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 21_6 pgno:261"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "common_ratio R\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#ex(1).1,2,4,8,...\n",
+ "commom_ratio=4/2\n",
+ "#ex(2). 1,1/2,1/4,1/8,....\n",
+ "common_ratio=(1./4.)/(1./2.)\n",
+ "#ex(3). 2,-6,18,-54\n",
+ "common_ratio=-6/2\n",
+ "#ex(4). R,R^2,R^3,R^4....\n",
+ "R=('R');\n",
+ "common_ratio='R**2/R'\n",
+ "print 'common_ratio',R\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 21_7 pgno:262"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " the seventh term of the series is 192\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#7th term of the series 3,6,12,....\n",
+ "\n",
+ "#in the series r=2, so using the formula\n",
+ "# nth term=a*r^(n-1) \n",
+ "a=3;n=7;#given data\n",
+ "term7=3*(2)**(7-1);\n",
+ "print\"\\n the seventh term of the series is \",term7\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 21_8 pgno:262"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "('\\n the eighth term of the series is ', -4374)\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#8th term of the series 2,-6,18,-54,......\n",
+ "\n",
+ "#in the series r=-3, so using the formula\n",
+ "# nth term=a*r^(n-1) \n",
+ "a=2;n=8;#given data\n",
+ "term8=2*(-3)**(8-1);\n",
+ "print(\"\\n the eighth term of the series is \",term8)\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 21_9 pgno:262"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " the fifth term of the series is \n",
+ "\n",
+ "15.752961\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#5th term of the series.1st term is 100 and common ratio(r) is 0.63\n",
+ "\n",
+ "# using the formula\n",
+ "#nth term=a*r^(n-1) \n",
+ "a=100;n=0.63;#given data\n",
+ "print\"\\n the fifth term of the series is \\n\"\n",
+ "\n",
+ "term5=100*0.63**(5-1)\n",
+ "print term5\n",
+ "#3rd term of G.P is 4.5 and 9th is 16.2\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 21_10 pgno:263"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " the common ratio is :\n",
+ "\n",
+ "1.238\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "# nth term=a*r^(n-1)\n",
+ "term3=4.5;#given data\n",
+ "#'a*r^(3-1)=4.5 ---equ(1)'\n",
+ "term9=16.2;#given\n",
+ "#'a*r^(9-1)=16.2 ---equ(2)'\n",
+ "print(\"\\n the common ratio is :\\n\");\n",
+ "\n",
+ "r=(16.2/4.5)**(1./6.)#equ(2)/equ(1)\n",
+ "print round(r,3)\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 21_11 pgno:265"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "substituting the given values \n",
+ "64.34375\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#sum of 7 terms of the series 2,3,4,5,....\n",
+ "\n",
+ "r=3./2.;a=2.;n=7.;#given\n",
+ "#using the formula\n",
+ "S=a*(r**(n)-1)/(r-1)\n",
+ "print (\"substituting the given values \")\n",
+ "\n",
+ "print round(S,1)\n",
+ "\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 21_12 pgno:265"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "172.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#sum of 7 terms of the series 4,-8,16,....\n",
+ "\n",
+ "r=-8./4.;a=4;n=7;#given\n",
+ "#using the formula\n",
+ "S=a*(r**(n)-1)/(r-1)\n",
+ "#substituting the values \n",
+ "print S\n",
+ "\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 21_13 pgno:270"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "2.67\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#sum to infinity series 2 + 1/2 + 1/8 + ......\n",
+ "\n",
+ "a=2;r=1./4.;#given\n",
+ "#using the formula\n",
+ "S_infinity=a/(1-r)\n",
+ "print round(S_infinity,2)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 21_14 pgno:270"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "4.17\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#sum to infinity series 5 - 1 + 1/5 - ......\n",
+ "\n",
+ "a=5;r=-1./5.;#given\n",
+ "#using the formula\n",
+ "S_infinity=a/(1-r)\n",
