### Numeical Methods (MATH-312)

To acquire basic knowledge related to numerical methods. To provide undersatnding of main sources of numerical errors and the power of numerical methods that minimizes these errors.

Learning Outcomes:

1. Learn basics of numerical methods.

2. define errors and their types, choice of numerical methods that best approximate the exact value.

3. find the solution of equations by using finite difference technique, Newtons's method, Fixed point Iteration method.

4. Solve the differential equations like parabolic, hyperbolic, elliptic equations.

Course Outlines:

1. Basic ideas, concepts, terminology, elements of numerical methods.

2. differntial formulation, solution domain and mesh, discretization, set of algebraic equations.

3. choice of numerical mesh, cartesian, polar-cylenderical, general orthogonal, regular orthogonal, arbitrary triangular meshes, discretization, truncation and dicretization error.

4. Polynomials and Finite differences: colocation type polynomials, finite difference operator algebra, forms of polynomials, relationship to Tylor series.

5. Solution of equation sets: Ill-conditioning, iterative solution methods, Decomposition, Eigen-value problem, system stability, charateristics of polynomials.

6. Ordinary differential equations: Order, methods of solving first order ordinary differential equations, higher order differential equations and their conversion  into set of first order ordinary equations.

7. Partial differential equations: variants of partial differential equations, choice of finite difference formulation and solution algorithm, elliptic, parabolic, hyperbolic equations.Finite volume approach.

Recommended Books:

1. Numerical Analysis by Richard L.Burden. John Doyuglas Faires, 9th Edition, Cengage Learning, 2010.

2. Applied Numerical Analysisn by Curtis F.Gerald. Patrick O. Wheatley. 7th Edition (August 10, 2003), Pearson.

Suggested Book:

Erwin Kryszig, "Advanced Engineering Mathematics", 10th Edition, John Willey & sons.