Columbia University Fu Foundation School of Engineering and Applied Science

APMA E4300: Introduction to Numerical Methods

Spring 2009

Lectures: Tuesdays and Thursdays, 1:10 - 2:25 pm
Location: 833 S. W. Mudd

Instructor: Edmond Chow
E-mail: <> (the best way to reach me)
Office Hours: No Office Hours on Sat. May 2. Remaining Office Hours: May 7, 1:00-2:30 pm (833 Mudd) and May 9, 2-5 pm (Engineering Library). Call me if you can't find me. Appointments can also be made for other times, and you can also catch me after each class.

Teaching Assistants:
Francois Monard <>, Office Hours: Mondays 3-4 pm
Weiwei Shen <>, Office Hours: Thursdays 3-4 pm
Timur Dykhne <>, Office Hours: Wednesdays 2-3 pm
TA office hours are held in 287 or 292 Engineering Terrace.

Announcements (in reverse chronological order)

Readings

An asterisk (*) denotes helpful but optional readings.

Assignments

Assignments are due at the beginning of class on the date indicated.

Course Description

Introduction to fundamental algorithms and analysis of numerical methods commonly used by scientists, mathematicians and engineers. This course is designed to give a fundamental understanding of the building blocks of scientific computing that will be used in more advanced courses in scientific computing and numerical methods for PDE's. 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

Vector calculus (MATH V1201), Ordinary differential equations (MATH E1210), and Linear algebra (APMA E3101) or their equivalents. A working knowledge of Matlab will also be helpful.

Topics

Topics will be covered in approximately this order:

Grading

50% Assignments (7 during the semester)
20% Midterm (Tue Mar 10, in class)
30% Final (Projected date: Tue May 12, 1:10 pm, 3 hours)

The Final Exam will cover material from the entire semester. Late assignments will not be graded except in exceptional circumstances (with documentation). Requests for regrading of assignments or exams must be accompanied by a written justification. Be careful that regrading in many cases can result in your grade going down!

Textbook and References

Required Text

Our in-class lectures will approach the material differently than the presentation in the textbook and thus you will have at least two perspectives on our topics. I will make a lot of references to the textbook, such as what sections to read to complement the lectures and what problems to try in the textbook. This is admittedly an expensive textbook, but it is also very clearly written.

As the subtitle of the textbook says, this book is both an introduction and a survey. As a survey, it covers about twice as many topics as we can cover in class. After this course is over, however, the text will also serve as a great reference and starting point for additional techiques for your work or research (if you decide to hold on to the book!). As an introduction, the text generally does not take topics to the same depth as many other textbooks, particularly in analysis. Thus we will generally cover methods and techniques not in the text (especially when we study the numerical solution of ODE's) and I will provide additional resources in these cases.

Supplementary Text

Some of the material in our course is covered in more detail in this supplementary text than in the required text. The authors are letting us use this text for free! (I'm sure you did not want to buy a second textbook!) Selected chapters are available on the CourseWorks web site for this course, and I will add more if necessary. 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

Matlab Resources