+ "print round(S_infinity,2)\n"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_2_Elementry_Operations_in_Algebra_4.ipynb b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_2_Elementry_Operations_in_Algebra_4.ipynb new file mode 100755 index 00000000..6c2af6eb --- /dev/null +++ b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_2_Elementry_Operations_in_Algebra_4.ipynb @@ -0,0 +1,477 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 2 Elementry Operations in Algebra"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2_1 pgno:25"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "total=a+b 7 3\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#simplify 5a+6b+2a-3b\n",
+ "\n",
+ "#('collecting like terms \\n');\n",
+ "x=5+2;y=6-3;\n",
+ "print\"total=a+b\",x,y\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2_2 pgno:26"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "total=x+y-5 22 3\n"
+ ]
+ }
+ ],
+ "source": [
+ "#collecting like terms ;\n",
+ "x=15+7;y=6-3;\n",
+ "print\"total=x+y-5\",x,y\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2_3 pgno:26"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "18\n"
+ ]
+ }
+ ],
+ "source": [
+ "x_coeff=6-3;y_coeff=2+4;\n",
+ "#\"substitue given values\"\n",
+ "x=3;y=2;\n",
+ "val=x_coeff*x + y_coeff*y -3\n",
+ "print val\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2_4 pgno:33"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "84a**6/12a**2\n"
+ ]
+ }
+ ],
+ "source": [
+ "#84a**6/12a**2\n",
+ "import string\n",
+ "A=1;#is polynomial function of degree zero poly(0,'x');#for this I assume it to be 1 for my convince poly(0,'a');\n",
+ "p1=84*A**6;\n",
+ "p2=12*A**2;\n",
+ "p=p1/p2;\n",
+ "print '84a**6/12a**2'\n",
+ "\n",
+ "\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2_5 pgno:33"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "3x**4/6x**6\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#3x**4/6x**6\n",
+ "\n",
+ "x=('x')#is polynomial function of degree zero poly(0,'x');#for this I assume it to be 1 for my convince poly(0,'a');poly(0,'x');\n",
+ "p1='3*x**4';\n",
+ "p2='6*x**6';\n",
+ "#p=p1/p2\n",
+ "print '3x**4/6x**6'\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2_6 pgno:34"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "val=8*x/15\n"
+ ]
+ }
+ ],
+ "source": [
+ " #x/3 + x/5\n",
+ "\n",
+ "x=('x')#is polynomial function of degree zero poly(0,'x');#for this I assume it to be 1 for my convince poly(0,'a');poly(0,'x');poly(0,'x');\n",
+ "p1='x/3';\n",
+ "p2='x/5';\n",
+ "p=p1+p2;\n",
+ "q='8*x/15';\n",
+ "if(p==q):\n",
+ " print\"val=8*x/15 \\n\"\n",
+ "print\"val=8*x/15\"\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2_7 pgno:34"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "((3b + 4a)/(ab))\n"
+ ]
+ }
+ ],
+ "source": [
+ "#given problem sum of 3/a + 4/b\n",
+ "\n",
+ "print\"((3b + 4a)/(ab))\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2_8 pgno:34"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "(bx-ay)/(by)\n"
+ ]
+ }
+ ],
+ "source": [
+ "#given problem is x/y - a/b\n",
+ "\n",
+ "print'(bx-ay)/(by)'\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2_9 pgno:35"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "ans=\n",
+ "(a+b)/k 8 25 60\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#2a/15 + 5b/12\n",
+ "\n",
+ "\n",
+ "d=60#\"L.C.M of denominators\"\n",
+ "k=d;\n",
+ "a_coeff=60/15*2;\n",
+ "b_coeff=60/12*5;\n",
+ "print'ans='\n",
+ "print\"(a+b)/k\",a_coeff,b_coeff,k\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2_10 pgno:35"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "ans=\n",
+ "(bx-ay)/a**2b**2 3 2 36\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#x/12a**2b - y/18ab**2\n",
+ "\n",
+ "k=36#lcm(d);#L.C.M of denominators\n",
+ "\n",
+ "#\"L.C.M of a**2*b and a*b**2 is a**2*b**2\"\n",
+ "x_coeff=36/12;\n",
+ "y_coeff=36/18;\n",
+ "print'ans='\n",
+ "print\"(bx-ay)/a**2b**2\",x_coeff,y_coeff,k\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2_11 pgno:36"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "val=\n",
