Math 321 Syllabus (981)

Dept. Math. Scie., KFUPM

K. Furati

Title: Introduction to Numerical Computing

Prerequisite: Math 202, ICS 101

Textbook: Numerical Mathematics & Computing, Cheney & Kincaid, 3rd edition, 94.

Objectives:

This course is intended to introduce the many facts of numerical computing, thus preparing the student for higher level and more specialized courses on the subject.

Course Description:

Floating-point arithmetic and error analysis. Solution of non-linear equations. Polynomial interpolation. Numerical integration and differentiation. Data fitting. Solution of linear algebraic systems. Initial and boundary value problems of Ordinary Differential Equations.

 Ch Chapter Title Section Section Title Week 1 Introduction 1.1 Programming Suggestions 1 1.2 Review of Taylor Series 2 Number Representation and Errors 2.2 Floating-Point Representation 2 3 Locating Roots of Equations 3.1 Bisection Method 3-4 3.2 Newton’s Method 3.3 Secant Method 4 Interpolation and Numerical Differentiation 4.1 Polynomial Interpolation 5-6 4.2 Errors in Polynomial Interpolation 4.3 Estimating Derivatives and Richardson Extrapolation 5 Numerical Integration 5.1 Definite Integral 7-8 5.2 Trapezoid Rule 5.4 An Adaptive Simpson’s Scheme 5.5 Gaussian Quadrature Formulas 6 Systems of Linear Equations 6.1 Naive Gaussian Elimination 9-10 6.2 Gaussian Elimination with Scaled Partial Pivoting 6.3 Tridiagonal and Banded Systems 6.4 LU Factorization 8 Ordinary Differential Equations 8.1 Taylor Series Methods 11-12 8.2 Runge-Kutta Methods 8.3 Stability and Adaptive Runge-Kutta Methods 10 Smoothing of Data and the Method of Least Square 10.1 The Methods of Least Squares 13 10.2 Orthogonal Systems and Chebyshev Polynomials 12 BVP for ODE 12.1 Shooting Method 14-15 12.2 A Discretization Method