Mathematics 331 (631)
 
Scientific Computing I

OFFICE HOURS:    Mon/Wed 1:00-2:00
Course Description
Prerequisites: Math 221, 224, and Computer Science 101 or equivalent. Errors. Curve fitting and function approximation, least squares approximation, orthogonal polynomials, trigonometric polynomial approximation. Direct methods for linear equations. Iterative methods for nonlinear equations and systems of nonlinear equations. Interpolation by polynomials and piecewise polynomials. Numerical integration. Single-step and multi-step methods for initial-value problems for ordinary differential equations, variable step size. Current algorithms and software.
Textbook
Numerical Analysis (7th edition), Richard L. Burden and J. Douglas Faires

 
Software (must be able to access and use at least one of these)<>
MATLAB, Mathematica, Maple, FORTRAN, C++


Course Grade
The Lagniappe semester grade will be based on 2 homework assignments (30%), one in-class exam (30%), and a take-home final exam (40%).


Course Content
We will cover part or all of these sections in the textbook:


CHAPTER 1 and 2 HOMEWORK DUE TUESDAY MAY 30


Chapter 1 - Matematical Preliminaries

    1.1, 1.2, 1.3
Chapter 1 Homework
1.1: 1c, 3c, 4c, 9
1.2: 1b, 2b, 4b, 5h, 6 (repeat 5h only), 11, 21
1.3: 3a, 4, 6c, 7b,13a, 16


Chapter 2 - Solutions of Equations in One Variable

    2.1, 2.2, 2.3, 2.4

Chapter 2 Homework
2.1: 3c, 5, 7a, 12
2.2: 5, 7, 11a, 12a
2.3: 1, 3, 6c, 19a, 24
2.4: 1b, 2 (repeat 1b only), 6, 8





Chapter 3 - Interpolation and Polynomial Approximation
 
    3.1, 3.2, 3.3, 3.4


NOTE: ALL PROBLEMS BELOW ARE FROM EDITION 7, CORRESPONDING EDITION 8 NUMBERS MAY VARY

Chapter 3 Homework
3.1: 1b, 2 (repeat part b only), 5, 13, 18
 3.2: 5, 7, 13, 16
3.3: 1a, 2 (repeat part a only), 5 (repeat part a only and use whatever software you like)
3.4: 11

 Chapter 4 - Numerical Differentiation and Integration
   
    4.1, 4.2, 4.3, 4.4, 4.6, 4.7


Chapter 4 Homework
4.1: 1a, 3a, 4 (repeat 3a), 14
 4.2: 1d, 8
4.3: 1e, 3 (repeat 1e), 7, 9, 10
 4.4: 4, 5, 16a 
 4.6: 1c, 2 (repeat 1c)
4.7: 1c, 2 (repeat 1c)

Chapter 5 - Initial-Value Problems for Ordinary Differential Equations

    5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.10, 5.11

DUE LAST DAY OF CLASS:

4.4: 22 (7th Edition), or 26 (8th Edition)
5.5: 5