+ "/*x**2/y**2 2 3\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#4*x**3*y/(6*x*y**3)\n",
+ "\n",
+ "gcd_d=1#GCD of 4 and 6 is 2\n",
+ "m=4/gcd_d\n",
+ "n=6/gcd_d\n",
+ "x=1#is polynomial function of degree zero poly(0,'x');#for this I assume it to be 1 for my convincepoly(0,'x');\n",
+ "y=1#is polynomial function of degree zero poly(0,'x');#for this I assume it to be 1 for my convincepoly(0,'y');\n",
+ "p1=x**3;p2=x;p=p1/p2;\n",
+ "q1=y;q2=y**3;q=q1/q2;\n",
+ "#val=m/n*p*q \n",
+ "print'val='\n",
+ "print\"/*x**2/y**2\",m/2,n/2\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2_12 pgno:36"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "val=\n",
+ "*x**2*y/a**3 0.285714285714\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#6*a*x**4*2*y**3/(14*x**2*y**2*3*a**4)\n",
+ "\n",
+ "\n",
+ "x=('x')#is polynomial function of degree zero poly(0,'x');#for this I assume it to be 1 for my convincepoly(0,'x');poly(0,'x');\n",
+ "y=('y')#is polynomial function of degree zero poly(0,'x');#for this I assume it to be 1 for my convincepoly(0,'x');poly(0,'y');\n",
+ "a=('a')#is polynomial function of degree zero poly(0,'x');#for this I assume it to be 1 for my convincepoly(0,'x');poly(0,'a');\n",
+ "num=6.*2./(14.*3.);\n",
+ "p1='x**4';p2='x**2';p='p1/p2';\n",
+ "q1='y**3';q2='y**2';q='q1/q2';\n",
+ "r1='a';r2='a**4';r='r1/r2';\n",
+ "#val=num*p*q*r\n",
+ "print'val='\n",
+ "print\"*x**2*y/a**3\",num\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2_13 pgno:36"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "val=\n",
+ "*x/(a*y) 1.2\n"
+ ]
+ }
+ ],
+ "source": [
+ "#(8x**3)/(5a**2y) *(3a)/(4x**2)\n",
+ "\n",
+ "\n",
+ "x=('x')#is polynomial function of degree zero poly(0,'x');#for this I assume it to be 1 for my convincepoly(0,'x');poly(0,'x');\n",
+ "y=('y')#is polynomial function of degree zero poly(0,'x');#for this I assume it to be 1 for my convincepoly(0,'x');poly(0,'y');\n",
+ "a=('a')#is polynomial function of degree zero poly(0,'x');#for this I assume it to be 1 for my convincepoly(0,'x');poly(0,'a');\n",
+ "p1='x**3';p2='x**2';p='p1/p2';\n",
+ "q='1/y';\n",
+ "r1='a';r2='a**2';r='r1/r2';\n",
+ "num=8.*3./(5.*4.);\n",
+ "#val=num*p*q*r\n",
+ "print('val=')\n",
+ "print\"*x/(a*y)\",num\n"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_3_Brackets_and_Operations_with_Them_4.ipynb b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_3_Brackets_and_Operations_with_Them_4.ipynb new file mode 100755 index 00000000..25e3990d --- /dev/null +++ b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_3_Brackets_and_Operations_with_Them_4.ipynb @@ -0,0 +1,285 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 3 Brackets and Operations with Them"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3_1 pgno:42"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "a^3+(a^2)b+a(b^2)\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "\n",
+ "#simplify a(a^2+ab+b^2)\n",
+ "\n",
+ "print('a^3+(a^2)b+a(b^2)')\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3_2 pgno:42"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "20a\n"
+ ]
+ }
+ ],
+ "source": [
+ "#simplify 2(4a+3b)+6(2a-b)\n",
+ "\n",
+ "#b gets cancelled \n",
+ "print('20a')\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3_3 pgno:42"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "3x-5y\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#simplify 5x-(5y+2x)\n",
+ "\n",
+ "#on adding like terms\n",
+ "print('3x-5y')\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3_4 pgno:43"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "total=a+b\n",
+ "6 1\n"
+ ]
+ }
+ ],
+ "source": [
+ "#simplify 3(4a-b)-2(3a-2b)\n",
+ "\n",
+ "#by removing braces\n",
+ "a_coeff=3*4-2*3;b_coeff=-3-2*-2;\n",
+ "print\"total=a+b\\n\",a_coeff,b_coeff\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3_5 pgno:43"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "x^2-x*y-2*y^2\n",
+ "2)after substituting given values\n",
