Subject Code: MA6LXXX Name: Mathematical Methods L-T-P: 3-1-0 Credit: 4
Prerequisite: None
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:
  1. B.S. Grawel, Numerical Methods
  2. M.K. Jain, S.R.K. Iyengar and R.K. Jain, Numerical Methods-problem and solutions, Wiley Eastern Limited, 2001.
  3. S. Ross, Introduction to Probability Models, Wiley India
  4. A.M. Gun, M.K. Gupta and B.S. Gupta, Fundamentals of Statistics
Reference Books:
  1. A.J. Hayter, Probability and Statistics, Duxbury, 2002
  2. J.B. Scarborough, Numerical mathematical analysis, oxford & IBH Publishing Co.Pvt.,2000
  3. R.W. Hamming, Numerical Methods for Scientist and Engineers, McGraw Hill, 1998
  4. J.H. Mathews and K.D. Fink, Numerical Methods using MATLAB, Pearson Education, 2004.