N.S.S. COLLEGE, CHERTHALA

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7 Νοε 2013 (πριν από 4 χρόνια και 6 μέρες)

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N.S.S. COLLEGE, CHERTHALA




DEPARTMENT OF MATHEMATICS




MM 1645: COMPUTER PROGRAMMING
-
II

PRACTICAL RECORD


Name of the Candidate

: ____________________________________________

Register Number


: ____________________________________________

Programme



: ____________________________________________

No. of Experiments

: ____________________________________________





Head of the Department





Faculty
-
in
-
Charge


Bona fide certified hereby that


Examiners:

1.







2.


CONTENTS



PART
-
I: LATEX

No.

Title of the Experiment

Page #

Date

1

Typesetting a Simple Document

3

12/12/12

2

Typesetting a Certificate

5

12/12/12

3

Typesetting the Certificate with large headlines

7

17/12/12

4

Typesetting a Simple Paragraph

9

17/12/12

5

Typesetting a Simple
Paragraph

11

17/12/12

6

Typesetting a Simple Paragraph

13

17/12/12

7

Typesetting Table columns without boarder lines

15

03/01/13

8

Typesetting Table columns without boarder lines

17

03/01/13

9

Typesetting a Simple Mathematics equation

20

14/01/13

10

Typesetting a Simple Mathematics Text

22

14/01/13

11

Typesetting a Simple Mathematics Theorem

24

28/01/13

12

Typesetting a Simple Research Paper

29

28/01/13

13

Different available Fonts in Tex

31

06/02/13

14

Different available Line Spacing in Tex

34

13/02/13

15

Typesetting a Sample Math Question Paper

36

20/02/13


Table of Latex commands for Math symbols

40

27/02/13







PART
-
II: PYTHON

No.

Title of the Experiment

Page #

Date

1

Python as a calculator to compute Simple Interest

46

01/03/13

2

Python as a calculator for temperature conversion

47

01/03/13

3

Program to find the GCD of two given numbers

48

04/03/13

4

Program to check whether a given number is even

49

04/03/13

5

Program to

check the primality of a given integer

50

06/03/13

6

Program to

list primes in a given range by SoE

51

06/03/13

7

Program to

generate terms of Fibonacci sequence

52

08/03/13

8

Program to slice/append words by string operations

53

08/03/13

9

Program to reverse the digits of a given number

54

11/03/13

10

Program to

sort a list of numbers or names

55

11/03/13

11

Program to find the norm of partition of an interval

56

12/03/13

12

Program to

find the angle & dot
-
product of vectors

57

12/03/13

13

Program to

solve an equation by Bisection method

58

14/03/13

14

Program to

solve by Regula
-
Falsi method

59

14/03/13

15

Program to

solve by Newton
-
Raphson method

60

25/03/13

16

Program to

evaluate integral by Trapezoidal rule

61

25/03/13

17

Program to

evaluate integral by Simpson’s 1/3 rule

62

26/03/13

18

Program to

evaluate integral by Simpson’s 3/8 rule

63

26/03/13

19

Program to

solve first order ODE by Euler method

64

27/03/13

20

Program to

solve first order ODE by RK method

65

27/03/13















PART
-
I

LATEX PROGRAMMING


























1. Typesetting a simple Document





1document.tex

\
documentclass{article}

\
begin{document}

This is my
\
emph{first}experiment with
\
LaTeX

\
end{document}
































2. Typesetting a Certificate






2certificate.tex

\
documentclass{article}

\
begin{document}

\
begin{center}

The
\
TeX nical Institute
\
\
[10pt]

Certificate

\
end{center}

\
noindent This is to certify that Mr.N.O.Vice has undergone a course at this
institute and is qualified to be a
\
TeX nician.


