Numerical Methods and Differential Equations

Course Aim:
The course introduces Ordinary Differential Equations (ODEs) and their classification.  It also presents different analytical and numerical methods for solving first and second order ODEs. It also explains the numerical methods used for solving linear algebraic equations and for performing differentiation, integration, interpolation, and curve fitting.
Course contents:
Introduction to numerical analysis – Error and error propagation – Nonlinear equation bracketing methods (bisection and false position – Open methods (simple fixed-point iteration and Newton-Raphson) – System of linear equations: Gauss-Seidel method – curve fitting – Interpolation (Newton divided difference, Lagrange interpolation) – Integration (Trapezoidal rule, Simpson’s 1/3 rule) – Differentiation – Ordinary differential equations.