Math 448 Course Policies

Numerical analysis--the science (and art) of using computers to find approximate solutions to problems in science, mathematics, or engineering for which the exact solution is either unattainable or is too tedious to obtain by exact methods.

Syllabus

Professor

Dr. Carla Martin
112 Roop Hall
Email: carlam (at) math (dot) jmu (dot) edu

Class Time

TuTh 2:00-3:15pm, Roop 105

Office Hours

Held in Roop 112:
Tues/Thurs 11:30am-2pm

Office hours are for going over problems that you are having with homework, tests, or lectures you have attended. They are not for making up missed lectures. Coming to class is your responsibility and lecture material will be crucial to course development and your success.

Required Materials

Scientific Computing, An Introductory Survey, 2nd Ed., by Michael T. Heath

USB memory stick used to transfer your computer programs between computers when working in the computer lab

(Optional): Matlab Software (Student Version). Available at Campus Bookstore.

Course Description

Math 448 revisits many themes of Math 248 in greater depth, with more emphasis on mathematical analysis, and with an enlightened eye toward algorithm improvement and refinement of techniques. Specifically, topics include error propagation and analysis of error, stability and condition, numerical linear algebra (including iterative methods), approximation methods (e.g., spline interpolation and least-squares techniques), numerical integration techniques, and time-permitting, additional topics such as digital filtering. Unlike Math 248, no class time will be devoted to computer programming per se; that is, students are expected to bring modest programming proficiency to the class. Most, if not all, of the numerical techniques to be studied are of practical utility.

Math 449 will extend the notions of 448 to the numerical solution of ordinary and partial differential equations.

Technology

Reasonable proficiency in a high-level programming language such as Matlab (preferred), Fortran 90, or C is expected.

Computer labs with Matlab and Fortran are Miller G080, Burruss B030, Burruss B130, and Roop 103. If desired, an account on a Linux server is availabe for you with Matlab and Fortran. See me for details.

Grading

Homework (mostly-weekly)30%
Programming Assignments (2)30%
Midterm Exam20%
Final Exam20%

Note: All assignments factor into your grade. This means: no grades will be dropped.

Your weighted average (as a percentage) determines your grade for the class on the standard 10pt scale (i.e. 100-90 = A to A-, 89-80 = B+ to B-, 79-70 = C+ to C-, 69-60 = D, below 60 = F). The grades for this class are generally not curved.

Extra Credit is available for attending the Department Colloquia on Monday afternoons. If you attend one or more of these colloquia, write a short paragraph summarizing the seminar and turn in for +1/2 point extra credit on a HW score.

Assignments

Lecture attendance is required, although attendance will not be recorded. The homework assignments will require a combination of written exercises and programming. The exercises will involve the design and analysis of algorithms and will require mathematical proofs in some cases.

Homework assignments will be accepted one date late with 20% penalty. No homework will be accepted more than one day past the due date. Late projects will not be accepted.

There will be two programming projects. These are of a larger-scale than the weekly HW assignments. To prepare you for your up and coming entrance into the real world, the final product of these projects will be an oral presentation. You will also have the opportunity to present the first project as a poster in the upcoming SUMS Conference on Saturday, October 18. There will be a midterm and a final. The final will be comprehensive, but will emphasize the material covered after the midterm.

Academic Integrity

Honesty with oneself and with others is of utmost importance in life. We will strictly abide by the JMU Honor Code. Any breach of the honor code results in failure in this course. I encourage working in groups but not copying in groups. Functionally or logically identical programs are considered violations of the honor code to be prosecuted rigorously. If you have any questions about what does or does not fit under the umbrella of academic integrity, please contact me.