# Math 341 Computational Methods

#### Basic Information

• Dr. Manil Suri, Math/Psych 419, (410) 455-2311, suri@umbc.edu,
office hours: MW 3:30-4:30 or by appointment
• Lectures: MW 1-2:15, Sondheim 109
• Text: Elementary Numerical Analysis by Atkinson and Han (3rd edition)
• Syllabus: 1.1-1.2, 2.1-2.2, 3.1-3.4 (upto page 102), 4.1-4.3, extra material on piecewise polynomial interpolation, 4.7 (and related 7.1 briefly), 5.1-5.3, 6.1-6.5, 8.1-8.5 (time permitting).
• Prerequisites: Math 152 (or 142), Math 221, CMSC 201.

#### Overview and Goals

Problems encountered in mathematics courses such as Calculus generally can be solved by paper and pencil, and yield nice, “closed form” answers in the form of numerical values, functions or formulas. In real world applications, however, problems are seldom so well behaved. For instance, integrals may be difficult or impossible to compute exactly, differential equations may have solutions that can only be expressed as infinite series, and systems of linear equations may be too large to solve by hand. Consequently, a large proportion of problems that mathematicians, engineers, scientists and other professionals “solve” are only done numerically, using computer power. This is what Math 341 introduces you to – various types of computational methods that can be used to tackle an array of mathematical problems (several of which you will have encountered before in other courses).

A common characteristic of these methods is that they are based on approximations of some sort: a numerical value may be replaced by a decimal expansion close to it, a function by a polynomial expansion, a problem by a “nearby” problem that is easier to solve. One of the key issues that we will learn in this course is how to analyze and control the resulting error in our computed answers. The goal will not only be to do this using theoretical means, but to also develop a “computational sixth sense” that will help us decide when computer solutions are to be trusted and when not.

A core component of the course will be to perform computations based on the methods we learn. We will exclusively use Matlab for this. While you may have varying degrees of exposure to this programming language, there will be adequate opportunities to improve your expertise in it as we go along. As a start, please go through Appendix D in the book (while accessing Matlab on a computer terminal) to familiarize yourself with the basics. (Note: You may wish to look into downloading the free software package “Octave” which is for the most part Matlab-compatible.)

To summarize, the main goals of the course are:

• Learning computational methods that will solve problems (integration, differential equations, linear systems, non-linear equations, etc) approximately
• Understanding, analyzing and assessing the errors in approximate solutions
• Gaining experience in performing numerical computations
• Writing and using simple Matlab programs.

#### Tests and Homework

• HOMEWORK is an essential part of the course. It will consist of both computer and paper and pencil problems. Homework for sections completed in any given week (M-W) will be due the next Wednesday. Homework assignments will be posted on Blackboard.
• TESTS will be given twice in the semester. The dates will be announced at least 2 weeks in advance.
• FINAL This will be cumulative. The final will be held on Wed, May 18 from 1-3 pm. Tentatively, this will be in the regular classroom, though it might be held in a computer lab instead.
• MAKE-UPS for tests will only be allowed under special circumstances with written documentation and prior approval if possible. If you miss something, contact me immediately (i.e. on that day) via e-mail (or phone).