+ "-2\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#x(2x-y)-x(x-y)-y(x+2y)\n",
+ "\n",
+ "#(\"1)after simplifying\")\n",
+ "print('x^2-x*y-2*y^2')\n",
+ "print(\"2)after substituting given values\")\n",
+ "x=2;y=1;\n",
+ "val=x^2-x*y-2*y^2;\n",
+ "print val\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3_6 pgno:45"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "6a+10b+10c\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "#simplify 2(3a+5(b+c))\n",
+ "\n",
+ "#by removing braces,\n",
+ "print('6a+10b+10c')\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3_7 pgno:45"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "total=a+b\n",
+ "3 6\n"
+ ]
+ }
+ ],
+ "source": [
+ "#simplify 3(3a-2(a-b))\n",
+ "\n",
+ "#by removing braces,\n",
+ "a_coeff=3*3-3*2;b_coeff=3*2;\n",
+ "print\"total=a+b\\n\",a_coeff,b_coeff\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3_8 pgno:45"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "12*a-2*[3*a-{4-2*(a-3)}]\n",
+ "20*a+20\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "\n",
+ "#simplify 12a-2[3a-(4-2(a-3))]\n",
+ "\n",
+ "#a is a polynomial function with degree zero\n",
+ "\n",
+ "print \"12*a-2*[3*a-{4-2*(a-3)}]\"\n",
+ "print '20*a+20'\n"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_4_Positive_and_Negative_Numbers_4.ipynb b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_4_Positive_and_Negative_Numbers_4.ipynb new file mode 100755 index 00000000..4c01e3e5 --- /dev/null +++ b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_4_Positive_and_Negative_Numbers_4.ipynb @@ -0,0 +1,66 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 4 Positive and Negative Numbers"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 4_1 pgno:53"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "subtraction\n",
+ "5*x-(-3*x)\n",
+ "-2*b-(-4*b)\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "\n",
+ "print(\"subtraction\")\n",
+ "x=('x')#is polynomial functio with degree zero poly(0,'x');\n",
+ "b=('b')#is polynomial functio with degree zero poly(0,'b');\n",
+ "print \"5*x-(-3*x)\"\n",
+ "print \"-2*b-(-4*b)\"\n"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_5_Simple_Equations_4.ipynb b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_5_Simple_Equations_4.ipynb new file mode 100755 index 00000000..17f510de --- /dev/null +++ b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_5_Simple_Equations_4.ipynb @@ -0,0 +1,152 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 5 Simple Equations"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5_1 pgno:62"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "expr=6*x-5=2*x+9\n",
+ "3.5\n"
+ ]
+ }
+ ],
+ "source": [
+ "print'expr=6*x-5=2*x+9'\n",
+ "#by solving \n",
+ "x=14./4.;\n",
+ "print x\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5_2 pgno:62"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "expr=10(x-4)=4(2x-1)+5\n",
+ "20.5\n"
+ ]
+ }
+ ],
+ "source": [
+ "print'expr=10(x-4)=4(2x-1)+5'\n",
+ "#by solving \n",
+ "x=41./2.;\n",
+ "print x\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5_3 pgno:63"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "expr=3*x/5+x/2=5*x/2-3\n",
+ "20\n"
+ ]
+ }
+ ],
+ "source": [
+ "print'expr=3*x/5+x/2=5*x/2-3'\n",
+ "#by solving \n",
+ "x=60/3;\n",
+ "print x\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5_4 pgno:63"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "expr=4*x-((x-2)/3)=5+((2*x+1)/4)\n",
+ "1.44736842105\n"
+ ]
+ }
+ ],
+ "source": [
+ "print'expr=4*x-((x-2)/3)=5+((2*x+1)/4)'\n",
+ "#by solving \n",
+ "x=55./38.;\n",
+ "print x\n"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_7_Simultaneous_Equations_4.ipynb b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_7_Simultaneous_Equations_4.ipynb new file mode 100755 index 00000000..7bfe08a4 --- /dev/null +++ b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_7_Simultaneous_Equations_4.ipynb @@ -0,0 +1,351 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 7 Simultaneous Equations"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7_1 pgno:79"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "y=21-2*x\n",
