From 6279fa19ac6e2a4087df2e6fe985430ecc2c2d5d Mon Sep 17 00:00:00 2001 From: kinitrupti Date: Fri, 12 May 2017 18:53:46 +0530 Subject: Removed duplicates --- ...ultiplicaton_of_Algebraical_Expressions_1.ipynb | 224 ++ ...tiplicaton_of_Algerbrraical_Expressions_2.ipynb | 224 ++ .../Chapter_11_Factors_4.ipynb | 676 ++++++ .../Chapter_12_Fractions_4.ipynb | 448 ++++ .../Chapter_13_Graphs_of.ipynb | 2290 ++++++++++++++++++++ ...hapter_13_Graphs_of_Quadratic_Functions_3.ipynb | 2290 ++++++++++++++++++++ .../Chapter_14_Quardartic_Equations_4.ipynb | 505 +++++ .../Chapter_16_Logarithms_4.ipynb | 716 ++++++ .../Chapter_18_Variation_4.ipynb | 461 ++++ .../Chapter_1_The_Meaning_of_Algebra_4.ipynb | 134 ++ ...pter_20_Rational_and_Irrational_Numbers_4.ipynb | 149 ++ .../Chapter_21_Series_4.ipynb | 526 +++++ ...apter_2_Elementry_Operations_in_Algebra_4.ipynb | 477 ++++ ...ter_3_Brackets_and_Operations_with_Them_4.ipynb | 285 +++ ...Chapter_4_Positive_and_Negative_Numbers_4.ipynb | 66 + 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Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8c.png create mode 100755 Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8c_1.png create mode 100755 Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8c_2.png create mode 100755 Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8c_3.png create mode 100755 Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8c_4.png (limited to 'Algebra_by_P._Abbott_And_M._E._Wardle') 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": [ + "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEZCAYAAACQK04eAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", + "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xm4JGV99vHvzTDDDiPgxaLgEQkBjDAoEHnh1UHBICqo\n", + "gcQFdVBMJG/ADRWMCGgEIho3jGYRZhRXEBVcwcggREBZBlmj+DLIMoxElkHZmV/+qKeHnqb7nDqn\n", + "a+2+P9fV13RVV9dz93NOP/OcX1VXKyIwM7PxsUbdAczMrFoe+M3MxowHfjOzMeOB38xszHjgNzMb\n", + "Mx74zczGjAd+m5KkCUkrJTX+90XS5yR9IOe2CyV9eIi2Fki6qGv5fkkTM91fU6Sf9TZ157DyNP6N\n", + 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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": { + "image/png": [ + "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEZCAYAAACXRVJOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", + "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3XnUJFV9//H3ZzYQWWUUmGGZn5woMREHF0KEgUdZghh3\n", + "OUZFHM2JgUQhQY3i8mNwS0xU/LmEoyAM4EKIBpQooMGZQTYVZRgQVFBGWUeEgQCjDjDf3x9VD9PT\n", + "09vTT1dX1a3P65w+09VVXXW/fefp2/d+q24pIjAzM5tRdgHMzKwa3CCYmRngBsHMzHJuEMzMDHCD\n", + "YGZmOTcIZmYGuEGwAki6QdKBZZdjkqRXSLpN0oOSnjXA9hOSbhvh8T8k6R5Jd45qn6mTtETSOWWX\n", + "o2ncICRC0mpJ6/IvvcnHp8Zw3KWSPtj6WkT8aURcVvSxp+BjwN9FxDYRcV37SkkbJD21iANL2h04\n", + 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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": { + "image/png": [ + "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEZCAYAAABsPmXUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", + "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3XuYJHV1xvHvyy7XBQElCiqwKBKjiwIKwQiyokRAFDUB\n", + "xKBcvERAEQUiN2XBBMErJgoSueyCgpFVvIsiAguIXJRFYEXRyCUgKAIrV0X25I+q2eltenZ6Zqr6\n", + "V/Xr9/M889jVXV11Dr2eqTlVfUoRgZmZ5WWF1AGYmVn1XNzNzDLk4m5mliEXdzOzDLm4m5llyMXd\n", + "zCxDLu6WHUmzJd0xyffuI+myqmMyGzQXdxsYSbdKekTSg5LulnSmpBmp4zLLkYu7DVIAu0TEGsAW\n", + "wEuBoyeyAZXqCK4pJE1LHYO1n4u7JRERdwEXALMkrSXp25J+L+k+Sd+S9KyRdSVdIunfJV0BPAw8\n", + "R9K+khZJ+pOk30h6V/c+JB0h6Q+SfivpLR3PrynprHJ/t0o6aqxfGJI+I+l2SYslXStpm7FykrSq\n", + 