2K6 CS 401 : ENGINEERING MATHEMATICS III

Module I: (13 hours)
Complex analytic functions and conformal mapping: Complex functions – limits. derivative, analytic function- Cauchy-Riemann equations- elementary complex functions such as powers, exponential function, logarithmic, trigonometric and hyperbolic functions- Conformal mapping – Linear fractional transformations- mapping by elementary functions
Module II: (13 hours)
Complex integration: Line integral, Cauchy’s integral theorem – Cauchy’s integral formula – Taylor’s series, Laurent series – residue theorem – evaluation of real integrals using integration around unit circle, around semicircle, integrating contours having poles on the real axis
Module III: (13 hours)
Jointly Distributed Random Variables: Joint distribution functions, independent random variables , covariance and variance of sums of random variables, joint probability distribution functions of random variables, conditional probability and conditional expectations. Curve fitting: Method of least squares, correlation and regression, line of regression.
Module IV: (13 hours)
Vibrating strings: One dimensional wave equation – D’ Alembert’s solution – solution by method of separation of variables One dimensional heat equation – solution of the equation by the method of separation of variable Solutions of Laplace’s equation over a rectangular region and a circular region by the method of separation of variable

Reference books
1. Kreyszig E. Advanced Engineering Mathematics. Wiley Eastern
2. Johnson, Miller and Freud. Probability and Statistics for Engineers, Pearson Education Asia.
3. Wylie .C.R. Advanced Engineering Mathematics, Mc Grawhill.
4. B.S. Grewal. Higher Engineering Mathematics, Khanna Publishers.
5. Freund. J.E. Mathematical Statistics, Prentice hall of India.