Introduction to Numerical Analysis I (Math 5610/6860) – Fall 2016

Lecture : MTW LCB 215 and Th AEB 350 all meet 10:45 AM– 11:35 AM

Instructor: Aaron Fogelson, LCB312, phone 581–8150, email: fogelson@math.utah.eduOffice hours: M 9:30-10:30, T 9:30-10:30, W 12:00-1:00

Course Web Site: http://www.math.utah.edu/~fogelson/5610_f16

Text: Kendall E. Atlinson, An Introduction to Numerical Analysis, 2nd Edition.

Material Covered:

1. Introduction, Errors, Floating Point Arithmetic.

2. Solving nonlinear scalar equations and systems of nonlinear equations.

3. Interpolation by polynomials, splines, and trigonometric polynomials.

4. Other approximation problems including least squares and minimax.

5. Numerical integration.

6. Direct methods for solving linear systems Ax = b.

7. Iterative methods for solving linear systems.

8. Some methods for calculating eigenvalues/eigenvectors of large matrices.

Problem Sets: Homework will consist of problems sets. Some problems will involveanalysis (paper and pencil) and some will involve writing programs and doingcomputations. Expect a problem set to be handled out weekly and to be duea week later. Homework is due when stated, late work will generally not beaccepted. You may consult with other students in the class, after you have thoughthard about the problems yourself. Each student should submit an individuallywritten solution set. Homework answers should be complete and written neatly.(If I can’t read it, it won’t count.) Answers will be posted online at the courseweb site. Check the course web site for homework assignments if you miss class.

Computing: MATLAB (or OCTAVE) will be used for some homework assignments.They are available on all Mathematics Department computers. A fairly inexpen-sive student version of MATLAB can be purchased if you want to install it on yourlaptop or desktop at home. Alternatively there is a free program called OCTAVEwhich has been designed to work like MATLAB and which has many of the fea-tures of MATLAB. It is also avialable on all Mathematics Department computers.You can find out about OCTAVE, including how to download a copy, by search-ing for octave.org. I do not plan to give lectures on how to use MATLAB (orOCTAVE) and you are expected to become familiar with it by working throughonline tutorials if you are not already experienced with it.

Evaluation: Homework Problems: 50%, Midterm Exam 20%, Final Exam 30%

Prerequisite: Prior work in multivarible calculus and linear algebra. For the sequel,5620 prior work in ordinary differential equations will be needed.

ADA Statement: The Americans with Disabilities Act requires that reasonable ac-commodations be provided for students with physical, sensory, cognitive, systemic,learning and psychiatric disabilities. Please contact me at the beginning of thequarter to discuss any such accommodations for the course.