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, 3^{rd} 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 |