Course Contents

Solution of Non-Linear Equations: Numerical methods for solution of nonlinear equations. Regula-falsi method, Newton’s Method. Rate and Conditions of Convergence for iterative and Newton’s method. System of Linear Equation: Gaussian elimination method. Triangular decomposition method and its various forms. Iterative methods (Jacobi, Gauss- Seidel) for solving system of linear equations. Interpolation: Finite and divided differences. Newton’s formula for interpolation. Inverse interpolation. Interpolation with unequal intervals, Cecteral difference interpolation formulas (Gauss & Strrilling). Various method including Aitkins and Lagrange interpolation, error estimates formulae for interpolation and its applications. Numerical Integration: Trapezoidal, Simpson and quadratic formula for evaluating integrals with error estimates. Difference and Numerical solution of Differential Equations: Formulation of difference equations, solution of linear (homogeneous and non- homogeneous) difference equations with constant coefficients, Euler and the modified Euler method.

Course Synopsis

To familiarize students with different numerical methods techniques used to find solution of different types of problems.

Course Learning Outcomes

Students will get familiar to different numerical methods techniques for different types of numerical problems. This will enhance their ability to find solution of different mathematical problems.