The course aims at acquiring the knowledge for: The solution of systems of linear equations, non-linear algebraic equations, ordinary differential equations, interpolation and approximation of data and numerical approximation of integrals.
The aim of the course is to understand the importance of numerical methods for solving scientific and technological problems for which either there is no analytical solution or it is very difficult to calculate it.
On completion of this course, students should be armed with numerical and computational techniques for solving a wide variety of fundamental mathematical problems that arise in various scientific areas.
Number representation in computers.
Linear systems: Direct methods (Gauss, factorization methods). Stability of linear systems. Iterative methods (Jacobi, Gauss-Seidel), calculation of eigenvalues.
Solving non-linear equations: Bisection, fixed point iteration, Newton-Raphson, secant methods. Newton method for nonlinear systems.
Interpolation: Polynomial interpolation in Lagrange and Newton form and interpolation error.
Numerical integration: Newton-Cotes formulas, simple and composite trapezoidal and Simpson integration rules.
Differential equations: Initial value problems for ordinary differential equations. Single step methods (Euler, Taylor, Runge-Kutta). Multi-step methods (Adams, predictor-corrector methods). Boundary value problems, Finite difference method.
Approximation theory: Discrete least squares, polynomial and exponential approximation.