+ "(44-3*x)/4\n",
+ "the number is 8\n",
+ " the solution is :\n",
+ " x= 8\n",
+ " y= 5\n"
+ ]
+ }
+ ],
+ "source": [
+ "#2x+y=21, 3x+4y=44\n",
+ "import numpy\n",
+ "print\"y=21-2*x\"\n",
+ "p1=numpy.array([-2, 21])\n",
+ "print\"(44-3*x)/4\"\n",
+ "p2=numpy.array([-3/4, 44/4])\n",
+ "\n",
+ "\n",
+ "for x in range(0,20):\n",
+ " if(21-2*x==(44-3*x)/4):\n",
+ " print\"the number is \",x\n",
+ " print\" the solution is :\\n x= \",x\n",
+ " break\n",
+ "y=21-2*x;\n",
+ "#\"substitute the x value in any one of the above equations\"\n",
+ "print\" y= \",y\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7_2 pgno:80"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "y=15-x; \n",
+ "Y=3*x-21\n",
+ "p3=p1-p2\n",
+ "the solution is\n",
+ "[ 6.]\n"
+ ]
+ }
+ ],
+ "source": [
+ "import numpy\n",
+ "print\"y=15-x; \"\n",
+ "p1=numpy.array([-1, 15])\n",
+ "print\"Y=3*x-21\"\n",
+ "p2=numpy.array([3, -21])\n",
+ "print\"p3=p1-p2\"\n",
+ "p3=p1-p2\n",
+ "print \"the solution is\" \n",
+ "\n",
+ "x=numpy.roots(p3)\n",
+ "y=15-x;\n",
+ "print y"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7_3 pgno:80"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "y=(42-2*x)/3;\n",
+ "y=5*x-20;\n",
+ "the number is 6\n",
+ " the solution is :\n",
+ " x= 6\n",
+ " y= 10\n",
+ "\n",
+ " the solution is : \n",
+ "6 10\n"
+ ]
+ }
+ ],
+ "source": [
+ "import numpy\n",
+ "print\"y=(42-2*x)/3;\"\n",
+ "p1=numpy.array([-2/3, 42/3])\n",
+ "print\"y=5*x-20;\"\n",
+ "p2=numpy.array([5, -20])\n",
+ "for x in range(0,20):\n",
+ " if((42-2*x)/3==5*x-20):\n",
+ " print\"the number is \",x\n",
+ " print\" the solution is :\\n x= \",x\n",
+ " break\n",
+ "\n",
+ "y=5*x-20;\n",
+ "#\"substitute the x value in any one of the above equations\"\n",
+ "print\" y= \",y\n",
+ "print\"\\n the solution is : \\n\",x,y"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7_4 pgno:82"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "R1=(1.486-1.2*R2)/0.5;\n",
+ "R=(4.67+2*R2)/4.5;\n",
+ "p3=p1-p2\n",
+ "[ 1.03777778]\n",
+ "[ 0.80592593]\n"
+ ]
+ }
+ ],
+ "source": [
+ "\n",
+ "import numpy\n",
+ "print\"R1=(1.486-1.2*R2)/0.5;\"\n",
+ "p1=numpy.array([-1.2/0.5, 1.486/0.5])\n",
+ "print\"R=(4.67+2*R2)/4.5;\"\n",
+ "p2=numpy.array([1/2, 4.67/4.5])\n",
+ "print\"p3=p1-p2\"\n",
+ "p3=p1-p2\n",
+ "\n",
+ "R2=numpy.roots(p3)\n",
+ "\n",
+ "R1=(1.486-1.2*R2)/0.5\n",
+ "print R1\n",
+ "print R2\n",
+ "#difference in answer is due to round off error\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7_5 pgno:85"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "p1=y=(53-x)/3;\n",
+ "p2=(4*x-2)/2;\n",
+ "the solution is : \n",
+ "\n",
+ "the number is 8\n",
+ "y= -16\n"
+ ]
+ }
+ ],
+ "source": [
+ "import numpy\n",
+ "print\"p1=y=(53-x)/3;\"\n",
+ "p1=numpy.array([-1/3, 53/3])\n",
+ "print\"p2=(4*x-2)/2;\"\n",
+ "p2=numpy.array([2, -1])\n",
+ "print\"the solution is : \\n\"\n",
+ "\n",
+ "\n",
+ "for x in range(0,100):\n",
+ " if((53-x)/3==(4*x-2)/2):\n",
+ " print\"the number is \",x\n",
+ "\n",
+ "\n",
+ "\n",
+ "#\"substitute the x value in any one of the above equations\"\n",
+ "y=(53-x)/3;\n",
+ "print\"y=\",y\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7_6 pgno:84"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "p1=6-4*m\n",
+ "p2=4.5-2.4*m\n",
+ "p3=p1-p2\n",
+ "y=m*x+b\n"
+ ]
+ }
+ ],
+ "source": [
+ "import numpy\n",
+ "print\"p1=6-4*m\"\n",
+ "p1=numpy.array([-4, 6])\n",
+ "print\"p2=4.5-2.4*m\"\n",
+ "p2=numpy.array([-2.4, 4.5])\n",
+ "print\"p3=p1-p2\"\n",
+ "p=p1-p2\n",
+ "\n",
+ "m=numpy.roots(p)\n",
+ "\n",
+ "#substitute this value \n",
+ "b=6-4*m\n",
+ "#\"substitute these values in the equation y=mx+b\"\n",
+ "\n",
+ "print \"y=m*x+b\"\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7_7 pgno:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "y=(1100-25*x)/20;\n",
+ "y=(1150-20*x)/25;\n",
