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 books:
- B.S. Grawel, Numerical Methods
- M.K. Jain, S.R.K. Iyengar and R.K. Jain, Numerical Methods-problem and solutions, Wiley Eastern Limited, 2001.
- S. Ross, Introduction to Probability Models, Wiley India
- A.M. Gun, M.K. Gupta and B.S. Gupta, Fundamentals of Statistics
Reference Books:
- A.J. Hayter, Probability and Statistics, Duxbury, 2002
- J.B. Scarborough, Numerical mathematical analysis, oxford & IBH Publishing Co.Pvt.,2000
- R.W. Hamming, Numerical Methods for Scientist and Engineers, McGraw Hill, 1998
- J.H. Mathews and K.D. Fink, Numerical Methods using MATLAB, Pearson Education, 2004.
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