This course presents mathematical and computational fundamentals of the numerical solution for scientific problems. It covers • Explicit and implicit methods for ordinary differential equations • Finite difference methods for partial differential equations (elliptic, parabolic, hyperbolic equations) • Finite element methods for elliptic equations • Consistency, convergence, stability of numerical methods • Solution of linear systems • Programming with Matlab

CILO-1: Demonstrate the basic concepts, including stability, convergence, error estimate, etc., in numerical methods of partial differential equations. CILO-2: Use classical numerical methods such as finite difference method, finite element method, to solve the model partial differential equations. CILO-3: Apply numerical methods of partial differential equations in real world problems.