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+ "## 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": { + "image/png": [ + "iVBORw0KGgoAAAANSUhEUgAAAX8AAAEZCAYAAAB/6SUgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", + "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xm4JHV1//H3h10YtqBmDAyMRAQNsqggiMAoYDAY0SjE\n", + "jc2fRgYDiCggewQBFxBjEBeYgGzjDgyLZiCOiGGHAcIiQ5JBUMAFR0BBkDm/P6ouc+dO33v79q3q\n", + "b9W3P6/n6Ydbt6u7zqHh3OpTVacUEZiZ2WBZLnUAZmbWfy7+ZmYDyMXfzGwAufibmQ0gF38zswHk\n", + "4m9mNoBc/M0mQNI7JD0o6QlJm6eOx6xXLv5mE/N54ICIWD0ibk8dzHCS/kXSYkmndXhuN0nXSvqd\n", + "pIclfV3SlBRxWjO4+FurqdSvbQHrA3f3Y3sTIekAYB/gjcBukg4fscoawKeAlwCvANYFPtfXIK1R\n", + "XPwtGUnTJH1P0q8k/UbSl8rfHy/pvGHrTS/3aJcrl+dJOlHST4E/AJ+QdNOI9z5E0iXlzytL+ryk\n", + "ByQ9IulMSauMEpMkHS1poaRHJZ0raQ1JKwNPAMsDt0ta0OG1Z0j6/IjfXSrpo5P893T58PeVNFvS\n", + 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"%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": { + "image/png": [ + "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEZCAYAAABsPmXUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", + "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3X28ZnO9//HXe2YIQ+rklG4wCqcyFYozHWQopyGiTkip\n", + "UP1+bgonlLsyKI1unQrduNlD0ak5R/cpCRM5pGaEoehkiIgwESI+54+1Lvua7Zq91957reu71rre\n", + "z8djP7rWdbPW59M1Pnvtz1rrsxQRmJlZu0xJHYCZmZXPxd3MrIVc3M3MWsjF3cyshVzczcxayMXd\n", + 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"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": { + "image/png": [ + 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"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": { + "image/png": [ + "iVBORw0KGgoAAAANSUhEUgAAAX8AAAEZCAYAAAB/6SUgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", + "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3XncbXPd//HXO3McU343hZw7RZEpJRSOMTeiGRk6uCMS\n", + "lSQdRclYMlUq00HGO0PKLGOmqHPMou77ZKiIHFOZ8v79sb6Xs12uYe9rD9/1vfbn+Xhcj66199pr\n", + "va/d8dlrf9Z3fZdsE0IIob+8IXeAEEIIvRfFP4QQ+lAU/xBC6ENR/EMIoQ9F8Q8hhD4UxT+EEPpQ\n", + "FP9QDEkHSDqtQ9taVNJ1kp6W9N1ObHOY/Swn6dYubfvnkjbuxrbD+BfFP4yZpK0k3SLpWUmPSrpZ\n", + "0q5d3GUnL0rZGXjM9vy29+7gdgc7EBjTh4ukxSRdKOkRSa9IeuugVQ4DvjPMazeS9KKkGyTNPei5\n", + "ZST9QtJjkp6QdKmkZZrMtH3KstNY/qZQH1H8w5hI2gs4iqoALWp7UeBzwAckzTnMa9r996Y2X99o\n", + 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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": { + "image/png": [ + "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEZCAYAAACQK04eAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", + "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xm4JGV99vHvzTDDDiPgxaLgEQkBjDAoEHnh1UHBICqo\n", + "gcQFdVBMJG/ADRWMCGgEIho3jGYRZhRXEBVcwcggREBZBlmj+DLIMoxElkHZmV/+qKeHnqb7nDqn\n", + "a+2+P9fV13RVV9dz93NOP/OcX1VXKyIwM7PxsUbdAczMrFoe+M3MxowHfjOzMeOB38xszHjgNzMb\n", + 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+ } + ], + "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": { + "image/png": [ + "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEZCAYAAACXRVJOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", + "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3XnUJFV9//H3ZzYQWWUUmGGZn5woMREHF0KEgUdZghh3\n", + "OUZFHM2JgUQhQY3i8mNwS0xU/LmEoyAM4EKIBpQooMGZQTYVZRgQVFBGWUeEgQCjDjDf3x9VD9PT\n", + "09vTT1dX1a3P65w+09VVXXW/fefp2/d+q24pIjAzM5tRdgHMzKwa3CCYmRngBsHMzHJuEMzMDHCD\n", + "YGZmOTcIZmYGuEGwAki6QdKBZZdjkqRXSLpN0oOSnjXA9hOSbhvh8T8k6R5Jd45qn6mTtETSOWWX\n", + 