## March 2, 2010

### SEMESTER II MA1151 MATHEMATICS II SYLLABUS

ANNA UNIVERSITY TIRUCHIRAPPALLI 620 024
Regulations 2007 Syllabus Common to all B.E. / B.Tech.
(Except B.E. Marine Engineering)
SEMESTER II MA1151 MATHEMATICS II

UNIT I MULTIPLE INTEGRALS 10+3
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.

UNIT II VECTOR CALCULUS 9+2
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.

UNIT III ANALYTIC FUNCTIONS 9+2
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.

UNIT IV COMPLEX INTEGRATION 10+2
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.

UNIT V LAPLACE TRANSFORMS 10+3
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.
L: 48 T: 12 Total: 60

TEXT BOOK
1. Grewal, B.S., “Higher Engineering Mathematics”, Thirty eighth Edition, Khanna
Publishers, New Delhi, 2005.

REFERENCES
1. Glyn James., “Advanced Modern Engineering Mathematics”, Third Edition,Pearson Education Ltd, New Delhi, 2004.
2. Venkataraman. M. K., “Engineering Mathematics”, Volume I and II Revised enlarged Fourth Edition, The National Publishing Company, Chennai, 2004.
3. Veerarajan. T., “Engineering Mathematics (for first year)”, Fourth Edition, Tata McGraw – Hill Publishing Company Limited, New Delhi, 2005.
4. V. Sundaram, R. Balasubramanian, K.A. Lakshminarayanan, “Engineering Mathematics”, Fifth Edition, Vikas Publishing house Pvt. Ltd., New Delhi, 2006.

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