Math 685/CSI 700/OR 682/STAT 682, Numerical Analysis (Spring 2007)

Monday, 4:30pm - 7:10pm, Robinson B220

Instructor: Daniel M. Anderson (231 Science and Technology I, 703.993.1482, danders1@gmu.edu)
Office Hours: Monday/Wednesday 2:30PM-4:00PM, and by appointment.

Text: Scientific Computing: An Introductory Survey (Second Edition) by Michael T. Heath.

Prerequisites: Sufficient recall of undergraduate linear algebra, differential equations and computer literacy including familiarity with Matlab.

Course Description: This course will cover the fundamental concepts of numerical methods for scientific computing. Students will learn how computational methods are constructed, and how they are used to solve problems arising from the sciences and engineering.

Homework: Homework will include problems assigned from the book and problems that will require the use of Matlab. More specific instructions will follow.

Grading Policy: The course grade will be based on homework (50%), a midterm exam (20%) and the final exam (30%).

Topics Covered/Schedule (approximately 1 chapter per week with a few exceptions)
Chapter 1 : Scientific Computing
Chapter 2 : Systems of Linear Equations
Chapter 3 : Linear Least Squares
Chapter 4 : Eigenvalue Problems
Chapter 5 : Nonlinear Equations
Chapter 6 : Optimization
Chapter 7 : Interpolation
Chapter 9 : Initial Value Problems for ODEs
Chapter 10 : Boundary Value Problems for ODEs
Chapter 12 : Fast Fourier Transform

FINAL EXAM: (Monday, May 14, 4:30-7:15pm)

Honor System: It is expected that each student in this class will conduct himself or herself within the guidelines of the Honor Code. All academic work should be done with the level of honesty and integrity that this University demands.

Help With Computing:

Set up an account on osf1.gmu.edu

Help with Matlab

Further Matlab Tips

Example Matlab m-file and function m-file
[sam_mfile.m]
[f1.m]

Schedule/Reading/Homework

1/22: Chapter 1: Scientific Computing, Homework 1: Exercise 1.6: Computer Problems 1.4, 1.7 (Due: Monday, January 29)

1/29: Chapter 2: Systems of Linear Equations, Homework 2: Exercises 2.7, 2.11 (in Matlab), 2.17: Computer Problems 2.1, 2.6 (Due: Monday, February 12)

2/5: Chapter 2: Systems of Linear Equations,

2/12: Chapter 3: Linear Least Squares, Homework 3: Exercises 3.1, 3.5, 3.14: Computer Problems 3.1 (Due: Monday, February 19)

2/19: Chapter 4: Eigenvalue Problems, Homework 4: Exercise 4.3: Computer Problems 4.4, 4.6 (Due: Monday, February 26)

2/26: Chapter 5: Nonlinear Equations Homework 5: Exercise 5.6, Computer Problems 5.2, 5.3a,b (also apply Newton's Method to the function f(x)=x^2 + 4 x + 4) (Due: Monday, March 5)

3/5: Chapter 5/6: Nonlinear Equations + Optimization, Homework 6: Exercises 6.5a,b, 6.8; Computer Problem 6.9a (Due: Monday, March 19)

3/19: Chapter 7: Interpolation, Takehome Midterm Exam (Due: 3/26/07)

3/26: Chapter 9: Initial Value Problems for ODEs Chapter 9 Homework Part 1 (Due: Monday, April 2)

4/2: Chapter 9: Initial Value Problems for ODEs Chapter 9 Homework Part 2 (Due: Monday, April 9)

4/9: Chapter 9/10: Boundary Value Problems for ODEs Chapter 10 Homework Part 1 (Due: Monday, April 23)

4/16: No class: Read Chapter 10 on Boundary Value Problems

4/23: Chapter 10: Boundary Value Problems for ODEs: Homework 10: Solve the previous homework problem using the collocation method (see previous homework for details) (Due: Monday, April 30)

4/30: Chapter 12: Fast Fourier Transforms Homework 11: TBA (Due: TBA)

5/7: Take-Home Final Exam to be distributed

5/14: Final Exam Due

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