Scilab Textbook Companion for Linear Control Systems by BS Manke

188 Pages·2017·0.58 MB·English

Scilab Textbook Companion for
Higher Engineering Mathematics
by B. S. Grewal1

Created by
Karan Arora and Kush Garg
B.Tech. (pursuing)
Civil Engineering
Indian Institute of Technology Roorkee
College Teacher
Self
Cross-Checked by
Santosh Kumar, IIT Bombay

July 31, 2019

1Funded by a grant from the National Mission on Education through ICT,
http://spoken-tutorial.org/NMEICT-Intro. This Textbook Companion and Scilab
codes written in it can be downloaded from the ”Textbook Companion Project”
section at the website http://scilab.in

Book Description

Title: Higher Engineering Mathematics

Author: B. S. Grewal

Publisher: Khanna Publishers, New Delhi

Edition: 40

Year: 2007

ISBN: 8174091955

1

Scilab numbering policy used in this document and the relation to the
above book.

Exa Example (Solved example)

Eqn Equation (Particular equation of the above book)

AP Appendix to Example(Scilab Code that is an Appednix to a particular
Example of the above book)

For example, Exa 3.51 means solved example 3.51 of this book. Sec 2.3 means
a scilab code whose theory is explained in Section 2.3 of the book.

2

Contents

3

List of Scilab Codes

4

List of Figures

5

Chapter 1

Solution of equation and curve
fitting

Scilab code Exa 1.1 finding the roots of quadratic equations

1
clear

2
clc

3
x=poly ([0], ’ x ’ );
4
p=2*(x^3)+x^2 -13*x+6
5
disp(” the
r o o t s
of
above
equation
are
”)
6
roots(p)

Scilab code Exa 1.2 finding the roots of equation containing one variable

1
clear

2
clc

3
x=poly ([0], ’ x ’ );
4
p=3*(x^3) -4*(x^2)+x+88
5
disp(” the
r o o t s
of
above
equation
are
”)
6
roots(p)

6

Scilab code Exa 1.3 finding the roots of equation containing one variable

1
clear

2
clc

3
x=poly ([0], ’ x ’ );
4
p=x^3 -7*(x^2) +36
5
disp(” the
r o o t s
of
above
equation
are
”)
6
roots(p)

Scilab code Exa 1.6 finding the roots of equation containing one variable

1
clear

2
clc

3
x=poly ([0], ’ x ’ );
4
p=x^4 -2*(x^3) -21*(x^2) +22*x+40
5
disp(” the
r o o t s
of
above
equation
are
”)
6
roots(p)

Scilab code Exa 1.7 finding the roots of equation containing one variable

1
clear

2
clc

3
x=poly ([0], ’ x ’ );
4
p=2*(x^4) -15*(x^3) +35*(x^2) -30*x+8
5
disp(” the
r o o t s
of
above
equation
are
”)
6
roots(p)

7

Scilab code Exa 1.11 forming an equation with known roots

1
clear

2
clc

3
x=poly ([0], ’ x ’ );
4
x1=poly ([0], ’ x1 ’ );
5
x2=poly ([0], ’ x2 ’ );
6
x3=poly ([0], ’ x3 ’ );
7
p=x^3 -3*(x^2)+1
8
disp(” the
r o o t s
of
above
equation
are
”)
9
roots(p)
10
disp(” l e t
”)
11
x1 =0.6527036
12
x2 = -0.5320889
13
x3 =2.8793852
14
disp(” so
the
equation
whose
r o o t s
are
cube
of
the
r o o t s
of
above
equation
i s
( x−x1 ˆ3) ∗( x−x2 ˆ3) ∗( x−
x3 ˆ3)=0 => ”)
15
p1=(x-x1^3)*(x-x2^3)*(x-x3^3)

Scilab code Exa 1.12 forming an equation under restricted conditions

1
clear

2
clc

3
x=poly ([0], ’ x ’ );
4
x1=poly ([0], ’ x1 ’ );
5
x2=poly ([0], ’ x2 ’ );
6
x3=poly ([0], ’ x3 ’ );
7
x4=poly ([0], ’ x4 ’ );
8
x5=poly ([0], ’ x5 ’ );
9
x6=poly ([0], ’ x6 ’ );
10
p=x^3 -6*(x^2) +5*x+8
11
disp(” the
r o o t s
of
above
equation
are
”)
12
roots(p)
13
disp(” l e t
”)

8

14
x1 = -0.7784571
15
x2 =2.2891685
16
x3 =4.4892886
17
disp(” now ,
s i n c e
we want
equation
whose sum of
r o o t s
i s
0 . sum of
r o o t s
of
above
equation
i s
6 , so
we
w i l l
d e c r e a s e ”)
18
disp(” value
of
each
root
by 2
i . e .
x4=x1−2 ”)
19
x4=x1 -2
20
disp(”x5=x2−2”)
21
x5=x2 -2
22
disp(”x6=x3−2”)
23
x6=x3 -2
24
disp(” hence , the
r e q u i r e d
equation
i s
( x−x4 ) ∗( x−x5 ) ∗(
x−x6 )=0 −−>”)
25
p1=(x-x4)*(x-x5)*(x-x6)