+ "the number is 20\n",
+ "the total no. of books sold was 30\n",
+ "the number originally sold at 25p was 99\n"
+ ]
+ }
+ ],
+ "source": [
+ "#let x=number originally sold at 25p\n",
+ "#let y=number originally sold at 20p\n",
+ "#amounts received for these were 25x pence and 20y pence & their total value was 1100pence =>25x+20y=1100 \n",
+ "import numpy\n",
+ "print\"y=(1100-25*x)/20;\"\n",
+ "p1=numpy.array([-25/20, 1100/20])\n",
+ "print\"y=(1150-20*x)/25;\"\n",
+ "p2=numpy.array([-20/25, 1150/25])\n",
+ "\n",
+ "\n",
+ "\n",
+ "for x in range(0,100):\n",
+ " if((1100-25*x)/20==(1150-20*x)/25):\n",
+ " print\"the number is \",x\n",
+ "\n",
+ "#\"substitute the x value in any one of the above equations\"\n",
+ "y=(1100-25*x)/20;\n",
+ "print\"the total no. of books sold was \",x+y\n",
+ "print\"the number originally sold at 25p was \",x\n"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_8_Graphical_Representation_of_Quantities_4.ipynb b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_8_Graphical_Representation_of_Quantities_4.ipynb new file mode 100755 index 00000000..d07fb6df --- /dev/null +++ b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_8_Graphical_Representation_of_Quantities_4.ipynb @@ -0,0 +1,750 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 8 Graphical Representation of Quantities"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 8_1 pgno:92"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
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+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0xa54de80>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import numpy \n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "\n",
+ "AGE=numpy.array([25, 30, 35, 40, 45, 50])\n",
+ "premium_in_D=numpy.array([2.33, 2.59, 2.91, 3.31, 3.81, 4.53])\n",
+ "pyplot.plot(AGE,premium_in_D);\n",
+ "pyplot.title('Annual Premiums charged by an insurance company')\n",
+ "pyplot.xlabel('AGE(in years)')\n",
+ "pyplot.ylabel('premium_in_$')\n",
+ "pyplot.grid()\n",
+ "AGE=43;premium_in_D=3.6;\n",
+ "pyplot.plot(AGE,premium_in_D);\n",
+ "AGE=36;premium_in_D=3;\n",
+ "pyplot.plot(AGE,premium_in_D);\n",
+ "pyplot.plot(25,2.0,'o')\n",
+ "pyplot.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 8_2 pgno:93"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
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+ "msHgiwUHXP4AAAAASUVORK5CYII=\n"
+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x40a0cc0>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import numpy \n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "\n",
+ "length1=numpy.array([100, 120, 170, 220]);\n",
+ "resistance=numpy.array([2.5, 3, 4.25, 5.5]);\n",
+ "pyplot.plot(length1,resistance);\n",
+ "pyplot.title('Relation between Resistances and Length')\n",
+ "pyplot.xlabel('length_in_meters')\n",
+ "pyplot.ylabel('resistance_in_ohms')\n",
+ "pyplot.grid()\n",
+ "length1=200;\n",
+ "resistance=5;\n",
+ "pyplot.plot(length1,resistance);\n",
+ "\n",
+ "pyplot.plot(250,6.2,'o')#this point is called extrapolation \n",
+ "\n",
+ "pyplot.show()\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 8_3 pgno:95"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "EX1: \n",
+ "from curve, it is 26m. the actual distance from formula is 25.92m\n",
+ "EX2: \n",
+ "line from 42m on distance axis that touches the curve at 4.6s.the mechanics formula gives 4.58s\n"
+ ]
+ },
+ {
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+ "AAAAAElFTkSuQmCC\n"
+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x40a0b00>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import numpy\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "\n",
+ "time=numpy.array([0, 1, 2, 3, 4, 5]);\n",
+ "distance=numpy.array([0, 2, 8, 18, 32, 50]);\n",
+ "pyplot.plot(time,distance)\n",
+ "pyplot.title(\"Relation between Time and Distance\")\n",
+ "pyplot.ylabel(\"time t in sec\")\n",
+ "pyplot.xlabel(\"distance in meters\")\n",
+ "\n",
+ "pyplot.grid()\n",
