AC35 MATHEMATICS—II
1. Complex Analysis 22 hours
1.1
Analytic
function, Cauchy- Riemann equations, Elementary functions of complex variable,
Harmonic functions.
1.2
Conformal
mapping, Linear fractional transformations.
1.3
Complex
line integral, Cauchy integral theorem,Cauchy integral formula, Cauchy
inequality, Lioville and Morera theorems.
1.4
Taylor
and Laurent series, Singularities and zeros, Poles, Residues and Residue
theorem.
1.5
Evaluation
of real integrals by contour integration.
I [12, 13, 14, 15]; II [10, 11, 12,
13, 14]
2.
Vector Analysis 20 hours
2.1
Vector
and scalar function and fields, Differentiation of vector
function, Tangent
vector to a curve in space.
2.2
Gradient,
Divergence, Curl.
2.3
Line
integral of vector functions, Independence of path, Green’s theorem.
2.4
Surface
integrals, Divergence theorem, Stoke’s theorem.
I [8, 9]; II [15]
3.
Partial Differential Equations 8 hours
3.1
Solution
of Partial Differential Equations by method of separation of variables.
3.2
One
dimensional wave and heat conduction equation, Laplace equation in two
variables.
I [11]; II [9]
4.
Probability Concepts 10 hours
4.1
Random
variable, Probability mass function and density function.
4.2
Expectation,
Mean and variance of a random variable.
4.3
Binomial,
Poisson and Normal distributions.
I [22]
Text Books
I. Erwin Kreyszig,
“Advanced Engineering Mathematics” 8th edition, John Wiley
and Sons (Asia) --- 2000
II. R. K. Jain and S. R.
K. Iyengar, “Advanced Engineering Mathematics”, Narosa Publishing House --- 2002
Reference Books
1. Peter V. O’neil,
“Advanced Engineering Mathematics” 4th edition Brooks / Cole
Publishing Company ---1995
