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# MATH 649 (04779), Spring 2009

## 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 544 and (541 or 549 or 645A)
Instructor:
Martin J. Mohlenkamp, mohlenka@ohio.edu, (740)593-1259, 315B Morton Hall.
Office hours: Monday 9:10-10am, Tuesday 9:10-10am, Thursday 9:10-10am, and Friday 9:10-10am.
Web page:
http://www.ohiouniversityfaculty.com/mohlenka/20093/649.
Class hours/ location:
MTuThF 12:10-12m in 313 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:
There are relatively few homework problems in the book, so we will attempt to do the majority of them. 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.
The exact problem numbers and due dates will be announced as we go.
Project:
You will do a written report and give a presentation on a project such as:
• Applying the methods we learned to a problem from your research or another class.
• Analyzing and presenting a research paper published in 2008 or 2009 on the numerical solution of differential equations.
• Summarizing and presenting one of the chapters in the book that we did not cover.
Tests:
There will be one mid-term test, in class.
Final Exam:
The final exam is on Friday, June 12, at 12:40pm in our regular classroom.
Your grade is based on homework 50%, test 15%, final exam 20%, and project 15%. 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.
Week Date Topic/Materials Skill/Homework/Test
Text Other
1 March 30 Introduction
1: Euler's method and beyond
March 31 1.1 Numerical ordinary differential equations; Lipschitz continuity read chapter 1
April 2 1.2 Euler method Mathematical autobiography due
April 3 1.3 homework problem numbers to be announced
2 April 6 1.4
2: Multistep methods
April 7 2.1 Linear multistep method read chapter 2
April 9 2.2
April 10 2.3 Layout skill starts
3: Runge-Kutta methods
April 16 3.2 Explicit and implicit methods
April 17 3.3 Flow skill starts
4 April 20 3.4
April 21
4: Stiff equations
April 23 4.1 Stiff equation read chapter 4
April 24 4.2 Logic skill starts
5 April 27 4.3
April 28 4.4
April 30 Review
May 1 Test on Chapters 1-4
8: Finite difference schemes
6 May 4 8.1 Poisson's equation; Discrete Poisson equation; Finite difference read chapter 8 (drop deadline with WP/WF)
May 5 8.2
May 7 8.3
May 8 Intros skill starts
16: The diffusion equation
7 May 11 16.1 Diffusion equation read sections 16.1-3
May 12 16.2
May 14 16.3 read sections 16.4-6
May 15 16.4 Symbols skill starts
8 May 18 16.5
May 19 16.6 Project outline due
17: Hyperbolic equations