Math 321 Syllabus (981) Dept. Math. Scie., KFUPM K. Furati

Math 321 Syllabus (981)
Dept. Math. Scie., KFUPM
K. Furati
Title:
Prerequisite:
Textbook:
Introduction to Numerical Computing
Math 202, ICS 101
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
1.2
Programming Suggestions
Review of Taylor Series
1
2
Number Representation
and Errors
2.2
Floating-Point Representation
2
3
Locating Roots of
Equations
4
Interpolation and
Numerical Differentiation
3.1
3.2
3.3
4.1
4.2
Bisection Method
Newton's Method
Secant Method
Polynomial Interpolation
Errors in Polynomial Interpolation
Estimating Derivatives and
Richardson Extrapolation
Definite Integral
Trapezoid Rule
An Adaptive Simpson's Scheme
Gaussian Quadrature Formulas
Naive Gaussian Elimination
Gaussian Elimination with Scaled
Partial Pivoting
Tridiagonal and Banded Systems
LU Factorization
Taylor Series Methods
Runge-Kutta Methods
Stability and Adaptive Runge-Kutta
Methods
5
Numerical Integration
6
Systems of Linear
Equations
8
Ordinary Differential
Equations
4.3
5.1
5.2
5.4
5.5
6.1
6.2
6.3
6.4
8.1
8.2
8.3
3-4
5-6
7-8
9-10
11-12
10
Smoothing of Data and
the Method of Least
Square
12
B VP for ODE
10.1
10.2
12.1
12.2
The Methods of Least Squares
Orthogonal Systems and Chebyshev
Polynomials
Shooting Method
A Discretization Method
13
14-15