MATH 4640

**Lectures:** MWF 1:05-1:55 pm

**Location:** Weber SST III, Lecture Room 1

**Instructor:** Edmond Chow

**E-mail:** (the best way to reach me)

**Office Hours:** Thursdays 3-5 pm in Klaus 1332 (or by appointment)

** Grader:** Huang Huang,

**Grader's Office Hours:** Wednesdays 3:30-4:30 pm in Skiles 140 (or by appointment)

Introduction to fundamental algorithms and analysis of numerical methods commonly used by scientists, mathematicians and engineers. Topics include numerical solutions of algebraic systems, linear least-squares, eigenvalue problems, solution of non-linear systems, interpolation, numerical integration and differentiation, initial value problems and boundary value problems for systems of ODE's. All programming exercises will be in Matlab.

**Prerequisites**

Linear and Discrete Mathematics (MATH 2602) and Differential Equations (MATH 2403/2413). Experience with Matlab or some other form of computer programming is highly recommended.

**Topics**

Topics will be covered in approximately the following order. If there is time, we will additionally introduce optimization methods and numerical methods for solving partial differential equations.

- Introduction, Matlab overview
- Error analysis I: truncation error, roundoff error, and floating point computation
- Solution of nonlinear equations
- Solution of linear systems (key topic: 2 weeks)
- Error analysis II: stability, conditioning, and backward error
- Large-scale linear systems and systems of nonlinear equations
- Polynomial interpolation and splines
- Numerical differentiation
- Numerical integration
- Numerical solution of ordinary differential equations (key topic: 2 weeks)
- Solution of two-point boundary value problems
- Least squares problems
- Matrix eigenvalue problems

**Grading and Due Dates
**

50% assignments (6 during the semester)

10% In-class Exam 1

15% In-class Exam 2

25% Final exam (Wed. Dec. 15, 2:50-5:40 pm)

Assignment 1 due - Sep 10

Assignment 2 due - Sep 24

Exam 1 - Oct 1

Assignment 3 due - Oct 15

Assignment 4 due - Oct 29

Assignment 5 due - Nov 12 (new date)

Exam 2 - Wed Nov 17 (new date)

Assignment 6 due - Dec 3

Final Exam - Dec 15

Your lowest grade out of the 6 assignments will be dropped from computing your final grade.

Requests for regrades of assignments or in-class exams must be submitted with a written explanation within a week of receiving back your assignment or exam. Note that your grade may decrease as well as increase after a regrade.

**Assignments**

Assignment deadlines are 5 pm on the due dates above, submitted at the grader's office (Skiles 140). You can also hand in your assignment at the beginning of class on the due date.

Late assignments. If you are ill, you can have a one-week extension on the assignment deadline, provided you have a doctor's note dated the same week. There is no need to send me e-mail beforehand, but attach your doctor's note to your assignment. Otherwise, late assignments are not accepted (since you only need to submit 5 of the 6 assignments).

**Exams**

The exams are cumulative, i.e., they cover all the material studied so far, and in particular, all material covered in lectures, readings, and assignments.

The in-class and final exams will be closed-book, but you are allowed the following cheat sheets: One page (one side) for Exam 1, One page (both sides) for Exam 2, Two pages (all four sides) for the Final Exam. This allows you to reuse your earlier cheat sheets or create new ones from scratch (you won't be required to hand in your cheat sheets). If you wish to typeset your notes (rather than handwrite them), the font size must be 12 points or larger. In the past, students have found it easier to handwrite rather than spend time typesetting formulas.

In addition, for the exams you are allowed to use a non-programmable and non-graphing scientific calculator.

**Textbook**

- Uri M. Ascher and Chen Greif, A First Course on Numerical Methods

Electronic copies of the textbook will be generously provided by the authors for our class at no cost. Please do not distribute the files for this text outside of class. The text is not yet published and, in return for the authors' generosity, it would be nice if we could give them our comments and suggestions on the text (I can collect your comments or you can write to the authors directly at the end of the course).

**Additional References**

- Michael T. Heath, Scientific Computing: An Introductory Survey, 2nd edition. The text also has very useful online learning tools (follow the web link).
- Cleve Moler, Numerical Computing with Matlab. Chapters of this book are available for free.

**Matlab Resources**

Georgia Tech College of Computing

KACB 1332

(404) 894-3086