\
begin{flushleft}

\
today

\
end{flushleft}

\
begin{flushright}

The Director
\
\

The
\
TeX nical Institute

\
end{flushright}

\
end{document}



















3. Typesetting the certificate with large headlines


3certificate.tex

\
documentclass[a4paper,12pt]{article}

\
usepackage[margin=3cm]{geometry}

\
begin{document}

\
begin{center}

\
large

\
textbf{The
\
TeX nical institute}
\
\
[10pt]

\
Large
\
textsc{Certificate}

\
end{center}

\
noindent This is to certify that Mr.N.O.Vice has undergone a course at this
institute and is
qualified to be a
\
TeX nician.

\
begin{flushleft}

\
today

\
end{flushleft}

\
begin{flushright}

The director
\
\

The
\
TeX nical Institute

\
end{flushright}

\
end{document}
















4. Typesetting a simple Paragraph




4paragraph.tex

\
documentclass{article}

\
begin{document}

Digital information technology contributes to the world by making it

easier to copy and modify information. Computers promise to make this easier for
all of us. Not everyone wants it to be easier. The system of copyright gives
software pro
grams "owners", most of whom aim to withhold software's potential
benefit from the rest of the public.

They would like to be the only ones who can copy and modify the software that
we use. The copyright system grew up with printing
---
a technology for mass
production copying. Copyright fit in well with this technology because it restricted
only the mass producers of copies. It did not take freedom away from readers of
books. An ordinary reader, who did not own a printing press, could copy books
only with pe
n and ink, and few readers were sued for that.

\
end{document}























5. Typesetting a simple Paragraph




5paragraph.tex

\
documentclass{article}

\
begin{document}

Digital information technology contributes to


the world by making it

easier to

copy and modify information.
\
\

Computers promise to make this


easier for all of us. Not everyone wants it to be easier. The system


of copyright gives software programs "owners", most of whom aim to withhold
software's potential benefit from the rest of


the public.



They would like to be the only ones who can copy and modify the software that
we use.The copyright system grew up with printing
---
a technology for mass
production copying.Copyright fit in well with

this technology because it restricted only
the mass producers of copies. It did not
take freedom away from readers of books. An ordinary reader, who did not own a
printing press, could copy books

only with pen and ink, and few readers were sued for that.

\
end{document}


















6.
Typesetting a simple Paragraph




6paragraph.tex

\
documentclass[a4paper]{article}

\
begin{document}

\
noindent Digital information technology contributes to


the world by making it

easier to copy and modify information.Computers promise to make this easier f
or
all of us.Not everyone wants it to be easier. The system


of copyright gives software programs "owners", most of whom aim to withhold
software's potential benefit from the rest of


the public.

They would like to be the only ones who can copy and modify
the software that
we use. The copyright system grew up with printing
---
a technology for mass
production copying. Copyright fit in well with this technology because it restricted
only the mass producers of copies. It did not take freedom away from readers
of
books. An ordinary reader, who did not own a printing press, could copy books
only with pen and ink, and few readers were sued for that.


\
end{document}




















7. Typesetting table columns without boarder lines


7table.tex

\
documentclass{article}

\
begin{document}

\
begin{center}

\
begin{tabular}{cr}

Planet & Diameter(km)
\
\
[5pt]

Mercury & 4878
\
\

Venus & 12104
\
\

Earth & 12756
\
\

Mars & 6794
\
\

Jupiter & 142984
\
\

Saturn & 120536
\
\

Uranus & 51118
\
\

Neptune & 49532
\
\

Pluto & 2274
\
\

\
end{tabular}

\
end{center}

\
end{document}



















8. Typesetting table columns without boarder lines


8table.tex

\
documentclass{article}

\
begin{document}

\
begin{center}

\
begin{tabular}{cr}

Planet & Diameter(km)
\
\
[5pt]