Scilab code Exa 1.13 finding the roots of equation containing one variable

1
clear

2
clc

3
x=poly ([0], ’ x ’ );
4
p=6*(x^5) -41*(x^4) +97*(x^3) -97*(x^2) +41*x-6
5
disp(” the
r o o t s
of
above
equation
are
”)
6
roots(p)

Scilab code Exa 1.14 finding the roots of equation containing one variable

1
clear

2
clc

3
x=poly ([0], ’ x ’ );
4
p=6*(x^6) -25*(x^5) +31*(x^4) -31*(x^2) +25*x-6
5
disp(” the
r o o t s
of
above
equation
are
”)
6
roots(p)

9

Scilab code Exa 1.15 finding the roots of equation containing one variable

1
clear

2
clc

3
x=poly ([0], ’ x ’ );
4
p=x^3 -3*(x^2) +12*x+16
5
disp(” the
r o o t s
of
above
equation
are
”)
6
roots(p)

Scilab code Exa 1.16 finding the roots of equation containing one variable

1
clear

2
clc

3
x=poly ([0], ’ x ’ );
4
p=28*(x^3) -9*(x^2)+1
5
disp(” the
r o o t s
of
above
equation
are
”)
6
roots(p)

Scilab code Exa 1.17 finding the roots of equation containing one variable

1
clear

2
clc

3
x=poly ([0], ’ x ’ );
4
p=x^3+x^2 -16*x+20
5
disp(” the
r o o t s
of
above
equation
are
”)
6
roots(p)

10

Scilab code Exa 1.18 Finding the roots of equation containing one variable

1
clear

2
clc

3
x=poly ([0], ’ x ’ );
4
p=x^3 -3*(x^2)+3
5
disp(” the
r o o t s
of
above
equation
are
”)
6
roots(p)

Scilab code Exa 1.19 Finding the roots of equation containing one variable

1
clear

2
clc

3
x=poly ([0], ’ x ’ );
4
p=x^4 -12*(x^3) +41*(x^2) -18*x-72
5
disp(” the
r o o t s
of
above
equation
are
”)
6
roots(p)

Scilab code Exa 1.20 Finding the roots of equation containing one variable

1
clear

2
clc

3
x=poly ([0], ’ x ’ );
4
p=x^4 -2*(x^3) -5*(x^2) +10*x-3
5
disp(” the
r o o t s
of
above
equation
are
”)
6
roots(p)

Scilab code Exa 1.21 Finding the roots of equation containing one variable

1
clear

11

2
clc

3
x=poly ([0], ’ x ’ );
4
p=x^4 -8*(x^2) -24*x+7
5
disp(” the
r o o t s
of
above
equation
are
”)
6
roots(p)

Scilab code Exa 1.22 Finding the roots of equation containing one variable

1
clear

2
clc

3
x=poly ([0], ’ x ’ );
4
p=x^4 -6*(x^3) -3*(x^2) +22*x-6
5
disp(” the
r o o t s
of
above
equation
are
”)
6
roots(p)

Scilab code Exa 1.23 Finding the solution of equation by drawing graphs

1
clear

2
clc

3
xset( ’ window ’ ,1)
4
xtitle(”My Graph”,”X a x i s ”,”Y a x i s ”)
5
x=linspace (1 ,3,30)
6
y1=3-x
7
y2=%e^(x-1)
8
plot(x,y1 ,”o−”)
9
plot(x,y2 ,”+−”)
10
legend(”3−x”,”%eˆ( x−1)”)
11
disp(” from
the
graph , i t
i s
c l e a r
that
the
point
of
i n t e r s e c t i o n
i s
n e a r l y
x=1.43 ”)

12

Figure 1.1: Finding the solution of equation by drawing graphs

Scilab code Exa 1.24 Finding the solution of equation by drawing graphs

1
clear

2
clc

3
xset( ’ window ’ ,2)
4
xtitle(”My Graph”,”X a x i s ”,”Y a x i s ”)
5
x=linspace (1 ,3,30)
6
y1=x
7
y2=sin(x)+%pi/2
8
plot(x,y1 ,”o−”)
9
plot(x,y2 ,”+−”)
10
legend(”x”,” s i n ( x )+%pi/2 ”)
11
disp(” from
the
graph , i t
i s
c l e a r
that
the
point
of
i n t e r s e c t i o n
i s
n e a r l y
x=2.3 ”)

Scilab code Exa 1.25 Finding the solution of equation by drawing graphs

13

Figure 1.2: Finding the solution of equation by drawing graphs

1
clear

2
clc

3
xset( ’ window ’ ,3)
4
xtitle(”My Graph”,”X a x i s ”,”Y a x i s ”)
5
x=linspace (0 ,3,30)
6
y1=-sec(x)
7
y2=cosh(x)
8
plot(x,y1 ,”o−”)
9
plot(x,y2 ,”+−”)
10
legend(”−sec ( x ) ”,” cosh ( x ) ”)
11
disp(” from
the
graph , i t
i s
c l e a r
that
the
point
of
i n t e r s e c t i o n
i s
n e a r l y
x=2.3 ”)

14