9 90 0 h hr rs s

clankjewishΗλεκτρονική - Συσκευές

10 Οκτ 2013 (πριν από 3 χρόνια και 6 μήνες)

44 εμφανίσεις

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M
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3
3


o
o
f
f


1
1
0
0




Mathematics: Paper IV(a)

N
N
U
U
M
M
E
E
R
R
I
I
C
C
A
A
L
L


A
A
N
N
A
A
L
L
Y
Y
S
S
I
I
S
S

UNIT
-
I:


(20 hours)

Errors in Numerical Computations:
Numbers and their Accuracy, Errors and their
Computation, Absolute, Relative and percentage errors, A general error formula, Error in
a series approximation.

S
S
o
o
l
l
u
u
t
t
i
i
o
o
n
n


o
o
f
f


A
A
l
l
g
g
e
e
b
b
r
r
a
a
i
i
c
c


a
a
n
n
d
d


T
T
r
r
a
a
n
n
s
s
c
c
e
e
n
n
d
d
e
e
n
n
t
t
a
a
l
l


E
E
q
q
u
u
a
a
t
t
i
i
o
o
n
n
s
s
:
:


T
T
h
h
e
e


b
b
i
i
s
s
e
e
c
c
t
t
i
i
o
o
n
n


m
m
e
e
t
t
h
h
o
o
d
d
,
,


T
T
h
h
e
e


i
i
t
t
e
e
r
r
a
a
t
t
i
i
o
o
n
n


m
m
e
e
t
t
h
h
o
o
d
d
,
,


T
T
h
h
e
e


m
m
e
e
t
t
h
h
o
o
d
d


o
o
f
f


f
f
a
a
l
l
s
s
e
e


p
p
o
o
s
s
i
i
t
t
i
i
o
o
n
n
,
,


N
N
e
e
w
w
t
t
o
o
n
n
-
-
R
R
a
a
p
p
h
h
s
s
o
o
n
n


m
m
e
e
t
t
h
h
o
o
d
d
,
,


G
G
e
e
n
n
e
e
r
r
a
a
l
l
i
i
z
z
e
e
d
d


N
N
e
e
w
w
t
t
o
o
n
n
-
-
R
R
a
a
p
p
h
h
s
s
o
o
n
n


m
m
e
e
t
t
h
h
o
o
d
d
,
,


R
R
a
a
m
m
a
a
n
n
u
u
j
j
a
a
n
n


s
s


m
m
e
e
t
t
h
h
o
o
d
d
,
,


M
M
u
u
l
l
l
l
e
e
r
r


s
s


m
m
e
e
t
t
h
h
o
o
d
d


UNIT
-
II:

(25 hours)

Interpolation :
Errors in polynomial interpolation, Forward dif
ferences, Backward
differences, Central Differences, Symbolic relations, Detection of errors by use of
D.Tables, Differences of a polynomial, Newton’s formulae for interpolation formulae,
Gauss’s central difference formula, Stirling’s central difference f
ormula, Interpolation
with unevenly spaced points, Lagrange’s formula, Error in Lagrange’s formula,
Derivation of governing equations, End conditions, Divided differences and their
properties, Newton’s general interpolation
.

UNIT
-
III:
(20 hours)

Curv
e Fitting: Least
-
Squares curve fitting procedures, fitting a straight line, nonlinear
curve fitting, Curve fitting by a sum of exponentials

N
N
u
u
m
m
e
e
r
r
i
i
c
c
a
a
l
l


D
D
i
i
f
f
f
f
e
e
r
r
e
e
n
n
t
t
i
i
a
a
t
t
i
i
o
o
n
n


a
a
n
n
d
d


N
N
u
u
m
m
e
e
r
r
i
i
c
c
a
a
l
l


I
I
n
n
t
t
e
e
g
g
r
r
a
a
t
t
i
i
o
o
n
n
:
:


N
N
u
u
m
m
e
e
r
r
i
i
c
c
a
a
l
l


d
d
i
i
f
f
f
f
e
e
r
r
e
e
n
n
t
t
i
i
a
a
t
t
i
i
o
o
n
n
,
,


E
E
r
r
r
r
o
o
r
r
s
s


i
i
n
n


n
n
u
u
m
m
e
e
r
r
i
i
c
c
a
a
l
l


d
d
i
i
f
f
f
f
e
e
r
r
e
e
n
n
t
t
i
i
a
a
t
t
i
i
o
o
n
n
,
,


M
M
a
a
x
x
i
i
m
m
u
u
m
m


a
a
n
n
d
d


m
m
i
i
n
n
i
i
m
m
u
u
m
m


v
v
a
a
l
l
u
u
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1
1
0
0






Mathematics: Paper IV(b)