Mercury & 4878
\
\




Venus &
12104
\
\

Earth & 12756
\
\




Mars & 6794
\
\

Jupiter & 142984
\
\




Saturn & 120536
\
\

Uranus & 51118
\
\




Neptune & 49532
\
\

Pluto & 2274
\
\



\
end{tabular}

\
end{center}

\
begin{center}

\
begin{tabular}{|l|r|}

\
hline

Planet & Diameter(km)
\
\



\
hline

Mercury &
74878
\
\



Venus & 12104
\
\

Earth & 12756
\
\




Mars & 6794
\
\

Jupiter & 142984
\
\




Saturn & 120536
\
\

Uranus & 51118
\
\




Neptune & 49532
\
\

Pluto & 2274
\
\




\
hline

\
end{tabular}

\
end{center}


\
begin{center}

\
begin{tabular}{|l|r|}

\
hline

Planet & Diameter(k
m)
\
\

\
hline

Mercury & 4878
\
\



\
hline



Venus & 12104
\
\



\
hline

Earth & 12756
\
\



\
hline



Mars & 6794
\
\



\
hline

Jupiter & 142984
\
\



\
hline



Saturn & 120536
\
\



\
hline

Uranus & 51118
\
\



\
hline



Neptune & 49532
\
\


\
hline

Pluto & 2274
\
\



\
hline

\
end{tabular}

\
end{center}

\
end{document}





9. Typesetting a simple Mathematics equation


9matheqn.tex

\
documentclass{article}

\
begin{document}

If $ a $ and $ b $ are real numbers,

then

\
[

(a+b)^2=a^2+2ab+b^2

\
]

\
end{document}





























10. Typesetting a simple Mathematics Text



10mathtext.tex

\
documentclass{article}

\
usepackage{amsmath}

\
newcommand{
\
norm}[1]{
\
ensuremath{
\
left
\
vert,#1,
\
right
\
vert}}

\
begin{document}

Let $X$ and $Y$ be normed linear spaces over $k$

and let $T:X
\
to Y$ be
linear operator.If there exist $c>0$ such that

\
begin{equation}

\
norm{Tx}
\
le c
\
norm{x}
\
quad
\
text{for every}

x
\
text{in}X

\
end{equation}

then we say that $T$ is a
\
emph{bounded

linear operator} from $X$ into $Y$ and we define

\
begin{equation}

\
norm{T}=
\
sup
\
l
eft
\
{
\
frac{
\
norm{Tx}}{
\
norm{x}}

~:x
\
in X,x
\
ne 0
\
right
\
}

\
end{equation}

called the norm of the operator $T$

\
end{document}
















11. Typesetting a simple Mathematics Theorem



11theorem.tex

\
documentclass[12pt,a4paper]{book}

\
usepackage{amsmath,amssymb}

\
usepackage{amsthm}

\
usepackage{mathrsfs}

\
newtheorem{thm}{Theorem}

\
newtheorem{defn}{Definition}

\
newtheorem{rem}{Remark}

\
newtheorem{exa}{Example}

\
newtheorem{corr}{Corollory}

\
newtheorem{res}{Result}

\
pagenumbering{
roman}

\
begin{document}

\
chapter{Connectedness}

\
section{Connected Spaces}

A topological space $X$ is said to be connected if it cannot be represented as the
union of two disjoint nonempty open sets.

Otherwise if $X=A
\
cup B$, where $A$ and $B$ are disjoint, nonempty and open,
then $X$ is said to be disconnected and $A,
\
: B$ is called a `disconnecction' or a
`separation' of $X$.

Connectedness of a space can be characterised as follows

\
begin{thm}

A
space $X$ is connected iff the only subsets of $X$ that are both open and
closed in $X$ are the empty set and $X$ itself.

\
end{thm}

\
begin{proof}

Suppose $A$ is a nonempty open subset of $X$, that is both open and closed in
$X$.

Consider $A$ and $B$
where $B=X
-
A.$ Then $A$ and $B$ are open, nonempty
and disjoint subsets of $X$.

$A $ is open by assumption; $B$ is open, since $A$ is closed. Also since $A$ is a
nonempty open subset of $X$, $X
-
A= B$ is nonempty. Also $X=A
\
cup B $
$
\
Rightarrow X $ is

disconnected.

Conversely, suppose $X$ is disconnected with $A,B$ as a disconnection.

