initial commit / add all books

11 files changed, 201 insertions, 0 deletions

diff --git a/2915/CH6/EX6.10/Ex6_10.sce b/2915/CH6/EX6.10/Ex6_10.sce
new file mode 100755
index 000000000..65e4316b1
--- /dev/null
+++ b/2915/CH6/EX6.10/Ex6_10.sce
@@ -0,0 +1,14 @@
+clc,clear

+//Example 6.10

+//To represent given complex number in trigonometric form

+

+z=-2 + -1*%i ;//given number

+x=real(z) ;//real part 

+y=imag(z) ;//imaginary part

+

+//theta is in third quadrant as x and y are -ve

+theta=180 + atand(y/x);

+r=sqrt(x^2+y^2) ;//modulus of z

+printf('z= %f + i* %f  can be written as: \n',real(z),imag(z))

+printf('z = sqrt(%.0f)*(cos(%.1f)+i*sin(%.1f))',r^2,theta,theta)

+

diff --git a/2915/CH6/EX6.11/Ex6_11.sce b/2915/CH6/EX6.11/Ex6_11.sce
new file mode 100755
index 000000000..146fc00a3
--- /dev/null
+++ b/2915/CH6/EX6.11/Ex6_11.sce
@@ -0,0 +1,22 @@
+clc,clear

+//Example 6.11

+//To determine product and ratio of complex numbers using formula

+

+//given values 

+z1 = 6*(cosd(70)+ %i*sind(70));

+z2 = 2*(cosd(31)+ %i*sind(31));

+

+//arguements of complex numbers

+theta1=phasemag(z1);

+theta2=phasemag(z2);

+//modulus of complex numbers

+r1=abs(z1);

+r2=abs(z2);

+theta_1p2 =theta1 + theta2  ;//theta1 + theta 2

+theta_1m2 =theta1 - theta2  ;//theta1 - theta 2

+//according to the formula used in book

+product = r1*r2*(cosd(theta_1p2)+%i*sind(theta_1p2));

+ratio = (r1/r2)*(cosd(theta_1m2)+%i*sind(theta_1m2));

+

+printf('z1*z2 = %.0f*(cos(%.0f)+i*sin(%.0f))\n',r1*r2,phasemag(product),phasemag(product))

+printf('z1/z2 = %.0f*(cos(%.0f)+i*sin(%.0f))\n',r1/r2,phasemag(ratio),phasemag(ratio))

diff --git a/2915/CH6/EX6.12/Ex6_12.sce b/2915/CH6/EX6.12/Ex6_12.sce
new file mode 100755
index 000000000..876856cfb
--- /dev/null
+++ b/2915/CH6/EX6.12/Ex6_12.sce
@@ -0,0 +1,13 @@
+clc,clear

+//Example 6.12

+//To find higher powers of complex number using demoivre theorem

+

+z= complex(1,1);

+r= abs(z);//modulus of z

+theta=phasemag(z) ;//arguement of z

+power=10;

+//using demoivre formula

+answer= (r^power)*(cosd(theta*power)+%i*sind(theta*power));

+//printf('(1+i)^10 = (%.0f)*(cos(%.0f)+ i*sin(%.0f))',r^power,theta*power,theta*power);

+printf('\n %.0f + %.0f*i',real(answer),imag(answer));

+printf('\n(OR)\n %.0f*i',imag(answer));

diff --git a/2915/CH6/EX6.13/Ex6_13.sce b/2915/CH6/EX6.13/Ex6_13.sce
new file mode 100755
index 000000000..09ab024c2
--- /dev/null
+++ b/2915/CH6/EX6.13/Ex6_13.sce
@@ -0,0 +1,22 @@
+clc,clear

+//Example 6.13

+//To determine the cube roots of i

+

+z=%i //given complex number

+//modulii for cuberoots

+r1=abs(z)^(1/3)

+r2=abs(z)^(1/3)

+r3=abs(z)^(1/3)