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"#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": { + "image/png": [ + "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEZCAYAAABsPmXUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", + "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3XuYJHV1xvHvyy7XBQElCiqwKBKjiwIKwQiyokRAFDUB\n", + "xKBcvERAEQUiN2XBBMErJgoSueyCgpFVvIsiAguIXJRFYEXRyCUgKAIrV0X25I+q2eltenZ6Zqr6\n", + "V/Xr9/M889jVXV11Dr2eqTlVfUoRgZmZ5WWF1AGYmVn1XNzNzDLk4m5mliEXdzOzDLm4m5llyMXd\n", + "zCxDLu6WHUmzJd0xyffuI+myqmMyGzQXdxsYSbdKekTSg5LulnSmpBmp4zLLkYu7DVIAu0TEGsAW\n", + "wEuBoyeyAZXqCK4pJE1LHYO1n4u7JRERdwEXALMkrSXp25J+L+k+Sd+S9KyRdSVdIunfJV0BPAw8\n", + "R9K+khZJ+pOk30h6V/c+JB0h6Q+SfivpLR3PrynprHJ/t0o6aqxfGJI+I+l2SYslXStpm7FykrSq\n", + 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+ "## 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": { + "image/png": [ + "iVBORw0KGgoAAAANSUhEUgAAAX8AAAEZCAYAAAB/6SUgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", + "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xm4JHV1//H3h10YtqBmDAyMRAQNsqggiMAoYDAY0SjE\n", + "jc2fRgYDiCggewQBFxBjEBeYgGzjDgyLZiCOiGGHAcIiQ5JBUMAFR0BBkDm/P6ouc+dO33v79q3q\n", + "b9W3P6/n6Ydbt6u7zqHh3OpTVacUEZiZ2WBZLnUAZmbWfy7+ZmYDyMXfzGwAufibmQ0gF38zswHk\n", + "4m9mNoBc/M0mQNI7JD0o6QlJm6eOx6xXLv5mE/N54ICIWD0ibk8dzHCS/kXSYkmndXhuN0nXSvqd\n", + "pIclfV3SlBRxWjO4+FurqdSvbQHrA3f3Y3sTIekAYB/gjcBukg4fscoawKeAlwCvANYFPtfXIK1R\n", + "XPwtGUnTJH1P0q8k/UbSl8rfHy/pvGHrTS/3aJcrl+dJOlHST4E/AJ+QdNOI9z5E0iXlzytL+ryk\n", + "ByQ9IulMSauMEpMkHS1poaRHJZ0raQ1JKwNPAMsDt0ta0OG1Z0j6/IjfXSrpo5P893T58PeVNFvS\n", + 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"code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": [ + "iVBORw0KGgoAAAANSUhEUgAAAX0AAAEZCAYAAAB7HPUdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", + "AAALEgAACxIB0t1+/AAAIABJREFUeJztnXecXFX5/9+fJJAAoQRQOgQUEDEiKE3EBAQEVOrPAipV\n", + "BEGadBB2V6UXFRCkhyJgBQWRbuhdIkj50oRQQ0mQDoE8vz/O3WR2Mpu9M3vvnHvvPO/Xa17ZO7ec\n", + "59nZPPfM55z7OTIzHMdxnM5gSOwAHMdxnPbhRd9xHKeD8KLvOI7TQXjRdxzH6SC86DuO43QQXvQd\n", + "x3E6CC/6jtMPkraU9KykNyWtEjsex8kCL/qO0z8nALub2bxm9u/YwTRC0nlp3pe0vaR7Jf0vuZEd\n", + "K2loe6J0ioQXfac0KKFdbQFLAw+3o71mkXS6pKWTnxeSdIakuST9VtKCyftLSzo9OWUuYG9gIWBN\n", + "4CvA/jFid+LiRd9pC5KWkvQXSS9LelXSKcn73ZIurDlutKTpkoYk2xMk/ULSbcDbwAGS7qm79r6S\n", + "/pr8PFzSCZKekfRSUhxH9BOTJP1U0tOSJks6X9J8koYDbwJDgX9LerzBub+RdELde3+TtE+Tv5eD\n", + "JT0h6Q1JD0naombf6ZL+VLN9rKTrk82jgZ8B6wK/AX5tZu8CpwCnJ+/3AEcBmNlvzew2M/vQzF4A\n", + "fges00ysTjXwou/kTiIjXAn8F1gGWAK4JNmdxgfke8APgJHAb4EVJX2yZv+2hCIGcAzwSWCV5N8l\n", + 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"%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": { + "image/png": [ + "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEZCAYAAABsPmXUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", + "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3X28ZnO9//HXe2YIQ+rklG4wCqcyFYozHWQopyGiTkip\n", + "UP1+bgonlLsyKI1unQrduNlD0ak5R/cpCRM5pGaEoehkiIgwESI+54+1Lvua7Zq91957reu71rre\n", + "z8djP7rWdbPW59M1Pnvtz1rrsxQRmJlZu0xJHYCZmZXPxd3MrIVc3M3MWsjF3cyshVzczcxayMXd\n", + 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"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": { + "image/png": [ + 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"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": { + "image/png": [ + "iVBORw0KGgoAAAANSUhEUgAAAX8AAAEZCAYAAAB/6SUgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", + "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3XncbXPd//HXO3McU343hZw7RZEpJRSOMTeiGRk6uCMS\n", + "lSQdRclYMlUq00HGO0PKLGOmqHPMou77ZKiIHFOZ8v79sb6Xs12uYe9rD9/1vfbn+Xhcj66199pr\n", + "va/d8dlrf9Z3fZdsE0IIob+8IXeAEEIIvRfFP4QQ+lAU/xBC6ENR/EMIoQ9F8Q8hhD4UxT+EEPpQ\n", + "FP9QDEkHSDqtQ9taVNJ1kp6W9N1ObHOY/Swn6dYubfvnkjbuxrbD+BfFP4yZpK0k3SLpWUmPSrpZ\n", + "0q5d3GUnL0rZGXjM9vy29+7gdgc7EBjTh4ukxSRdKOkRSa9IeuugVQ4DvjPMazeS9KKkGyTNPei5\n", + "ZST9QtJjkp6QdKmkZZrMtH3KstNY/qZQH1H8w5hI2gs4iqoALWp7UeBzwAckzTnMa9r996Y2X99o\n", + 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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", + "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xe8HVW5//HPNyH0DleRGoyUiwQCXmJQIgnNgBK8qFyU\n", + "FooFuRRRQIqCPzWCDcSCSEsuiCggTeliAJEiQiABQVBCVXpvBvL8/pg5zM7h5Jzd1+y9v+/X67yy\n", + "Z8/sPc95ss88e9aaWUsRgZmZ9a5hqQMwM7O0XAjMzHqcC4GZWY9zITAz63EuBGZmPc6FwMysx7kQ\n", + "WFeSNEHSw018vzMkPSPppma9p1lZuBCYDUHSeGArYOWIGNeifYyQdJ6kByTNk7T5ANscJ+mp/OfY\n", + "AdYfLWmNAZ4/oxUxW/dwIbBSkjQ8dQwV1gDmRMRrLd7PdcCuwL+A+e70lPQ5YAdgg/xn+/w5JB0u\n", 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+ "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", + 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+ { + "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": { + "image/png": [ + "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEZCAYAAAB4hzlwAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", + "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3XmYXGWZ9/HvLyEJewB5JexR2UQxgAMDAkNEliCDoMii\n", + "IPvoiBpF4JWACg6oLOK4va4sAZRNFIRhDUsGRGQZCCCLgBoRlCCSMOwk5H7/OKc7RVPdXemu6uec\n", + "p36f66qLOnVO1bnvtNZd51nOo4jAzMwMYFTqAMzMrDpcFMzMrJeLgpmZ9XJRMDOzXi4KZmbWy0XB\n", + "zMx6uSiYlSRNlvSXIb73QEk3tzsms5HmomCVJ2m2pBclPSfpSUlnSVomdVxmOXJRsDoI4F8jYjlg\n", + "U+CfgC8uzgeo1IngqkLS6NQxWP25KFitRMRfgauBd0paQdJ/SXpK0jOSLpe0es+xkmZKOlHSLcAL\n", + 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], + "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": { + "image/png": [ + "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEZCAYAAAB4hzlwAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", + 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"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": { + "image/png": [ + "iVBORw0KGgoAAAANSUhEUgAAAYgAAAEaCAYAAAAL7cBuAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", + "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xm4HGWZ/vHvHZZhC4uIkSUYlAFFxAAKKDoEGVmiojMC\n", + "MqOjAXXiwqKAsoyM4PhzQwfBQY0bQVwYFURkUBYlQRFRIYEAoiwJmwhiWAJBBPL8/qi3TaXT3ady\n", + "uqq76pz7c13nOl1LV91d53S//b5PV5ciAjMzs3YThh3AzMzqyQ2EmZl15AbCzMw6cgNhZmYduYEw\n", + "M7OO3ECYmVlHbiBqRtIcSW8f5X23lLREkirItUzSc8ve7lgm6QuSPjTsHHUm6SRJZw87Ry9NyFgV\n", + "NxAVkLRI0tL0Yv1HSWdLWr/g3SP9FN3Pq/52x4g7I2Ji1Ozklro3LpKmpIxL0s8iSSf2u92IeHdE\n", + 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"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" + ] + }, + { + "data": { + "image/png": [ + "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEZCAYAAACQK04eAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", + "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xu0JFV59/HvjxFE7jfDTYYRfEGNoMQIGjSOoAjKLYoo\n", + "wcggUZfRRRR0CSQxg0YFTSJe3hVv4AAxOohyD8owMIKoGHCGiyAXw7yIMgMIA8iIAvO8f9TuqTpN\n", + 