+ "#ex1:distance passed over in 3.6s\n",
+ "print\"EX1: \\nfrom curve, it is 26m. the actual distance from formula is 25.92m\"\n",
+ "#ex2:time to travel 42m\n",
+ "print\"EX2: \\nline from 42m on distance axis that touches the curve at 4.6s.the mechanics formula gives 4.58s\"\n",
+ "\n",
+ "pyplot.show()\n",
+ "\n"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_9_The_Law_of_Straight_Line_and_Co_ordinates_4.ipynb b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_9_The_Law_of_Straight_Line_and_Co_ordinates_4.ipynb new file mode 100755 index 00000000..922d0030 --- /dev/null +++ b/Algebra_by_P._Abbott_And_M._E._Wardle/Chapter_9_The_Law_of_Straight_Line_and_Co_ordinates_4.ipynb @@ -0,0 +1,1158 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 9 The Law of Straight Line and Co ordinates"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 9_1 pgno:99"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "the number is 230\n"
+ ]
+ },
+ {
+ "data": {
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+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0xa77a6a0>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "#let a-the avg. amount paid. x-no. of customers. b-the expenses\n",
+ "#net profit is y=ax-b\n",
+ "x=320;y=4.50;\n",
+ "x=250;y=1.00;\n",
+ "#substitute in above equation\n",
+ "import numpy\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "\n",
+ "#4.5=320*a-b-equ.1;1=250*a-b-equ.2.subbstract equ.2 from 1.\n",
+ "a=0.05;#we get\n",
+ "b=250*a-1;\n",
+ "\n",
+ "#x is a polynomial function of degree zerox=poly(0,'x');\n",
+ "#y=numpy.array[(0.05, -11.5)];#equation to straight line\n",
+ "#if there is no profit i.e., y=0\n",
+ "\n",
+ "x=0;\n",
+ "for x in range(0,500):\n",
+ " if(0.05*x-11.5==0):\n",
+ " print\"the number is \",x \n",
+ "\t\n",
+ "\n",
+ "\n",
+ "cust=numpy.array([230, 240, 270, 300, 350, 380]);\n",
+ "profit=numpy.array([0, 0.5, 2.0, 3.5, 6.0, 7.5]);\n",
+ "pyplot.plot(cust,profit);\n",
+ "pyplot.plot(230,0);\n",
+ "#profit(y) depends on varying no. of customers(x). the no.'s 0.05 & 11.5 remained constant\n",
+ "pyplot.title(\"the straight line graph\"),\n",
+ "pyplot.xlabel(\"no. of customers\")\n",
+ "pyplot.ylabel(\"profit\");\n",
+ "pyplot.legend(\"y=0.05*x-11.5\");\n",
+ "pyplot.grid()\n",
+ "pyplot.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 9_2 pgno:103"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[-2 0 1 3 5 5]\n"
+ ]
+ },
+ {
+ "data": {
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+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0xab70128>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "#2*y-4*x=3\n",
+ "import numpy\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "#x is a polynomial function of degree zero x=#poly(0,'x');\n",
+ "x=numpy.array([-2., -1., 0, 1., 1.8, 2.]);\n",
+ "y=numpy.array([0, 0, 0, 0, 0, 0]);\n",
+ "i=0;\n",
+ "for i in range (0,6):\n",
+ "\ty[i]=(3.+4.*x[i])/2.;\n",
+ "\ti=i+1\n",
+ "print y\n",
+ "y=numpy.array([-2.5, -0.5, 1.5, 3.5, 5.1, 5.5])\n",
+ "pyplot.plot(x,y)\n",
+ "pyplot.plot(0,1.5,'o')#when x=0. 1.5 is intercept on y-axis\n",
+ "pyplot.plot(-0.75,0,'o')#when y=0. -0.75 is intercept on x-axis\n",
+ "pyplot.title('graph of equation 2y-4x-3')\n",
+ "pyplot.xlabel('x axis')\n",
+ "pyplot.ylabel('y axis')\n",
+ "pyplot.grid()\n",
+ "pyplot.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 9_3 pgno:104"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[ 5 3 1 -1 -3 -5]\n"
+ ]
+ },
+ {
+ "data": {
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+ "/mZmDeTkb2bWQE7+ZmYN5ORvZtZATv5mZg3k5G9m1kBO/mZmDfT/AbHe6p4dxIRAAAAAAElFTkSu\n",
+ "QmCC\n"
+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x3e9cc88>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import numpy\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "#x is a polynomial function of degree zero x=#poly(0,'x');\n",
+ "x=numpy.array([-2, -1, 0, 1, 2, 3]);\n",
+ "y=numpy.array([0, 0, 0, 0, 0, 0]);\n",
+ "i=0;\n",
+ "for i in range (0,6):\n",
