4CH6.1(MA)-Mathematics-IV |
Units: I |
Complex Variables: Analytic functions, Cauchy-Riemann equations, Elementary
conformal mapping with simple applications, Line integral in complex domain,
Cauchy’s theorem, Cauchy’s integral formula, Taylor’s series, Laurent’s series,
Poles, Residues, evaluation of simple definite real integrals using the theorem of
residues. Simple contour integration.
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Units: II |
Introduction to Statistics: Probability distribution: Bimodal, Poisson, Uniform, Normal,
Correlation and Regression, Linear regression, Confidence limits, types of errors, testing of
hypothesis based on normal, Chi-square test, F-test, Z-test, Student’s T-test. Comparison of
means and variances. |
Units: III |
Optimisation Techniques: Basic concepts of optimization: continuity of functions,
Unimodal versus Multimodal functions, Concave and Convex functions.
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Units: IV |
Unconstrained single variable optimisation: Newton, Quasi-Newton, Secant
method, Dichotomous search, Fibonacci method, Golden Section method.
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Units: V |
Introduction to Dynamic programming: Deterministic Dynamic programming,
Probabilistic Dynamic programming.
Introduction to Integer programming: The Branch and Bound algorithm for Binary layer
programming, the Branch and Scan algorithm for mixed integer programming.
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Text/ Reference Books |
1. Gaur, Y. N., and Kaul, C. L., “Higher Engineering Mathematics,” Book 2, Jaipur
Publishing House, Jaipur.
2. Gupta, S.P., “Mathematical Statistics”.
3. Kapoor, J.N. and Saxena, “Mathematical Theory of Statistics,” S. Chand & Co., New
Delhi
4. Rao, S.S., “Optimisation Techniques,” John Wiley, New Delhi
5. Kambo, N.S., “Optimisation Techniques”.
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