Then $X=A
\
cup B $ where $ A, B $ are open, $A
\
cap B=
\
emptyset$ and

$A
\
neq
\
emptyset , B
\
neq
\
emptyset $.

Now $A=X
-
B
\
Rightarrow A$ is closed.

Thus $A$ is a nonempty

proper subset of $X$, which is both open and closed.

\
end{proof}

\
begin{defn}

\
noindent A connected subspace of $X$ is a subspace $Y$ which is connected as a
topological space in its own right.

\
end{defn}

This is equivalent to the condition that

\
beg
in{thm}

A subspace $Y$ of $X$ is connected if $Y$ is not contained in the union of two
open subsets of $X$, whose intersection with $Y$ are disjoint and nonempty.

\
end{thm}

\
begin{proof}

For if $Y$ is not connected with $A,B$ as a separation, then

$$Y
=A
\
cup B$$

$A,
\
: B$ are nonempty sets with $A
\
cap B=
\
emptyset $.

By the definition of relative topology on $Y$,

$$A=Y
\
cap C
\
quad
\
textrm {and}
\
quad B=Y
\
cap D$$

where $C,D$ are open in $X$. Then

$$Y=(Y
\
cap C)
\
cup (Y
\
cap D)$$

Thus $Y$ is contained in the union of two open subsets of $X$, whose intersection
with $Y$ are disjoint and nonempty.

\
end{proof}

\
end {document}












12. Typesetting a simple Research Paper




12RPaper.tex

\
documentclass{book}

\
title{This is a Res
earch Paper}

\
author{Dr.Janard Sureshkumar
\
\
Dept of Mathematics, N.S.S.College

\
footnote{Mob. 9496590767}}

\
date{
\
today}

\
begin{document}

\
maketitle

\
chapter{
\
TeX}


\
section{Just what is
\
TeX}

\
TeX{} {
\
LARGE$ =
\
tau
\
epsilon
\
chi$ (tau epsilon chi)}, is
a computer
language designed for use in typesetting; in particular, for typesetting math and
other technical (from greek ``techne" = art/craft, the stem of `technology')
material.


In the late 1970s, Donald Knuth was revising the second volume of his
multivolume magnum opus The Art of Computer Programming, got the galleys,

looked at them, and said (approximately) "blecch"! He had just received his first

samples from the new typesetting system of the publisher's, and its quality was so
far below that of

the first edition of Volume 2 that he couldn't stand it. Around the
same time, he saw a new book by Patrick Winston that had been produced
digitally, and ultimately realized that typesetting meant arranging 0's and 1's (ink
and no ink) in the proper patte
rn, and said (approximately), "As a computer
scientist, I really identify with patterns of 0's and 1's; I ought to be able to do
something about this", so he set out to learn what were the traditional rules for
typesetting math, what constituted good typog
raphy, and (because the fonts of
symbols that he needed really didn't exist) as much as he could about type design.
He figured this would take about 6 months. (Ultimately, it took nearly 10 years,
but along the way he had lots of help from some people who

are well known to
many readers here

Hermann Zapf, Chuck Bigelow, Kris Holmes, Matthew
Carter and Richard Southall are acknowledged in the introduction to Volume E,
Computer Modern Typefaces, of the Addison
-
Wesley Computers and Typesetting
book series.)

