Math 321 Syllabus (991)
Department of Mathematical Sciences
Title: Introduction to Numerical Computing
Prerequisite: Math 202, ICS 101
Textbook: Numerical Mathematics & Computing, Cheney & Kincaid, 3ed edition
Objectives:
1-To acquaint students with the potentialities of the modern computer for solving the numerical
problems that will arise in their professions.
2-To give students an opportunity to honor their skills in programming and problem solving.
3-To help students arrive at an understanding of the important subject of errors.
Week |
Section |
Section Title |
Chapter Title |
1-2 |
1.1 |
Programming Suggestions |
1-Introduction 2-Number Representation and Errors |
1.2 |
Review of Taylor Series |
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2.2 |
Floating Point Representation |
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3-4 |
3.1 |
Bisection Method |
3-Locating Roots of Equations |
3.2 |
Newton’s Method |
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3.3 |
Secant Method |
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5-6 |
4.1 |
Polynomial Interpolation |
4-Interpolation and Numerical Differentiation |
4.2 |
Errors in Polynomial Interpolation |
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4.3 |
Estimating Derivatives and Richardson Extrapolation |
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Exam I |
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7-8 |
5.1 |
Definite Integral |
5-Numerical Integration |
5.2 |
Trapezoid Rule |
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5.4 |
An Adaptive Simpson’s Scheme |
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5.5 |
Gaussian Quadrature Formulas |
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9-10 |
6.1 |
Naïve Gaussian Elimination |
6-Systems of Linear Equations |
6.2 |
Gaussian Elimination with Scaled Partial Pivoting |
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6.3 |
Tridiagonal and Banded Systems |
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6.4 |
LU Factorization |
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11 |
7.1 |
First-degree and Second-Degree Splines |
7-Approximation by Spline Functions |
7.2 |
Natural Cubic Splines |
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Exam II |
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12-13 |
8.1 |
Taylor Series Methods |
8-Ordinary Differential Equations 10-Smoothing of Data and the Method of Least Squares |
8.2 |
Runge-Kutta Methods |
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8.3 |
Stability and Adaptive Runge-Kutta Methods |
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10.1 |
The Methods of Least Squares |
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14-15 |
12.1 |
Shooting Method |
12-Boundary Value Problems for Ordinary Differential Equations |
12.2 |
A Discretization Method |
Grading Policy
Exam I |
15% |
Exam II |
15% |
Final Exam |
30% |
Computer Assignment & Homework |
40% |
Instructor: Dr. Faisal A. Fairag office: 5-416 Tel: 860-4463 email: ffairag@kfupm.edu.sa
office hours: 3:20- 4:00 Mon OAB
10:15-10:55 Wed. 5-416
Also by appointment