|
Campus
|
College of E&ME
|
|
Programs
|
PG
|
|
Session
|
Fall Semester 2016
|
|
Course Title
|
Numerical Analysis
|
|
Course Code
|
MTH-851
|
|
Credit Hours
|
3-0
|
|
Pre-Requisutes
|
Linear Algebra, ODEs and PDEs
|
|
Course Objectives
|
To teach numerical techniques for solving algebraic equations, ODEs and PDEs
|
|
Detail Content
|
- Review of Calculus
- Algorithms and Convergence, Error
- Solutions of equations in one variable by Bisection Method, Fixed point iteration, Newton-Raphson Method, Secant Method, Method of False Position, Solution of system of equations, Newton-Raphson Method
- Error Analysis for interactive methods
- Interpolation and polynomial approximation: Lagrange Interpolating Polynomial,
- Newton’s Interpolating Divided Difference Formulae, Error Analysis
- Cubic Spline Interpolation, (Clamped and Natural)
- Numerical Differentiations
- Numerical Integration: Simpson’s’ Rule, Trapezoidal Rule
- Composite Trapezoidal Rule, Composite 1/3, 3/8-Simpson’s’ Rule, Adaptive Quadrature Method
- Multiple Integrals
- Improper Integrals
- Iterative Techniques in Matrix Algebra:
- Norms of Vectors and Matrices, Schwarz Inequality, Eigen values & Eigenvectors Iterative Technique for Solving Linear Systems: Jacobi Iterative Method, Guess Seidel Iterative
- Error Estimates and Iterative Refinement (SOR)
- Least Square Approximation, Orthogonal Polynomials and Least Square Approximations
- Elementary Theory of Initial Value Problems for Ordinary Differential Equations: Euler’s Method, Higher Order Taylor’s Method
- Runga–Kutta Method
- Error Control and the Runga-Kutta-Felberg Method
- RungaKutta Method for a System of Differential Equations and Error Analysis
- Linear Shooting Method for Boundary Value Problems for ODEs.
- Shooting Method for Non-Linear Problems
- Finite Difference Methods for Linear and Nonlinear Problems
- Numerical Solutions to Partial Differential Equations
- Elliptic Partial Differential Equations (Poisson Equation)
- Parabolic Partial Differential Equations (Heat Equation)
- Hyperbolic Partial Differential equations (Wave Equation)
- Finite Element Method
|
|
Text/Ref Books
|
- R.L.Burden and J.D. Faires: Numerical Analysis; Prindle, Weber & Smith
- E.Kreyszing: Advanced Engineering Mathematics (8th Ed)
- Curtis F.Gerald Patrick O. Wheatley: Applied Numerical Analysis, (7th Ed) Addison-Wesley
- Donald Greenspan & Vincenzo Casulli: Numerical Analysis For Applied Mathematics, Science and Engineering, Addison-Wesley
- David Kahaner: Numerical Methods and Software, Prentice
|
|
Time Schedule
|
Fall 2015
|
|
Faculty/Resource Person
|
Dr M. Umar Farooq
PhD (NUST), Pakistan
Discipline: Mathematics
Specialization: Differential Equations
|
|