\
e
nd{document}




13. Different available fonts in Tex





13fonts.tex

\
documentclass[a4paper,12pt]{article}

\
usepackage{multirow, array}

\
newcolumntype{L}{>{
\
large}c<{}}

\
renewcommand{
\
arraystretch}{1.2}

\
begin{document}

\
section{font sizes}


The available
font sizes are
\
texttt{10pt, 11pt, 12pt}

\
section{font sizes}

\
begin{tabular}{|l|l|l|l|}

\
hline

\
tiny India


&
\
verb|
\
tiny India |


&
\
large India

&
\
verb|
\
large India |
\
\

\
scriptsize India

&
\
verb|
\
scriptsize India |


&
\
Large India

&
\
verb|
\
Large I
ndia |
\
\

\
footnotesize India &
\
verb|
\
footnotesize India |


&
\
LARGE India

&
\
verb|
\
LARGE India |
\
\

\
small India


&
\
verb|
\
small India |



&
\
huge India

&
\
verb|
\
huge India |
\
\

\
normalsize India

&
\
verb|
\
normalsize India |


&
\
Huge India

&

\
verb|
\
Huge India |
\
\


\
hline

\
end{tabular}

\
section{Font styles}

\
begin{tabular}{|L|l|l|l|}

\
textbf{India}

&
\
verb|
\
textbf{ India}|


&
\
bfseries India

&
\
verb|
\
bfseries India |
\
\

\
textsc{ India}

&
\
verb|
\
textsc{ India}|


&
\
scshape India

&
\
verb|
\
s
cshape India |
\
\

\
textit{ India }

&
\
verb|
\
textit{ India }|


&
\
itshape India

&
\
verb|
\
itshape India |
\
\

\
textsl{ India }

&
\
verb|
\
textsl{ India }|


&
\
slshape India

&
\
verb|
\
slshape India |
\
\

\
textsf{ India }

&
\
verb|
\
textsf{ India }|


&
\
sffamily

India

&
\
verb|
\
sffamily India |
\
\

\
texttt{ India }

&
\
verb|
\
texttt{ India }|


&
\
ttfamily India

&
\
verb|
\
ttfamily India |
\
\

\
end{tabular}

\
end{document}































14. Different available line spacing in Tex



14spaces.tex

\
documentclass {article}

\
begin {document}

\
section{Word Spacing}

MathematicsPhysics
\
\


Mathematics Physics
\
\


Mathematics
\
, Physics
\
\


Mathematics ~ Physics
\
\


Mathematics
\
quad{} Physics
\
\


Mathematics
\
qquad{} Physics
\
\


\
section{Horizontal Spaces}


Mathematics
\
hspace{2cm}Physics
\
\



Mathematics
\
hspace{2mm}Physics
\
\



Mathematics
\
hspace{10pt}Physics
\
\



Mathematics
\
hspace{
-
5cm}Physics
\
\



Mathematics
\
hfill Physics

\
subsection{Vertical}


Mathematics
\
vspace{2c
m}Physics
\
\



Mathematics
\
vspace{2mm}Physics
\
\



Mathematics
\
vspace{10pt}Physics
\
\



Mathematics
\
vspace{
-
5cm}Physics
\
\



Mathematics
\
vfill Physics

\
end{document}












15. Typesetting a sample Mathematical Question Paper

15mathqp.tex

\
documentclass[a4paper,11pt]{article}

\
usepackage{amsmath,amssymb}

\
usepackage[left=2cm,right=2cm,top=1.5cm,bottom=1.5cm]{geometry}

\
addtolength{
\
topmargin}{2.5mm}

\
renewcommand{
\
baselinestretch}{1.1}

\
newcommand{
\
score}[1]{
\
hfill($#1$~marks)}

\
newco
mmand{
\
me}{
\
mathrm e}

\
newcommand{
\
mi}{
\
mathrm i}

\
newcommand{
\
partialder}[2]{
\
frac{
\
partial^#1}{
\
partial #2^#1}}

\
newcommand{
\
partialderz}[2]{
\
frac{
\
partial^#1 z}{
\
partial #2^#1}}

\
pagestyle{empty}

\
renewcommand{
\
baselinestretch}{1.1}

\
begin{documen
t}

\
begin{center}


\
textsc{
\
Large College of Engineering, Perumon}


\
smallskip


\
large First Series Test
-

February~2011


\
smallskip


\
normalsize


CS/IT/EE/EC
-

401
-

\
textbf{Engineering Mathematics
\
,
-
\
,III}

\
end{center}

\
noindent Time~:~
\
textit{2} hours
\
hfill Max. Marks~:~
\
textit{50}

\
noindent
\
rule[10pt]{
\
textwidth}{0.9pt}

\
begin{center}


\
textbf{
\
large Part A}

(
\
itshape Answer all questions. Each question carries 5 marks)

\
end{center}

\
begin{enumerate}


\
item Using Cauchy
-
Riemann equations, show that $f(z)=z^3$ is analytic in the
entire $z$
-
plane and find its derivative.


