Probability and Statistics : Random variables (rv) and their properties, some standard discrete and continuous rv, Expectation, Variance, moments, moment generating functions, functions of a rv, their distribution and moments, joint, marginal and conditional distribution and independence of rvs, Hypothesis testing.
Numerical solutions of systems of linear equations: Gauss elimination, LU decomposition, Gauss-Jacobi and Gauss-Seidel methods.
Numerical methods of ODE and PDE: Runge-Kutta and finite difference methods for ODE, Finite difference methods for solving 2-D Laplace’s equation, Poisson’s equation, 1-D heat equation : Bender Schmidt, Crank Nicholson method and Du Fort Frankel methods, 1-D wave equation using Explicit method. Consistency and stability analysis.
Text/Reference Books:
- Grawel, B.S. Numerical Methods, Khanna Publishers
- Jain, M.K., Iyengar, S.R.K. and Jain, R.K. Numerical Methods-problem and solutions, Wiley Eastern Limited
- Ross, S. Introduction to Probability Models, Wiley India
- Gun, A.M., Gupta, M.K. and Gupta, B.S., Fundamentals of Statistics
- Hayter, A.J., Probability and Statistics, Duxbury
- Scarborough, J.B., Numerical mathematical analysis, Oxford & IBH Publishing Co.Pvt.
- Hamming, R.W., Numerical Methods for Scientist and Engineers, McGraw Hill
- Mathews, J.H. and Fink, K.D., Numerical Methods using MATLAB, Pearson Education.
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