MA101 :
Mathematics

I
(4

0

0)
4 credits
UNITI
1
5
hrs
Differential
Calculus:
Determination of n
th
derivative of standard functions. Leibnitz’s theorem and
Problems.
Polar curves. Pedal equations of polar curves. Radius
of curvature
–
Cartesian, parametric, polar and
pedal forms.
Partial Derivatives, Euler’s Theorem. To
tal differentiation. Differentiation of Composite and implicit
functions. Jacobians and their properties.
Errors and approximations.
UNIT II
1
1
Hrs
Integral Calculus:
Reduction formulae for the integration of sin
n
x, cos
n
x, tan
n
x, cot
n
x, sec
n
x, cosec
n
x
a
nd sin
m
x cos
n
x. Substitutional problems.
Tracing of standard curves in Cartesian, Parametric and Polar forms.
Applicatio
ns to find area and length of given curves.
UNIT
III
10 hrs
Analytical Solid Geometry:
Direction cosines and direction ratio
s. Planes and Straight lines,
shortest distance between two skew lines. Right Circular Cone and Right Circular Cylinder.
UNIT
IV
0
8
hrs
Differential Equations of First order:
Solution for Homogeneous, exact and linear differential
equations.
Differential equations reducible to above types.
Orthogonal
traject
ories of Cartesian and Polar curves.
UNITV
08
hrs
Differential Equations of Second & Higher Order:
Linear differential eq
uations of second and higher
order with constant coefficients. Method of Variation of Parameters. Cauchy’s and Legendre’s linear
differential equations.
Text Book
:
“Higher Engineering Mathematics”, B. S. Grewal,
, Khanna Publications,
40
th
Edition,
2005
(Ch. No’s 2,3 & 4)
Reference Books
:
1. “
Advanced Engineering Mathematics”, K. A. Stroud, 5
th
Edition.
2. “
A
dvanced
Engineering Mathematics”,
Erwin Kreyszig
, 8
th
Edition
1
MA151
:
Mathematics

II
(4

0

0)
4 credits
UNIT I
1
3
hrs
Differential Calculus
:
Rolle’s theorem
–
Geomertical Interpretat
ion
.
Lagrange’s and Cauchy’s mean value theorems. Taylor’s
Theorem for a function of a single variable
and Maclaurin’s series expansions.
Indeterminate Forms

L’Hospital’s rule
.
Taylor’s theorem for functions of two variables,
Maxima and Minima for f
unction
s
of two variables.
Lagrange’s method of undetermined multipliers
for extreme values (with one subsidiary condition).
UNIT II
1
3
hrs
Laplace Transforms
:
Definition

Transforms of elementary functions. Periodic function. Inverse
Laplace Transforms. Convolution theorem. Laplace transforms of derivatives and integrals of function
s
.
Solutions of linear differential equations. Unit
step function and unit impulse function.
Simple examples
on LRC circuits.
UNIT III
08
hrs
Integral Calculus
:
Multiple Inte
grals

Evaluation by change of order of integration
and change of
variables.Applications
t
o area and volume.
UNIT IV
06 hr
s
Special functions
:
Beta and gamma
f
unctions.
Differentiation under
the integral sign
UNIT V
1
2
hrs
Ve
ctor Calculus
:
Introduction to vector calculus. Directional derivatives. Gradient of a scalar field,
Divergence and Curl of a vector field.
Integral Theorems: Green’s, Stoke’s
and Ga
uss’s theorems
with
examples
.
Text Book :
“Higher Engineering Mathe
matics” B. S. Grewal,
Khanna Publication
s,
40
th
Edition,
2005
(Ch. No’s 2, 5 & 7)
Reference Books
:
1. “Advanced Engineering Mathematics” K. A. Stroud, , 5
th
Edition.
2. “A
dvanced
Engineering M
athematics
”
Erwin Kreyszig
, 8
th
Edition.
2
MA
201: LINEAR ALGEBRA
52 Hrs
Unit 1
M
atrices
and Gaussian Elimination
12
Hrs
Introduction
to 3