FOURIER SERIES AND INTEGRAL TRANSFORMS


UNIT
-

I: ( 20 hours)

Fourier series :

Fourier series, Theorems, Dirichlet's conditions, Fourier series for eve
n and odd
functions, Half range Fourier series, Other forms of Fourier series

P
P
r
r
e
e
s
s
c
c
r
r
i
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b
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d
d


t
t
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x
x
t
t


B
B
o
o
o
o
k
k
:
:




Scope as in
A course of

Mathematical Analysis

by Shanthi
Narayan and P.K Mittal, Published by S. Chand & Company, Chapter 10.



UNIT
-

II:
(25 hours
)


L
aplace transforms:

Definition of Laplace transform, linearity property
-

Piecewise continuous
function.

Existence of Laplace transform, Functions of exponential order and of class A.
First and second shifting theorems of Laplace transform, Change of scale
p
roperty
-

Laplace transform of derivatives, Initial value problems, Laplace
transform of integrals, Multiplication by
t
, Division by
t
, Laplace transform of
periodic functions and error function, Beta function and Gamma functions.
Definition of Inverse Lapl
ace transform, Linearity property, First and second
shifting theorems of inverse Laplace transform, Change of scale property, Division
by p, Convolution theorem, Heaviside’s expansion formula (with proofs and
applications).


UNIT
-

III
: (25 hours)


Four
ier transforms :

Dirichlet's conditions, Fourier integral formula (without
proof), Fourier transform, Inverse Theorem for Fourier transform, Fourier sine and
cosine transforms and their inversion formulae. Linearity property of Fourier
transforms, Change o
f scale property, Shifting theorem, Modulation theorem,
Convolution theorem of Fourier transforms, Parseval's identity, Finite Fourier sine
transform, Inversion formula for sine transform, Finite Fourier cosine Transform,
Inversion formula for cosine trans
form.


UNIT
-

IV:
(20hours)


Applications of Laplace and Fourier transforms :

Applications of Laplace transforms

to the solution of ordinary differential
equations with constant coefficients and variable coefficients, Simultaneous
9
9
0
0


h
h
r
r
s
s


(
(
3
3


h
h
r
r
s
s
/
/


w
w
e
e
e
e
k
k
)
)


M
M
a
a
t
t
h
h
e
e
m
m
a
a
t
t
i
i
c
c
s
s


6
6


o
o
f
f


1
1
0
0




ordinary differential e
quations, Partial differential equations. Applications of
Fourier transforms to initial and boundary value problems.



P
P
r
r
e
e
s
s
c
c
r
r
i
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d
d


t
t
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x
x
t
t


B
B
o
o
o
o
k
k
:
:




Scope as in
Integral transforms
by

A.R. Vasist
h
a & Dr.
R.K. Gupta Published by Krishna Prakashan Media Pvt. Ltd. Me
erut.

Chapter I, Chapter II: all sections except 2.3 and 2.18; Chapter III: sections 3.1,
3.2, 3.3, 3.4; Chapter VI: Sections 6.1 to 6.20 except 6.16; Chapter VII: Sections
7.1 to 7.4; Chapter VIII: Section 8.2.)

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k
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:
:




O
O
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b
b
y
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R
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.
.
V
V
.
.
C
C
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,


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M
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C
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y








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m
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7
7


o
o
f
f


1
1
0
0




M
M
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:
:






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Unit
-
IV:

(20 hours)

Projectiles, Range on an inclined plane, Collision of

elastic bodies, Newton’s
experimental law, Impact of sphere on a plane, Direct and oblique impact of two spheres,
Loss of kinetic energy by impact, Simple harmonic motion, Examples of simple
harmonic motion, Simple pendulum, Simple equivalent pendulum.

Pr
escribed text books:

1
. The elements of Statics and Dynamics, Part
-
I


Statics by

S.L. Loney, Book


palace, New Delhi.

2
. The elements of Statics and Dynamics, Part
-
II
-
Dynamics by S.L.Loney, AITBS

9
9
0
0


h
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1
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Publications and distributions (Reg
d), Delhi

Reference Book:

Mechanics by P. Durai Pandian, Laxmi Durai Pandian, Muthamizh Jaya Prakasan, S.
Chand and Company


limited.






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M
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h
h
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(
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3


h
h
r
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s
/
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w
w
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)