\
item Prove that


$
\
log(1+r
\
me^{
\
mi
\
theta})=
\
frac{1}{2}
\
log
\
bigl(1+2r
\
cos
\
theta+r^2
\
bigr)+
\
mi
\
tan
^{
-
1}


\
frac{r
\
si
n
\
theta}{1+r
\
cos
\
theta}$


\
item
\
begin{enumerate}


\
item Form the pde by eliminating the arbitrary function $
\
phi$ from the
relation
\
\



$
\
phi(x^2+y^2+z^2,x+y+z)=0$.
\
score{2
\
frac{1}{2}}


\
item Form the pde representing the fa
mily of surfaces
$z=f
\
left(
\
frac{xy}{z}
\
right)$ by eliminating the arbitrary function
$f$.
\
score{2
\
frac{1}{2}}


\
end{enumerate}


\
item
\
begin{enumerate}


\
item Find the general integral of the pde
\
quad $px^2(y^3
-
z^3)+q y^2(z^3
-
x^3)=z^2(x^3
-
y^3)$.
\
score{3}


\
item If $(x
-
a)^2+(y
-
b)^2+z^2=1$ is a complete integral of the pde
$z^2(1+p^2+q^2)=1$, evaluate its singular


integral.
\
score{2}


\
end{enumerate}

\
end{enumerate}

\
begin{center}


\
textbf{
\
large Part B}
\
\



(
\
itshape Each question carries 15 marks)

\
end{center}

\
begin{enumerate}


\
item
\
begin{enumerate}


\
item If $f(z)$ is a regular function of $z$, prove that


$
\
displaystyle


\
left(
\
partialder{2}{x}+
\
partialder{2}{y}
\
right)|f(z)|
^2=4|f'(z)|^2


$
\
score{5}


\
item If $
\
mi^{
\
alpha+
\
mi
\
beta}=
\
alpha+
\
mi
\
beta$, prove that


$
\
alpha^2+
\
beta^2=
\
me^{
-
\
frac{(4n+1)
\
pi}{2}}$
\
score{5}


\
item Considering only the principal value, prove that the real part of
$(1+
\
mi
\
sqrt{3})^{1+
\
mi
\
sqrt{3}}$ is
\
\



$
\
displaystyle2
\
me^{
-
\
frac{
\
pi}{
\
sqrt{3}}}
\
cos
\
left(
\
frac{
\
pi}{3}+
\
sqrt{3}
\
log 2
\
right)$
\
score{5}


\
end{enumera
te}


\
smallskip


\
centerline{
\
bfseries OR}


\
smallskip


\
item
\
begin{enumerate}


\
item If $u
-
v=(x
-
y)(x^2+4xy+y^2)$ and $f(z)=u+
\
mi v$ is an analytic
function of $z=x+
\
mi y$, find $f(z)$ in terms of $z$.
\
score{7}


\
item Disc
uss the mapping defined by $w=
\
me^z$ and find the image of $
-
1<x<1$ under $w=
\
me^z$.
\
score{8}


\
end{enumerate}


\
item
\
begin{enumerate}


\
item Solve $p^2q^2+x^2y^2=x^2q^2(x^2+y^2)$.
\
score{6}


\
item Find a complete integral of $pqz=p+q$.
\
score{5}


\
item Show that $pqz=p^2(xq+p^2)+q^2(yp+q^2)$ is a Clairaut's equation.
Hence find a complete integral of


the equation.
\
score{4}


\
end{enumerate}


\
small
skip


\
centerline{
\
bfseries OR}


\
smallskip




\
item
\
begin{enumerate}


\
item Solve the pde $
\
partialder{3}{x}
-
2
\
frac{
\
partial^3 z}{
\
partial
x^2
\
,
\
partial y}
-
\
frac{
\
partial^3 z}{
\
partial x
\
,
\
partial
y^2}+2
\
partialderz{3}{y}=
\
me^{x+y
}$
\
score{8}