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+ "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": { + "image/png": [ + "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEZCAYAAACQK04eAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", + "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xm4ZFV97vHvy9DIJMjwiCikxVwCGKFR4MqFq42KwRE1\n", + "eK8DKipJ5N44o4IRaTQCcYjGYDTJFRrFGVFBYwQjjRABBWlkjMOlEaRpiYwKKtC//LHXgeqi6px9\n", + "Tq1de6+q9/M89VC7atde71l9arHOb+9apYjAzMymx3ptBzAzs/HywG9mNmU88JuZTRkP/GZmU8YD\n", + "v5nZlPHAb2Y2ZTzw25wkLZa0VlLnf18kfVzSu2ruu1zSe0do6zBJ5/ds3yVp8UKP1xXp33qntnNY\n", + "czr/Rrbxk7RK0tNKbDcijoiIv667e7oNyzOvATAiNo+IVXX3N2uLB34bJAB1rV1JG4wxywPNttDm\n", + "grXUR1YYD/y2DkmfBnYEzkqliyN7nj5U0vWSbpH0zp7XSNJRkn4q6T8lfUHSI4YcfxtJX5d0m6Rf\n", + "Sfpuev1D2u0pMb1G0vXAt9MxviRptaTbJZ0nabee469TvpH0dkk3SbpR0uEDZvFbpTx3Srpo5jlJ\n", + 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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": { + "image/png": [ + "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEZCAYAAACXRVJOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", + 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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": { + "image/png": [ + 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"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": { + "image/png": [ + "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEZCAYAAACXRVJOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", + "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xu4HGWV7/HvLyQEuSNRIAHMkWeUcRSDCjJCQpTLRFBQ\n", + "wccREYOeUZjjoINXRA/B2+gcFW9nOApCAEWG0QFFBXQQCKCoKCEgqIBEuRkQAhOIGiDr/FG1Saez\n", + "e+++VVfVW7/P8+wnu7qru961K7vWfteqqlZEYGZmNqXsAZiZWTU4IZiZGeCEYGZmOScEMzMDnBDM\n", + "zCznhGBmZoATghVA0k2S5pU9jjGSXi3pTkmrJD2/i/XnS7pziNv/qKT7Jd0zrPdMnaRFks4pexxN\n", + "44SQCEnLJa3OD3pjX58fwXYXS/pI62MR8dyIWFL0tnvwKeAfI2KLiLih/UlJayU9s4gNS9oZOB7Y\n", + "NSJmFrGNRPkCqRJMLXsANjQBvCIiflj2QKpEkoCdgZsnW7WgIewMPBARD/T6QklTI+LxAsZUCZJm\n", + "A5dHxP8Y7+nRjsbAM4RGkDRF0qfyssXtkv5X/lfxlPz55ZL2a1l/vem6pP+QdK+khyRdKek5+eNv\n", + "BY4A3pvPSL7V/n6Spkv6rKS7869TJG2cPzdf0l2Sjpe0QtI9kha2bPcgSb+U9N/5eu/qEJ8kfTDf\n", + 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"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": { + "image/png": [ + "iVBORw0KGgoAAAANSUhEUgAAAX8AAAEZCAYAAAB/6SUgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", + "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xu4JFV97vHv6wAy3EGCw30GRFFUBoxIgsKgEpGjjGIU\n", + "SEAB4zEmAhIwKpycmdGDhKCAlyPeQATxQoyQoAJBYYSAjhdmE5SLwGEQCDBcBsJVkPmdP6o29DS9\n", + 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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 \ No newline at end of file diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8a.png b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8a.png new file mode 100755 index 00000000..b965bd13 Binary files /dev/null and b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8a.png differ diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8a_1.png b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8a_1.png new file mode 100755 index 00000000..b965bd13 Binary files /dev/null and b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8a_1.png differ diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8a_2.png