• This web page describes an activity within the Department of Mathematics at Ohio University, but is not an official university web page.
• If you have difficulty accessing these materials due to visual impairment, please email me at mohlenka@ohio.edu; an alternative format may be available.

# MATH 649 (04992), Winter 2011

## Numerical Analysis: Differential Equations

Catalog Description:
In-depth treatment of numerical methods for ordinary differential equations; introduction to methods for partial differential equations.
Desired Learning Outcomes:
Students will be able to:
• Utilize numerical algorithms for solving differential equations.
• Analyze the convergence, stability, accuracy, and efficiency of such algorithms.
• Prove the fundamental theorems upon which such analysis is based.
• Prerequisites:
MATH 545. You can substitute 544 and (560A or 541 or 549 or 645A)
Instructor:
Martin J. Mohlenkamp, mohlenka@ohio.edu, (740)593-1259, 315B Morton Hall.
Office hours: MTuWThF 2:10-3pm.
Web page:
http://www.ohiouniversityfaculty.com/mohlenka/20112/649.
Class hours/ location:
MTuWThF 3:10-4pm in 322 Morton Hall.
Text:
A First Course in the Numerical Analysis of Differential Equations (Cambridge Texts in Applied Mathematics) (Paperback), by Arieh Iserles; Cambridge University Press; 2nd edition (December 29, 2008) ISBN-10: 0521734908, ISBN-13: 978-0521734905.
Homework:
You will do a couple of problems from the book each week. To build your mathematical writing skills:
• Your solutions must be typeset in LaTeX, on which you will be given assistance.
• We will use the Good Problems program of skill handouts.
Presentation:
During the final couple of weeks, you will be assigned a section (or half a section) in the book to present as if you were giving a formal seminar. You will use LaTeX (e.g. slides or beamer documentclass) to prepare pdf for slides, and only use the blackboard for unexpected questions.
Tests:
There will be one mid-term test, in class.
Final Exam:
The final exam is on Wednesday, March 16, 2:30-4:30pm in our regular classroom.
Your grade is based on homework 50%, test 20%, final exam 20%, and presentation 10%. An average of 90% guarantees you at least an A-, 80% a B-, 70% a C-, and 60% a D-. Grades are not the point.
Attendance:
Attendance and participation is very important in this course, since the learning model is based on group in-class activities. I do not count attendance in your grade, since absences will penalize you through your loss of learning.
On the homework you may use any help that you can find, but you must acknowledge in writing what help you received and from whom or where. The test and final exam must be your own work, and without the aid of notes, etc. Dishonesty will result in a zero on that work, and possible failure in the class and a report to the university judiciaries.
Special Needs:
If you have specific physical, psychiatric, or learning disabilities and require accommodations, please let me know as soon as possible so that your learning needs may be appropriately met.
Learning Resources:
• LaTeX, Python, and Matlab resources.
• ## Schedule

Subject to change, especially the exercise due dates.
Week Date Section Skill/Homework/Test
1
January 3 Introduction
1: Euler's method and beyond
January 4 1.1 LaTeX skill starts
January 5 1.2 Mathematical autobiography due (LaTeX template)
January 6 1.3
January 7 Exercise 1.2
2
January 10 1.4
2: Multistep methods
January 11 2.1 Layout skill starts
January 12 2.2 Exercise 1.5
January 13 2.3
January 14 Exercise 2.1
3
January 17 Martin Luther King, Jr. Day holiday
3: Runge-Kutta methods
January 18 3.1 Flow skill starts. (drop deadline)
January 19 3.2 Exercise 2.6
January 20 3.3
January 21 Exercise 3.2
4
January 24 3.4
January 25 Logic skill starts
4: Stiff equations
January 26 4.1 Exercise 3.8
January 27 4.2
January 28 Exercise 4.4
5
January 31 4.3
February 1 4.4
February 2 Exercise 4.8
February 3 Review
February 4 Test on Chapters 1-4
6
8: Finite difference schemes
February 7 8.1 (drop deadline with WP/WF)
February 8 8.2 Intros skill starts
February 9 Exercise 8.1
February 10 8.3
February 11 Exercise 8.6
7
16: The diffusion equation
February 14 16.1
February 15 16.2 Symbols skill starts
February 16 Exercise 16.1
February 17 16.3
February 18 Exercise 16.4
8
February 21 16.4
February 22 16.5 Graphs skill starts
February 23 Exercise 16.9
February 24 16.6
February 25 Exercise 16.11
9
17: Hyperbolic equations
February 28 17.1 Presentations start?
March 1 17.2
March 2 Exercise 17.4
March 3 17.3
March 4 Exercise 17.7
10
March 7 17.4
March 8 17.5
March 9 Exercise 17.12
March 10
March 11 Review Exercise 17.15
12
March 16 Wednesday 2:30-4:30pm, Final Exam

Martin J. Mohlenkamp