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.ohio.edu/people/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:
    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.
    Grade:
    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.
    Academic Dishonesty:
    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:
  • Your classmates are your best resource. Use them!
  • 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
    Last modified: Mon Dec 27 14:52:19 EST 2010