Anna University-Mathematics 2nd sem B.E Syllabus

Anna University-Regulation 2008, Credit System Mathematics 2nd sem B.E Civil Engineering Syllabus 

MA2161                  MATHEMATICS – II                             L T P C                     3 1 0 4

Unit-I  Ordinary Differential Equations                                                                          12
Higher order linear differential equations with constant coefficients – Method of variation of
parameters – Cauchy’s and Legendre’s linear equations – Simultaneous first order linear
equations with constant coefficients.

Unit-II Vector Calculus                                                                                               12
Gradient Divergence and Curl – Directional derivative – Irrotational and solenoidal vector fields
– Vector integration – Green’s theorem in a plane, Gauss divergence theorem and stokes’
theorem (excluding proofs) – Simple applications involving cubes and rectangular parallelpipeds.

Unit-III Analytic Functions                                                                                         12 

Functions of a complex variable – Analytic functions – Necessary conditions, Cauchy – 

Riemann equation and Sufficient conditions (excluding proofs) – Harmonic and orthogonal 

properties of analytic function – Harmonic conjugate – Construction of analytic functions – 

Conformal mapping : w= z+c, cz, 1/z, and bilinear transformation. 

Unit-IV Complex Integration                                                                                     12 

Complex integration – Statement and applications of Cauchy’s integral theorem and Cauchy’s 

integral formula – Taylor and Laurent expansions – Singular points – Residues – Residue 

theorem – Application of residue theorem to evaluate real integrals – Unit circle and semi-

circular contour(excluding poles on boundaries). 

Unit-V Laplace Transfrom                                                                                         12 

Laplace transform – Conditions for existence – Transform of elementary functions – Basic 

properties – Transform of derivatives and integrals – Transform of unit step function and 

impulse functions – Transform of periodic functions. 

Definition of Inverse Laplace transform as contour integral – Convolution theorem (excluding 

proof) – Initial and Final value theorems – Solution of linear ODE of second order with constant 

coefficients using Laplace transformation techniques. 

 

                                                                                                     TOTAL : 60 PERIODS 

TEXT BOOK: 

1. Bali N. P and Manish Goyal, “Text book of Engineering Mathematics”, 3rd Edition, Laxmi 

Publications (p) Ltd., (2008). 

2. Grewal. B.S, “Higher Engineering Mathematics”, 40th Edition, Khanna Publications, Delhi, 

(2007). 

 

REFERENCES 

1. Ramana B.V, “Higher Engineering Mathematics”,Tata McGraw Hill Publishing Company, 

New Delhi, (2007). 

2. Glyn James, “Advanced Engineering Mathematics”, 3rd Edition, Pearson Education, (2007). 

3. Erwin Kreyszig, “Advanced Engineering Mathematics”, 7th Edition, Wiley India, (2007). 

4. Jain R.K and Iyengar S.R.K, “Advanced Engineering Mathematics”, 3rd Edition, Narosa 

Publishing House Pvt. Ltd., (2007

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