F11_CSE202_Numerical_Analysis_and_Algorithms

=CSE202: Numerical Analysis and Algorithms=

Program:
BS(CS)

Semester:
Fall 2011

Instructor:
H. bin Zubair

**Course Lead:**
H. bin Zubair

**Credit Hours:**
3 credit hours

Prerequisite(s):
MTS-101 (Calculus 1.). CSE141 (Introduction to Programming).

Course Description:
This is a Bachelors-standard course of numerical analysis. It imparts the basic ideas necessary for the numerical solution of applied problems originating from diverse fields. The course uses Matlab as the demonstration tool of various concepts and techniques, such as root finding for non-linear equations, interpolation, and problem solving using ODE models. Although Matlab use is recommended to students to have a firsthand view of the concepts, the use of common programming languages such as C, Fortran, and Python is also encouraged. This course gives the first numerical computation exposure to BS students, and therefore all numerically originated ideas and techniques are formulated without requiring any previous knowledge to build on, other than basic computer programming techniques, and concepts from Calculus.

Course Objectives:
At the culmination of the course, successful students are expected to be able to:
 * Identify problems belonging to the numerical domain.
 * Differentiate between problems that be addresses using the different techniques learnt.
 * Describe the basis philosophy of numerical analysis with clarity of concepts.
 * Analyze interpolation problems and apply knowledge of numerical extrapolation to solve them.
 * Use different time integration schemes to solve initial value problems based on ordinary differential equations.
 * Apply finite difference discretization techniques to discretize and solve boundary value problems based on ordinary differential equations.

Books:
The following textbook will be pursued closely: The following books are recommended for reference.
 * Numerical Methods for Mathematics, Science and Engineering, by John. H. Mathews. 2nd. Edition; Prentice Hall India (or the US Edition). Available from URDU Bazar; Paramount Books. etc.
 * Applied Numerical Analysis by Gerald & Wheatley, 5th. Edition or Later. (Available from URDU Bazar; Paramount books etc.)
 * Templates for the Solution of Linear Systems. (available free of cost on the Internet).

Grading Policy:
The following grading policy is implemented for this course:
 * **Assessment** ||= **Points** ||
 * First Term Exam (closed book exam) ||= 20 ||
 * Second Term Exam (closed book exam) ||= 20 ||
 * Group Programming Projects (small scale) ||= 20 ||
 * Terminal Exam (closed book) ||= 40 ||

**Topics Covered (Salient Outlines) **
The following is a rough dissemination of topics into an approximate number of lectures. Fixed point iterations Bracketing methods of locating roots. Newton-Raphson and Secant methods. Iteration for non-linear systems. Newton's method for systems ||= 8 || Properties of vectors and matrices Upper and Lower triangular linear systems Gaussian elimination Matrix inversion Different LU decompositions ||= 5 || Stationary methods, Jacobi, Gauss-Seidel, SOR Non-stationary algorithms, and preconditioning ||= 3 || General polynomial approximation of degree n Lagrange's polynomial of degree n. Newton's polynomial of degree n. ||= 4 || Differentiation techniques and algorithms Integration techniques and algorithms ||= 1 || Formulae and techniques Time integration schemes Euler, Heun's RK methods. Devising new time integration schemes (stability issues) Finite difference discretization and boundary value problems. ||= 4 ||
 * __**Topics**__ ||= __**Approximate # of lectures**__ ||
 * __**Review of calculus**__ ||= 3 ||
 * __**Non-linear equations and systems. (Intro)**__
 * __**Direct methods for Linear System****s (Intro)**__
 * **__Iterative methods for linear systems (Intro)__**
 * **__Interpolation and polynomial approximation (Intro)__**
 * __**Numerical Calculus (Intro)**__
 * __**Solution of ordinary differential equations ODEs (Intro)**__