+

+//arguements for cuberoots

+theta1= (phasemag(z)+360*0)/3

+theta2= (phasemag(z)+360*1)/3

+theta3= (phasemag(z)+360*2)/3

+

+cube_root_1 = r1 *(cosd(theta1)+ %i*sind(theta1))

+cube_root_2 = r2 *(cosd(theta2)+ %i*sind(theta2))

+cube_root_3 = r3 *(cosd(theta3)+ %i*sind(theta3))

+

+printf('cuberoot 1: %f + %f*i\n',real(cube_root_1),imag(cube_root_1))

+printf('cuberoot 2: %f + %f*i\n',real(cube_root_2),imag(cube_root_2))

+printf('cuberoot 3: %f + %f*i\n',real(cube_root_3),imag(cube_root_3))

diff --git a/2915/CH6/EX6.15/Ex6_15.sce b/2915/CH6/EX6.15/Ex6_15.sce
new file mode 100755
index 000000000..0fe744500
--- /dev/null
+++ b/2915/CH6/EX6.15/Ex6_15.sce
@@ -0,0 +1,24 @@
+clc,clear

+//Example 6.15

+//To convert from polar to cartesian coordinates

+

+//part(a)

+r=2 ;

+theta=30 ;

+x=r*cosd(theta) ;

+y=r*sind(theta) ;

+printf('(a)(x,y)= (%f,%f)\n',x,y) ;

+

+//part(b)

+r=3 ;

+theta=3*%pi/4 ;

+x=r*cos(theta) ;

+y=r*sin(theta) ;

+printf('(b)(x,y)= (%f,%f)\n',x,y) ;

+

+//part(c)

+r=-1 ;

+theta=5*%pi/3 ;

+x=r*cos(theta) ;

+y=r*sin(theta) ;

+printf('(c)(x,y)= (%f,%f)',x,y) ;

diff --git a/2915/CH6/EX6.16/Ex6_16.sce b/2915/CH6/EX6.16/Ex6_16.sce
new file mode 100755
index 000000000..78ab025be
--- /dev/null
+++ b/2915/CH6/EX6.16/Ex6_16.sce
@@ -0,0 +1,32 @@
+clc,clear

+//Example 6.16

+//To convert from cartesian to polar coordinates

+

+//part(a)

+x=3 ;

+y=4 ;

+

+//53.13 is in same quadrant as(3,4)

+r=sqrt(x^2+y^2) ;

+theta=atand(y/x) ;

+printf('PART A\n(r,theta)= %f,%f',r,theta) ;

+printf('\nOR\n') ;

+r=-sqrt(x^2+y^2) ;

+//tan theta is +ve in 3rd quadrant

+//so 180 + 53.33 is also a permissible value 

+theta=180 + atand(y/x) ;

+printf('(r,theta)= %f,%f',r,theta) ;

+

+//part(b)

+x=-5 ;

+y=-5 ;

+

+//225 is in same quadrant as(-5,-5)

+//tan theta is +ve in 3rd quadrant

+r=sqrt(x^2+y^2) ;

+theta=180+ atand(y/x) ;

+printf('\n\nPART B\n(r,theta)= %f,%f',r,theta) ;

+printf('\nOR\n') ;

+r=-sqrt(x^2+y^2) ;

+theta= atand(y/x) ;

+printf('(r,theta)= %f,%f',r,theta) ;

diff --git a/2915/CH6/EX6.17/Ex6_17.sce b/2915/CH6/EX6.17/Ex6_17.sce
new file mode 100755
index 000000000..a6c7aa5f8
--- /dev/null
+++ b/2915/CH6/EX6.17/Ex6_17.sce
@@ -0,0 +1,11 @@
+clc,clear

+//Example 6.17

+//to express an equation in polar coordinates

+

+RHS=9 ;

+//Note that LHS is basically an equation of circle

+//But at any instant , it is numberically same as 9

+LHS_numerically=RHS  ;

+r=sqrt(LHS_numerically) ;

