Math 449 - Fall 2012

Section Information

Section Time Location Instructor Office Hours (Cupples I, Room 17)
1 Mon Wed Fri 3:00PM - 4:00PM Cupples I, 218 Renato Feres Tue Thu 12:00PM - 2:00PM

Please include Math 449 in the subject line of any email message that pertains to this course. It will help avoid accidental deletion of your still unread message. My e-mail address is feres@math.wustl.edu.

Topics

Topics include computer arithmetic, number systems and errors; roots of equations; interpolations and splines; least square; numerical differentiation and integration; numerical solution of linear systems, matrix equations, and eigensystems; numerical methods for ordinary differential equations; (time permitting) boundary-value problems and partial differential equations.

Prerequisites: CSE 131 or 200 (or other computer background wit permission of the instructor); Math 217 and 309.)

Text

Numerical Methods Using MATLAB by John H. Matthews and Kurtis D. Fink, fourth edition. I expect that most students will already have some acquaintance with MATLAB, but what you need to get started is minimal and can be learned very quickly. The textbook gives in an appendix a brief introduction to MATLAB. Other reference texts are easily available and you can find plenty of information online.

Homework

Weekly homework assignments will be posted on the above course plan on Fridays and collected the following Friday in class. Late assignments will not be accepted after the solutions are posted (also on the course plan). Please hand your assignments in to the instructor at the beginning of class.

Homework problems will contain a mixture of theoretical problems, often from the textbook, and problems that require computer solutions. The latter must be accompanied by a correct, well-documented computer program, and will be judged for its understandability. Solutions to the theoretical problems should also be written clearly and logically. If a proof is required, it should be complete but concise.

You are allowed (and encouraged) to collaborate on homeworks and to discuss them with me before (or after) the due date.

Exams and grades


Grades will be based on the homework assignments, midterm exam, and take home final. There will be 11 homework assignments, of which the least score will be dropped. Your grade will be calculated as follows: Let H be the total of the 10 best homework scores, out of 100; E1 the midterm score, out of 100; E2 the final exam score, out of 100. Then the final score, S, is given by

S = 0.60*H+0.20*E1+0.20*E2


The final grade will be given according to the following ranges (if the grade distribution of the whole class is significantly lower than usual, then "curving" may be considered, but it is unlikely to be needed):

Numerical Range Letter Grade
[90, 100] A-, A, A+
[80, 90) B-, B, B+
[65, 80) C-, C, C+
[50, 65) D
[0, 50) NCR (F)


In assigning pluses and minuses I will observe the following policy: A+ is reserved for the very top scores, and is given sparingly. I expect that only a very small number of students will received an A+. The ranges of letters B and C will be divided roughly evenly into +, -, and unsigned grade, but the exact ranges will take into account the full set of class scores so as to minimize borderline cases. Therefore, these ranges will not be determined until after the full set of class scores are known at the very end of the course.

Course plan


Week Chapter/Section Assignments
Aug 29 - Aug 31

8/29
8/31
Chapter 1
 Do Assignment 00 on getting started with Matlab.
(It won't be collected and is not for grade.)
This is not necessary if you are already acquainted with Matlab.
Sept 03 - Sept 07

9/3 (Labor Day)
9/5
9/7
Chapter 2
 Homework 1 due 9/07/2012
Solutions
Sept 10 - Sept 14

9/10
9/12
9/14
Chapter 2/3
 Homework 2 due 9/14/2012
Solutions
Sept 19 - Sept 23


9/17
9/19
9/21
Chapter 3
 Homework 3 due 9/21/2012
Solutions
Sept 24 - Sept 28

9/24
9/26
9/29
Homework: 9/28
Chapter 3/4
 Homework 4 due 9/28/2012
Solutions
Oct 01 - Oct 05

10/1
10/3
10/5
Homework: 10/05
Chapter 4
 Homework 5 due 10/05/2012
Solutions
Oct 8 - Oct 12

10/8
10/10
10/12
Homework: 10/12
Chapter 4/5
 Homework 6 due 10/05/2012
Solutions
Oct 15 - Oct 19


10/15
10/17 MIDTERM EXAM
10/19 (Fall break)
Chapter 5
 Mid term exam 10/12/2012
Solutions
Oct 22 - Oct 26

10/22
10/24
10/26
Homework: 10/31
Chapter 5
Oct 29 - Nov 02

10/29
10/31
11/02 (no class today)
Chapter 6
 Homework 7 due 10/31/2012
Solutions
Nov 05 - Nov 9

11/5
11/7
11/9
Homework: 11/9
Chapter 7
 Homework 8 due 11/12/2012
Solutions
Nov 12 - Nov 16


11/12
11/14
11/16
Homework: 11/16
Chapter 9
 Homework 9 due 11/19/2012
Solutions
Nov 19 - Nov 23

11/19
11/21 (Thanksgiving)
11/23 (Thanksgiving)
Chapter 9
 Homework 10 due 12/03/2012
Solutions
Nov 26 - Nov 30

11/26
11/28
11/30
Homework: 11/30
Chapter 9/10
 Homework 11 due 12/07/2012
Solutions
Dec 03 - Dec 07

12/3
12/5
12/7
Homework: 12/07
Chapter 10
 Final due 12/14/2012
Solutions
December 13

FINAL EXAM DUE

Mathematics software

Homework assignments will often contain questions requiring the use of mathematical software. The textbook uses Matlab and this is the sofware I am most familiar with. Other programs such as Mathematica, Maple, R, etc., would also work fine, but I may not be able to provide assistance in using them. GNU Octave works essentially identically to Matlab and is free to download. R is also free.

Matlab is installed in most PCs in the computer lab at Eads, and I believe in the engineering computers. (Presently, I do not know if it is available at the business school computers.) I do not assume that you are already familiar with it.

Here are some links to information about the free software mentioned above:


Renato Feres
feres@math.wustl.edu
Cupples I, Room 17
(314) 935 - 6752 (office phone)

Department of Mathematics
Washington University
Campus Box 1146
Saint Louis
Missouri, 63130 USA.


Last Updated: August 10, 2012