Module I: (13 hours)
Complex analytic functions and conformal mapping: Complex functions \u2013 limits. derivative, analytic function- Cauchy-Riemann equations- elementary complex functions such as powers, exponential function, logarithmic, trigonometric and hyperbolic functions- Conformal mapping \u2013 Linear fractional transformations- mapping by elementary functions
Module II: (13 hours)
Complex integration: Line integral, Cauchy\u2019s integral theorem – Cauchy\u2019s integral formula \u2013 Taylor\u2019s series, Laurent series \u2013 residue theorem \u2013 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 \u2013 D\u2019 Alembert\u2019s solution \u2013 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\u2019s equation over a rectangular region and a circular region by the method of separation of variable<\/p>\n\n\n\n
Reference books
1. Kreyszig E. Advanced Engineering Mathematics. Wiley Eastern<\/a>
2. Johnson, Miller and Freud. Probability and Statistics for Engineers, Pearson Education Asia.
3. Wylie .C.R. Advanced Engineering Mathematics, Mc Grawhill.<\/a>
4. B.S. Grewal. Higher Engineering Mathematics, Khanna Publishers.<\/a>
5. Freund. J.E. Mathematical Statistics, Prentice hall of India. <\/p>\n\n\n\n