+

+printf('The equation in terms of polar coordinates is : r =%.0f',r)

diff --git a/2915/CH6/EX6.19/Ex6_19.sce b/2915/CH6/EX6.19/Ex6_19.sce
new file mode 100755
index 000000000..32d451137
--- /dev/null
+++ b/2915/CH6/EX6.19/Ex6_19.sce
@@ -0,0 +1,11 @@
+clc,clear

+//Example 6.19

+//to express an equation in polar coordinates

+

+//Given equation is : y=x

+y_by_x =1; //ratio of y and x

+tan_theta = y_by_x;

+theta=atand(tan_theta); //azimuth angle

+

+printf('The given equation in polar coordinates is :  theta = %.0f degree\n',theta)

+printf('\nNote: Polar form is same regardless of value of r ')

diff --git a/2915/CH6/EX6.3/Ex6_3.sce b/2915/CH6/EX6.3/Ex6_3.sce
new file mode 100755
index 000000000..952bb7556
--- /dev/null
+++ b/2915/CH6/EX6.3/Ex6_3.sce
@@ -0,0 +1,9 @@
+clc,clear

+//Example 6.3

+//To solve the given equation

+

+sec_theta = 1/2

+cos_theta = 1 / sec_theta

+printf('cos(theta) = %f as calculated\n',cos_theta)

+printf('But value of cos function can never exceed unity\n')

+printf('Thus, NO SOLUTION exists')

diff --git a/2915/CH6/EX6.4/Ex6_4.sce b/2915/CH6/EX6.4/Ex6_4.sce
new file mode 100755
index 000000000..79b55174d
--- /dev/null
+++ b/2915/CH6/EX6.4/Ex6_4.sce
@@ -0,0 +1,23 @@
+clc,clear

+//Example 6.4

+//To solve the given equation

+

+//Given equation is cos_theta = tan_theta

+//simplyfying given equation, we get

+//(sin_theta)^2 + sin_theta - 1 = 0

+//Solve for sin_theta as follows

+p=[1 1 -1]

+sin_theta= roots(p)

+printf('Values of sin(theta) after simplifying and solving = %f and %f\n',sin_theta(1),sin_theta(2))

+printf('Eliminate %f as sin_theta cant be below -1',sin_theta(1))

+

+//Since sin_theta is +ve, 2 solutions exist. in 1st and 2nd quadrant

+theta_1=asin(sin_theta(2));  //in 1st quadrant

+theta_2=%pi-asin(sin_theta(2));//the reflection in 2nd quadrant

+

+printf('\n\nSOLUTIONS:\n')

+printf('%f radians\n%f radians',theta_1,theta_2)

+

+printf('\n\nGENERAL SOLUTIONS:\n')

+printf('%f + integer multiples of 2pi \n',theta_1)

+printf('%f + integer multiples of 2pi \n',theta_2)

diff --git a/2915/CH6/EX6.9/Ex6_9.sce b/2915/CH6/EX6.9/Ex6_9.sce
new file mode 100755
index 000000000..5e6306d2d
--- /dev/null
+++ b/2915/CH6/EX6.9/Ex6_9.sce
@@ -0,0 +1,20 @@
+clc,clear

+//Example 6.9

+//To find the result of basic operations on 2 given complex numbers

+

+z1 = complex(-2,3)

+z2 = complex(3,4)

+

+summ = z1+z2

+difference = z1-z2

+product = z1*z2

+ratio = z1/z2

+mag_z1= abs(z1) //modulus of z1

+mag_z2= abs(z2)//modulus of z2

+//printf('Note: Please go through complex nos scilab syntaxes to comprehend this example code\n\n')

+printf('z1 + z2 = %.0f + %.0f*i\n',real(summ),imag(summ))

+printf('z1 - z2 = %.0f + %.0f*i\n',real(difference),imag(difference))

+printf('z1 * z2 = %.0f + %.0f*i\n',real(product),imag(product))

+printf('z1 / z2 = %f + %f*i\n',real(ratio),imag(ratio))

+printf('|z1|= sqrt(%.0f)= %f \n',mag_z1^2,mag_z1)

+printf('|z2| = %.0f',mag_z2)