SYLLABUS FOR SEMESTER - II (MATHS)

09MA201                        MATHEMATICS-II                                 

              (Common to First Semester Part Time B.E., Mechanical Engineering)         

1. VECTOR CALCULAS                                                                                  

Gradient divergence and curl-Directional derivative-Irrotational and solenoidal vector fields-Vector integration-Green’s theorem in a palne, Gauss divergence theorem and stokes theorem (excluding proofs)-Simple applications involving cubes and rectangular parallelepipeds.

2. ANALYTIC FUNCTIONS                                                                                

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,l/z,and bilinear transformation.

3. COMPLEX INTEGRATION                                                                        

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).

4. LAPLACE TRANSFORM                                                                           

Laplace transform-Conditions for existence-Transform of elementary functions-Basic properties-Theorem of derivatives and integrals-Transform of unit step function and impulse functions-Transform of periodic functions.

5. INVERSE LAPLACE TRANSFORM                                                            

Inverse Laplace Transform-Convolution theorem (excluding proof)-Initial and Final value theorems-Solution of linear ODE of second order with constant coefficients using Laplace transformation techniques.        

Total Hrs: 60

TEXT BOOKS

1. Veerarajan T, “Engineering mathematics (For semester I and II)”, 2^nd Edition, Tata McGraw Hill Education Pvt. Ltd., New Delhi, 2009.
2. P. Kandasamy, K. Thilagavathy and K. Gunavathy, “Engineering Mathematics (For I year B.E., B.Tech)”, 9^th Edition, S. Chand & Co. Ltd. New Delhi, 2009.

REFERENCE BOOKS

1. Grewal. B.S, “Higher Engineering Mathematics”, 40^th Edition, Khanna publications, Delhi, 2007.
2. Ramana. B.V, “Higher Engineering Mathematics”, Tata McGraw Hill Publishing company, New Delhi, 2007.
3. Glyn James, “Advanced Engineering mathematics”, 3^rd Edition, Wiley India, 2007