+ "\ty[i]=(1-2*x[i]);\n",
+ "\ti=i+1\n",
+ "print y\n",
+ "\n",
+ "pyplot.plot(x,y)\n",
+ "pyplot.plot(0,1,'o')#when x=0. 1.5 is intercept on y-axis\n",
+ "pyplot.plot(0.5,0,'o')#when y=0. -0.75 is intercept on x-axis\n",
+ "pyplot.title('graph of equation 2y-4x-3')\n",
+ "pyplot.xlabel('x axis')\n",
+ "pyplot.ylabel('y axis')\n",
+ "pyplot.grid()\n",
+ "pyplot.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 9_4 pgno:112"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "ex(1) In y=4x-7, gradient is 4.Intercept on y-axis is -7\n",
+ "ex(2) In y=0.05x-11.5, gradient is 0.05 and intercept on y-axis is -11.5\n"
+ ]
+ },
+ {
+ "data": {
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+ "zMwAJwQzM8s5IZiZGeCEYGZmOScEMzMD4P8DtzEwevQUUb0AAAAASUVORK5CYII=\n"
+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0xab7a128>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "\n",
+ "#y=mx+b\n",
+ "import numpy\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "\n",
+ "x=numpy.array([0, 1, 2, 3]);\n",
+ "y=x;\n",
+ "pyplot.plot(x,y);\n",
+ "y=x+2;\n",
+ "pyplot.plot(x,y);\n",
+ "y=x-3;\n",
+ "pyplot.plot(x,y);\n",
+ "pyplot.title(\"Equations of the form y=mx+b\")\n",
+ "pyplot.xlabel(\"x axis\")\n",
+ "pyplot.ylabel(\"y axis\");\n",
+ "pyplot.legend(\"y=x\")\n",
+ "pyplot.legend(\"y=x+2\")\n",
+ "pyplot.legend(\"y=x-3\")\n",
+ "pyplot.grid()\n",
+ "#m is constant, b is fixed distance. (x,y) vary for different points on the line \n",
+ "\n",
+ "#ex(1)\n",
+ "print\"ex(1) In y=4x-7, gradient is 4.Intercept on y-axis is -7\"\n",
+ "#ex(2)\n",
+ "print\"ex(2) In y=0.05x-11.5, gradient is 0.05 and intercept on y-axis is -11.5\"\n",
+ "pyplot.show()\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 9_5 pgno:114"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[2 3 1 0]\n",
+ "[-3.5 -5. -2.1875 2.5 ]\n",
+ "the solution of the equation is\n",
+ "x=\n",
+ "y= 3 1\n"
+ ]
+ },
+ {
+ "data": {
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+ ],
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0xa7e1f98>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import numpy\n",
+ "import matplotlib\n",
+ "from matplotlib import pyplot\n",
+ "%matplotlib inline\n",
+ "#x is a polynomial function of degree zero x=#poly(0,'x');\n",
+ "#graph of x+2*y=5\n",
+ "x=numpy.array([0, -1, 2, 5]);\n",
+ "y=numpy.array([0, 0, 0, 0]);\n",
+ "i=0;\n",
+ "for i in range (0,3):\n",
+ "\ty[i]=(5-x[i])/2;\n",
+ "\ti=i+1\n",
+ "print y\n",
+ "y=numpy.array([2.5, 3, 1.5, 0])\n",
+ "pyplot.plot(x,y);\n",
+ "#graph of 3*x-2*y=7\n",
+ "x=numpy.array([0, -1, 7./8., 4]);\n",
+ "y=numpy.array([0, 0, 0, 0]);\n",
+ "y=(3*x-7)/2;\n",
+ "\n",
+ "for i in range (0,3):\n",
+ "\ty[i]=(3*x[i]-7)/2;\n",
+ "\ti=i+1\n",
+ "print y\n",
+ "y=numpy.array([-3.5, -5, -2.1875, 2.5 ])\n",
+ "pyplot.plot(x,y)\n",
+ "for x in range(1,100):\n",
+ " if((5-x)/2==(3*x-7)/2):\n",
+ " break\n",
+ "\n",
+ "print\"the solution of the equation is\"\n",
+ "y=(5-x)/2;\n",
+ "print\"x=\\ny= \",x,y\n",
+ "pyplot.plot(x,y)\n",
+ "\n",
+ "\n",
+ "pyplot.plot(x,y)\n",
+ "pyplot.plot(1,3,'x')#when x=0. 1.5 is intercept on y-axis\n",
+ "pyplot.plot(0.5,0,'o')#when y=0. -0.75 is intercept on x-axis\n",
+ "pyplot.title('graph of equation 2y-4x-3')\n",
+ "pyplot.xlabel('x axis')\n",
+ "pyplot.ylabel('y axis')\n",
+ "#pyplot.legend(\"x+2*y=5\",\"3*x-2*y=7\");\n",
+ "\n",
+ "pyplot.grid()\n",
+ "pyplot.show()"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/README.txt b/Algebra_by_P._Abbott_And_M._E._Wardle/README.txt new file mode 100755 index 00000000..f81c84a7 --- /dev/null +++ b/Algebra_by_P._Abbott_And_M._E._Wardle/README.txt @@ -0,0 +1,10 @@ +Contributed By: Konasani Sai Dheeraj +Course: btech +College/Institute/Organization: K L University +Department/Designation: ECE +Book Title: Algebra +Author: P. Abbott And M. E. Wardle +Publisher: Teach Yourself, Britain +Year of publication: 1991 +Isbn: 0-340-54914-9 +Edition: 3
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