MA1151 - MATHEMATICS II |
LAPLACE TRANSFORMS |
Transforms of elementary functions – Basic properties – Transforms of derivatives and integrals
– Initial and final value theorems – Inverse Laplace transforms – Convolution theorem –
Solution of Ordinary Differential Equations with constant coefficients using Laplace transforms
– Transform of periodic functions – Solution of integral equations. |
VECTOR CALCULUS |
Gradient, Divergence and Curl – Directional derivative – Irrotational and Solenoidal vector
fields – Vector integration – Problem solving using Green’s theorem, Gauss divergence theorem
and Stoke’s theorem – Simple applications and verifications. |
ANALYTIC FUNCTIONS |
Necessary and Sufficient conditions (without proof) – Cauchy-Riemann equations – Properties
of analytic functions – Harmonic conjugate – Construction of Analytic functions – Conformal
mapping: w = z+a, az, 1/z, Z2 and bilinear transformation. |
MULTIPLE INTEGRALS |
Double integration – Cartesian and Polar Co-ordinates – Change of order of integration – Area as
a double integral – Change of variables between Cartesian and Polar Co-ordinates – Triple
integration – Volume as a triple integral. |
COMPLEX INTEGRATION |
Problems solving using Cauchy’s integral theorem and integral formula – Taylor’s and Laurent’s
expansions – Residues – Cauchy’s residue theorem – Contour integration over unit circle –
Semicircular contours with no pole on real axis. |
Text Books |
1. Grewal, B.S., “Higher Engineering Mathematics”, Thirty eighth Edition, Khanna
Publishers, New Delhi, 2005.
2. Venkataraman. M. K., “Engineering Mathematics”, Volume I and II Revised enlarged
Fourth Edition, The National Publishing Company, Chennai, 2004. |
Reference Books |
1. Glyn James., “Advanced Modern Engineering Mathematics”, Third Edition,Pearson
Education Ltd, New Delhi, 2004.
2. Veerarajan. T., “Engineering Mathematics (for first year)”, Fourth Edition, Tata McGraw
– Hill Publishing Company Limited, New Delhi, 2005.
3. Bali N. P and Manish Goyal, “ Text book of Engineering Mathematics”, Third edition,
Laxmi Publications(p) Ltd., 2008. |
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