\
item Solve $r
-
s+2q
-
z=x^2y^2$
\
score{7}


\
end{enumerate}

\
end{enumerate}

\
end{document}














PART
-
II

PYTHON PROGRAMMING























1. Use of python as a calculator to compute simple interest


$ python3

>>>
p=50000

>>> r=9

>>> n=5

>>> p

50000

>>> r

9

>>> n

5

>>> si=p*n*r/100

>>> si

22500





















2. Use of python as a calculator for temperature conversion

$ python3

# To convert 12
0
C to equivalent Faranheit scale

>>> c=12

>>> f=(c+9/5)+32

>>> f

53

#

To convert 41
0
Faranheit to equivalent
0
C scale

>>> f=41

>>> c=(f
-
32)*5/9

>>> c

5

# To convert 316K to equivalent
0
C scale

>>> k=316

>>> c=k
-
273

>>> c

43

# To convert 113
0
C to equivalent Kelvin scale

>>> c=113

>>> k=c+273

>>> k

336













3. Program
to compute the GCD of two given numbers

print()

a=int (input(‘Enter the first number a:’))

b=int (input(‘Enter the second number b:’))


while b!=0:


a, b=b, a%b


print(‘GCD of a and b is:’, a)


Output is:

$ python3 gcd.py

Enter the first number a: 21

Enter the second number b: 5

GCD of a and b is: 1


$ python3 gcd.py

Enter the first number a: 14

Enter the second number b: 9

GCD of a and b is: 1


$ python3 gcd.py

Enter the first number a: 26

Enter the second number b: 12

GCD of a and b is: 2












4. Program to check whether a given number is even or odd

print()

a=int (input(‘Enter the first number a:’))

if a%b = = 0:


print(‘given number is even’)

else:


print(‘given number is odd’)




Output is:

$ python3 evench.py

Enter the first number a:

21

given number is odd’


$ python3 evench.py

Enter the first number a: 18

given number is even’


$ python3 evench.py

Enter the first number a: 56

given number is even’













5.
Program to

check the primality of a given integer

print()

n=int
(input(‘Enter the given number, n:’))

for k in range(n):


if n% k= = 0:


print(‘The given integer’, n, ‘is not prime’)


status=’not prime’


break;

if status!=’not prime’:

print(‘The given integer’, n, ‘is prime’)




Output is:

$ py
thon3 primech.py

Enter the given number, n: 21

The given integer 21 is prime


$ python3 primech.py

Enter the given number, n: 56

The given integer 21 is not prime


$ python3 primech.py

Enter the given number, n: 31

The given integer 31 is prime








6.
Program to

list primes in a given range by SoE

print()

n=int (input(‘Enter the upper limit of the given range, n:’))

for a in range(2,n):


for k in range(2,a);


if a% k= = 0:


print(a, ‘is’, k, ‘*’, a/k)


else:


print(a, ‘is prime’)


Output is:

$ python3 primelist.py

Enter the upper limit of the given range, n: 7

2 is 2*1

3 is prime

4 is 2*2

5 is prime

6 is 2*3

7 is prime

$ python3 primelist.py

Enter the upper limit of the given range, n: 9

2 is 2*1

3

is prime

4 is 2*2

5 is prime

6 is 2*3

7 is prime

8 is 2*4

9 is prime


7.
Program to

generate the terms of Fibonacci sequence up to a given integer

print()

n=int(input(‘Enter a given integer, n:’))

a,b = 0,1

while a<n:


print(a)


a,b = b, a+b



Outpu
t is:

$ python3 fib.py

Enter a given integer, n: 50

0

1

1

2

3

5

8

13

21

34


$ python3 fib.py

Enter a given integer, n: 100

0

1

1

2

3

5

8

13

21

34

55

89


8.
Program to slice/append words by string operations

print()

s=’nsscollege’

print(s)


n=len(s)

print(‘The length of the string s is:’,n)


s=s[0:2]+’ ’+s[3:]

print()


s=s+’ ’

s=s+’cherthala’

print()


print(s[:3])


s=’mm’+’’+s[0:]

print(s)



Output is:

$ python3 string.py

nsscollege

The length of the string s is: 10

nss college

nss college cherthala

nss

mm nss college cherthala






9.
Program to reverse the digits of a given number

print()

s='1234567890'

print('The given number is:')

print(s)

n=len(s)

digits=[int(s[k]) for k in range(n)]

print('The digits of the given number are:')

first=digits

print(first)

digits.reverse()

print('reverse order of the digits of the given number is:')

print(digits)

sum=sum(first)

print('The sum of the digits of the number is:', sum)


Output is:

$ python3 reverse.py

The given number is:

12345678
90

The digits of the given number are:

[1, 2, 3, 4, 5, 6, 7, 8, 9, 0]

reverse order of the digits of the given number is:

[0, 9, 8, 7, 6, 5, 4, 3, 2, 1]

The sum of the digits of the number is: 45


10.
Program to

sort a list of numbers or names

print()

print('The list of given numbers is:')

s=[31,27,13,24,15,26,17,18,9,10]

print(s)

s.sort()

print('sorted order of the list is:')

print(s)

print('The list of given names is:')

s=['rsp','vk','tns','tss','npk','rk','js','dv','vv','jj']

print(s)

s.sort()

print('sorted order of the list is:')

print(s)


Output is:

$ python3 sort.py

The list of given number is:

31,27,13,24,15,26,17,18,9,10

sorted order of the list is:

31,27,13,24,15,26,17,18,9,10

The list of given names is:

['rsp', 'vk', 'tns', 'tss', 'npk', 'rk', 'js', 'dv', 'vv', 'jj']

sorted order of the list is:

['dv', 'jj', 'js', 'npk', 'rk', 'rsp', 'tns', 'tss', 'vk', 'vv']

11.
Program to

find the dot
-
product of vectors

print()

a=[1,2,3]

print('The first vector is:',
a)

b=[4,5,6]

print('The second vector is:',b)

d=0

for k in range(3):


d=d+a[k]*b[k]

print('The dot
-
product of a and b is:', d)


Output is:

$ python3 dot.py

The first vector is: [1, 2, 3]

The second vector is: [4, 5, 6]

The dot
-
product of a and b is: 32

















12.
Program to

find the norm of partition of an interval

print()

import math

print('Enter the given partition of the interval as an array:')

p=[0.0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0]

print('The given partition is:')

print(p)

n=len(p)

print('The lengths of various subintervals are:')

s=[(p[k]
-
p[k
-
1]) for k in range(n)]

print(s)

norm=max(s)

print('The norm of the given partition is:')

print(norm)


Output is:

Enter the given partition of the interval as an array:

The give
n partition is:

[0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0]

The lengths of various subintervals are:

[
-
1.0, 0.1, 0.1, 0.09999999999999998, 0.10000000000000003,
0.09999999999999998, 0.09999999999999998, 0.09999999999999998,
0.10000000000000009, 0.09999999999999998, 0.09999999999999998]

The norm of the given partition is:

0.10000000000000009


13.
Program

to

solve an equation by Bisection method


14.
Program to

solve by Regula
-
Falsi method


15.
Program to

solve by Newton
-
Raphson method


16.
Program to

evaluate integral by Trapezoidal rule


17.
Program to

evaluate integral by Simpson’s 1/3 rule


18.
Program

to

evaluate integral by Simpson’s 3/8 rule


19.
Program to

solve first order ODE by Euler method


20.
Program to

solve first order ODE by Runge
-
Kutta method