Solution of equations and Eigen value problems: linear interpolation methods, method of false position, Newton’s method, statement of fixed point theorem, fixed point iteration, solution of linear system by Gaussian elimination, LU decomposition and partial pivoting, Gauss-Jordon method and iterative methods, inverse of a matrix by Gauss Jordon method, Eigen value of a matrix by power method, Simulation/case study in short circuit analysis. Initial value problems for ordinary differential equations: single step methods, Taylor series method, Euler and modified Euler methods, fourth order Runge – Kutta method for solving first and second order equations, Simulation/case study in transient stability analysis, midterm stability analysis, etc.
Linear programming: Formulation, graphical and simplex methods, Big-M method.
Regression & interpolation: linear least squares regression, functional and nonlinear regression, Simulation/case study in state estimation, optimal power flow etc.
Unconstrained one dimensional optimization techniques: Necessary and sufficient conditions. Unrestricted search methods: quadratic interpolation methods, cubic interpolation and direct root methods.
Unconstrained n- dimensional optimization techniques: Direct search methods, random search, descent methods, steepest descent, conjugate gradient, Simulation.
Constrained optimization techniques: necessary and sufficient conditions, equality and inequality constraints, Kuhn-Tucker conditions, penalty function method, Simulation/Case study in economic operation of power systems. Dynamic programming, principle of optimality, recursive equation approach, application to shortest route, cargo-loading, allocation and production schedule problems, Simulation/case study in transmission system expansion.
Practice session: Simulation and coding of different computational methods as mentioned above.