Math 310 : Numerical Analysis

Fall 2002, UAF

Instructor: Ed Bueler
Office: Chapman 301C. 
Office hours are online and on the back of many assignments.
Phone: 474-7693, eMail: ffelb@uaf.edu 		Class Time:  MWF 10:30 -- 11:30 am Chapman 104
Text: Cheney & Kincaid, Numerical Mathematics and Computing, 4th ed.
Web Site: www.math.uaf.edu/~bueler/

The Course and Grade:  This course will introduce you to numerical analysis and methods. You will be expected to understand both the theory and the practice of the topics we study. Calculus and some exposure to differential equations, to matrices, and  to programming are assumed. We will use the mathematical programming language Matlab from the beginning, and on every assignment.
    Three hourlong in-class exams will be given, with the last being at the final time but for one hour.  In the second half of the semester a substantial final project will represent your own interests.  Weekly homework makes up the remainder of the grade:
Part
Exams
 
 
Project
Homework		 Grade-Fraction
15%
15%
15%
25%
30%		 Dates
Monday Oct. 14
Friday Nov. 15
10:15-11:15 am Dec. 18 (Final Exam time)
Due 10:15 am Dec. 18 (Final Exam time)
weekly

Topics: The Project:  The topic for your project is yours to choose! More information will be given at the time the projects are assigned (mid October) but a brief description here may encourage you.  The topic may be close or not so close to those covered in class. As an example, suppose you chose to study stiff differential equations. You could, with this topic: (1) give a variety of algorithms for and examples of stiff equations, (2) study a particular stiff set of equations coming from an applied problem and come up with the best numerical solution, or (3) examine the theory of stiffness and present some theorems.
    I will want a proposal for your project around Nov. 1 (details at the appropriate time), and I reserve the right to disapprove or to recommend changes. I expect that we discuss your project as you work on it, even if only by email. And there will be a limit on the amount of program code you can include in your project--say, four pages--so that numerical analysis and not programming is the focus of your work. The grade for the project will be determined by both the quality of the work and the difficulty of the topic.

Programming in this course:  The true programming content of this class is small. An elementary knowledge of looping and array syntax will be what is required.  
    For both the project and homework you will be expected to turn numerical algorithms into functioning programs.  You will use Matlab unless you make a strong argument to me that you can do what is needed in some other language.  Matlab is available in a student version ($99 direct from Mathworks at www.mathworks.com/products/studentversion ) and free in the Chapman 103 lab and other locations on campus. Matlab has an interpreted environment with straightforward plotting and data viewing commands, but it really excels at making vector and matrix operations very easy.  Matlab tutorial:   I don’t assume that you are familiar with Matlab already. It is easy to learn, even if you have no exposure to serious programming. For the first few weeks of the course, I will offer a tutorial, partly in class, to help you get started. It will be in the Chapman 103 lab.  See www.math.uaf.edu/~bueler/MatlabEx.htm for a brief online tutorial.

Numerical Recipes:  Please examine (and perhaps consider buying) Numerical Recipes, by Press, et. al. It is a "Recommended" text for this course, available in the bookstore. I have also put it on reserve at the library. Any edition and either language, i.e. in C or in Fortran, will do since it is the explanations not the code which really matter. The entire book is available section by section on the web at www.nr.com , including the source for programs as printed in the book.

Policies and makeup exams:   The department has reasonable policies on incompletes, late withdrawals, early final examinations, etc.  See www.dms.uaf.edu/dms/Policies.html .  Note that you are covered by the UAF Student Code of Conduct (p. 22 of the catalog and at www.uaf.edu/catalog/current/undergrad/regs3.html#Student_Code_of_Conduct ).
    I will create makeup versions of the exams if needed, but you must let me know at least two class days before the exam.  The makeup must occur no later than two class days after the exam date.

Prerequisites and related Courses:    At least one of Math 302 Differential Equations or Math 314 Linear Algebra is the prerequisite.  Both differential equations and linear algebra are topics here, but it is possible to function in this class if one has a bit of exposure to one and more substantial exposure to the other.  There is no course which represents the programming requirement, and indeed almost no programming theory or data structures are required.  But you must be able to write a program that inputs from and outputs to the user, and (for instance) a program that tests if a number is prime.  See me soon if you are worried about these prerequisites.
    There are two related courses, ES 301 Engineering Analysis and PHYS 220 Introduction to Computational Physics, which relate to this course.  Both of those are about how to use computers to apply mathematics to engineering/physics problems, as is MATH 310.  Questions of why procedures work and how fast and how accurately will be much more prominent in MATH 310.