D geometr
y, geometry of system of linear equations
,
Gaussian Elimination
,
Matrix notation and multiplication, Triangular factorization, Inverses and transposes.
Unit
2
Vector spaces
& Linear Equations
14 Hrs
Vector spaces
, subspaces,
linear independe
nce, b
asis and dimension,
fundamental
subspaces, linear transformations.
Unit
3
Orthogonality
12
Hrs
Orthogonal subspaces
,
inner products, projections and l
east squares approximations.
Gram

Schmidt Orthogonalization.
Unit
4
Eigen Values and Eigen Vectors
06
Hrs
Eigen values and eigen
vectors, Cayley

Hamilton theorem, Power method of finding the
dominant eigenvalue and the corresponding eigen vector, Diagonalization.
Unit 5
Fourier Series
08 Hrs
Periodi
c and orthogonal functions. General orthonormal expansions. Even and odd functions.
Dirichlet’s conditions. Fourier Series expansions, harmonics. Half

range Series.
Text Book
:
G. Strang, Linear Algebra and its applications,
4
th
edition,
Thomson
Brooks/Cole
,
2
nd
Indian reprint
200
7.(
ch.nos.1,2,3,5,6)
Ref
erence Book
:
B S Grewal, Higher
Engineering Mathematics
39
th
Edition , Khanna Publishers,2005 .
(ch. nos. 2, 10)
MA251:
METHODS OF APPLIED MATHEMATICS
52 Hrs
Unit 1
Complex Variables
:
11 Hrs
Limits, Continuity and differentiability of functions of complex variables. Analytic functions.
Cauchy
–
Riemann equations in Cartesia
n and Polar forms

consequences..
Conformal transformations: z
2
,
e
Z
, trigonometric functions, z + a
2
/ z (z ≠ 0) and
Bilinear transformations.
Unit
2
Complex Integration
09 Hrs
Line integral, Cauchy’s theorem
and corollaries, Cauchy’s integral formula.
Taylor’s and Laurent’s series expansions of functions.
Isolated singularities and Cauchy’s Residue theorem
.
Unit
3
Numerical Methods
17 Hrs
Roots of transcendental equations using Bisection, Regula

Falsi and Newton

Raphson Methods.
Finite Differences, Newton
–
Gregory forward and backward interpolation formulae.
Stirling’s and Bessel’s interpolation formulae, Lagrange’
s interpolation formulae
and Newton’s divided difference interpolation formula.
Numerical Integration using Trapezoidal Rule, Simpson’s one third rule, Simpson’s three
eighth rule and Weddle’s rule.
Numerical solutions of first order Ordinary Different
ial Equations

Taylor’s series method,
Modified Euler’s , Runge

Kutta 4
th
order methods.
Unit 4
Partial Differential Equations (P.D.E) Part 1:
08 Hrs
Formation of Partial differential equations by elimination of arbitrary constan
ts
and arbitrary functions. Solution by direct integration.
Solutions of equations of the type: Pp + Qq = R and Charpit’s method.
s
Unit
5
Partial Differential Equations(P.D.E)Part :2
07 Hrs
Solution of PDE’s by the method of separation of variables, one dimensional Heat and Wave equations.
Solution of two dimensional and three dimensional Laplace’s equations in Cartesian and Polar systems.
Solution of Homogeneous and Non

Homogeneo
us Linear PDEs.
Text Book :
B S Grewal, Higher
Engineering Mathematics 39
th
Edition, Khanna Publishers.
(ch. nos. 17, 18, 19, 20,27,28,30)
Reference Book
s
:
1
. KA Stroud, Advanced Engineering Mathematics 4
th
Edition, MacMillan Publi
cations,2003.
2
. Murray R Spiegel, Complex Variables, Schaum’s Outline Series, Tata McGraw
Hill Publications, 1981
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