Syllabus for Math 310 Numerical Analysis (UAF, Bueler, Fall 2012)

Math 310 Numerical Analysis

Fall 2012, UAF

Instructor: Ed Bueler
Office Hours online: Chapman 301C
http://www.dms.uaf.edu/~bueler/
474-7693 elbueler@alaska.edu

Time: MWF 10:30--11:30am
Place: Gruening 202
Text: A. Greenbaum and T. Chartier, Numerical Methods:
Design, Analysis, and Computer Implementation
of Algorithms, Princeton 2012.

This course will introduce you to numerical analysis. You'll learn methods for solving certain problems of applied mathematics on computers, and why those methods work. We will reconsider and solve problems in calculus, linear algebra, and differential equations, and in areas that are new to you.

You will be expected to understand both the theory and the practice of numerical analysis. Both theory and practice will be learned through lecture, homework and exams. Some problems will ask you to explain a concept and some to demonstrate an idea by a short hand calculation. We will use the mathematical programming language Matlab (or the free equivalent Octave) from the beginning, and on every assignment. On the homework you will be expected to turn numerical algorithms into functioning programs.

A combination of lectures and homework together make up the core of the class. Getting the most out of both of these is your responsibility. I have a responsibility to make them worth your time. You should ask questions in class, about the lecture content and about homework assignments.

Exams, Homework, and Grade: 60% of your grade will be determined by in-class, closed-book exams:

25%
35%

Midterm Exam
Final Exam

Friday, Oct. 26 (in-class)
Friday, Dec. 14, 10:15 am--12:15 pm (in-class)

40% of the grade will be determined by approximately 10 graded homework assignments. These will combine book exercises and, as stated above, use of Matlab.

The course grade will be determined by points on the exams and homework, according to the schedule at right --->

The schedule represents a guarantee. I will use plus/minus grades as illustrated. Percent
93 - 100 %
90 - 92 %
87 - 89 %
82 - 86 %
79 - 81 %
76 - 78 %
68 - 75 %
65 - 67 %
60 - 64 %
57 - 59 %
0 - 56 %
Grade
A
A-
B+
B
B-
C+
C
D+
D
D-
F

Prerequisites: Calculus (through Math 202 Calculus III), plus either Math 302 Differential Equations or Math 314 Linear Algebra. The catalog also says "knowledge of programming" is recommended, and that is true, but your knowledge can be pretty shallow. But you must not be afraid to start playing with short programs from the first day. You must be willing and able to start learning Matlab immediately. This turns out to be pretty easy for students who take responsibility for it immediately.

Matlab tutorial: I do not assume that you are familiar with Matlab already. It has an interpreted environment with straightforward plotting and data viewing commands. It really excels at making vector and matrix operations easy. The textbook starts with a great tutorial introduction, and the first assignment focusses on getting started with Matlab. The true programming content of this class is small. An elementary understanding of loops ("for" loops) and conditionals ("if" statements), and of functions/procedures, is all that is needed. For the homework you will be expected to turn numerical algorithms into functioning Matlab programs.

Getting a copy of Matlab or Octave:

Matlab is available in a fully-functional student version you can use on any computer you have (about $100 direct from Mathworks at www.mathworks.com/products/studentversion). UAF has a site license so Matlab can be installed for free on any university machine; you should call OIT at 450-8300 and request this. It is already available at some locations on campus.
Octave is free and the syntax and commands are the same. Its graphics and toolboxes are not quite as capable as their Matlab versions, but I use Octave for my professional work. All codes in the class will be developed in Octave and checked for functionality in Matlab. Get Octave at http://www.gnu.org/software/octave/. Binaries for Windows and MacOSX are at http://octave.sourceforge.net/. Linux people should get it through a package manager. Online documentation for Matlab works fine as documentation for Octave.

Supplementary text: There is a very nice, easy, free book by Cleve Moler, the Matlab creator:
C. Moler, Numerical Computing with Matlab
http://www.mathworks.com/moler/index_ncm.html
It is not quite a good text for the course---it does not quite have the mathematical ideas---but it is fun. Moler is a great "role model" to follow for actual numerical programming. You can download individual chapters as PDF or you can buy a copy through SIAM Press. We will use some of the programs from this book.

Policies and Makeup exams: The Dept of Mathematics and Statistics has reasonable policies on incompletes, late withdrawals, early final examinations, etc. See www.dms.uaf.edu/dms/Policies.html. You are covered by the UAF Student Code of Conduct. I will work with the Office of Disabilities Services (203 WHIT, 474-7043) to provide reasonable accommodation to student with disabilities. I will create makeup versions of the Exams if necessary, provided you have a convincing reason for me to do so and you let me know at least two class days before the exam.