b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8a_2.png new file mode 100755 index 00000000..b965bd13 Binary files /dev/null and b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8a_2.png differ diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8a_3.png b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8a_3.png new file mode 100755 index 00000000..b965bd13 Binary files /dev/null and b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8a_3.png differ diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8a_4.png b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8a_4.png new file mode 100755 index 00000000..b965bd13 Binary files /dev/null and b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8a_4.png differ diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8b.png b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8b.png new file mode 100755 index 00000000..dfa9a8f3 Binary files /dev/null and b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8b.png differ diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8b_1.png b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8b_1.png new file mode 100755 index 00000000..dfa9a8f3 Binary files /dev/null and b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8b_1.png differ diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8b_2.png b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8b_2.png new file mode 100755 index 00000000..dfa9a8f3 Binary files /dev/null and b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8b_2.png differ diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8b_3.png b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8b_3.png new file mode 100755 index 00000000..dfa9a8f3 Binary files /dev/null and b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8b_3.png differ diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8b_4.png b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8b_4.png new file mode 100755 index 00000000..dfa9a8f3 Binary files /dev/null and b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8b_4.png differ diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8c.png b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8c.png new file mode 100755 index 00000000..6ad3b6c4 Binary files /dev/null and b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8c.png differ diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8c_1.png b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8c_1.png new file mode 100755 index 00000000..6ad3b6c4 Binary files /dev/null and b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8c_1.png differ diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8c_2.png b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8c_2.png new file mode 100755 index 00000000..6ad3b6c4 Binary files /dev/null and b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8c_2.png differ diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8c_3.png b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8c_3.png new file mode 100755 index 00000000..6ad3b6c4 Binary files /dev/null and b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8c_3.png differ diff --git a/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8c_4.png b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8c_4.png new file mode 100755 index 00000000..6ad3b6c4 Binary files /dev/null and b/Algebra_by_P._Abbott_And_M._E._Wardle/screenshots/cha8c_4.png differ -- cgit