Math 2090 Fall Semester 2016

Numerical Solutions of Ordinary Differential Equations
MWF 11:00-11:50, 524 Thackeray Hall

Office Hours

MWF 3:00 - 4:00, and by appointment
Office: Thackeray 606
Phone: (412) 624 5681

This course is an introduction to modern methods for the numerical solution of initial and boundary value problems for systems of ordinary differential equations, stochastic differential equations, and differential algebraic equations. We will discuss the principal classes of numerical methods and of their theory, including convergence and stability considerations, consistency order, step size selection and adaptivity, the effects of stiffness, geometric integration, invariant and Hamiltonian dynamics.

Written homework and several computational projects will be assigned. The suggested programming language for computer assignments is Matlab, software produced by The MathWorks. The Matlab language provides extensive library of mathematical and scientific function calls entirely built-in. Matlab is available on Unix and Windows in the university computing labs. The full set of manuals is on the web in html and also in Adobe PDF format. The "Getting Started" manual is a good place to begin and is available both in html format and in Adobe PDF format. The full reference manual as well as manuals for each of the many toolboxes are all available.

Course materials

  • Numerical Methods for Ordinary Differential Equations: Initial Value Problems, by David F. Griffiths and Desmond J. Higham.
  • Syllabus
  • Matlab Primer
  • Matlab Tutorial: Postscript; HTML
  • Introduction to Matlab exercises by Dr. Mike Sussman: Preliminaries; Beginning Matlab
    Additional references
  • Solving Ordinary Differential Equations I, Nonstiff Problems, by Ernst Hairer, Syvert P. Nørsett, Gerhard Wanner. Springer.
  • Solving Ordinary Differential Equations II, Stiff and Differential-Algebraic Problems, by Ernst Hairer, Gerhard Wanner. Springer.
  • Geometric Numerical Integration Structure-Preserving Algorithms for Ordinary Differential Equations, by Ernst Hairer, Christian Lubich, Gerhard Wanner. Springer.
  • Numerical Methods for Ordinary Differential Equations, Second Edition, by J. C. Butcher. John Wiley & Sons.
  • Numerical Methods for Ordinary Differential Equations: The Initial Value Problem, by J. D. Lambert. John Wiley & Sons.
  • Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, by Uri M. Ascher and Linda R. Petzold. SIAM.
  • Numerical Methods for Fluid Dynamics, by Dale Durran. Springer.
  • Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations, by Willem Hundsdorfer and Jan G. Verwer. Springer.
  • Numerical Solution of Stochastic Differential Equations, by Peter E. Kloeden and Eckhard Platen. Springer.

  • Homework Assignments

  • Homework 1, Due Wednesday, September 21, 2016: p.17 #1.10, 1.11, 1.14; p.30 #2.2, 2.3, p.40 #3.4, 3.5, 3.7, 3.8; computational project 1
  • Homework 2, Due Monday, October 10, 2016: p.58 #4.3, 4.10, 4.12, 4.13; p.70 #5.2, 5.3, 5.9, 5.12, 5.14; computational project 2
  • Homework 3, Due Wednesday, October 21, 2016: p.89 #6.3, 6.6, 6.17, 6.18, 6.20-bonus; computational project 3
  • Homework 4, Due Friday, November 11, 2016: p. 107 #7.8, 7.10; p. 118 #8.7, 8.12, 8.15; computational project 4
  • Homework 5, Due Wednesday, December 7, 2016: p. 174 #12.1; computational project 5; p. 205 #14.7, 14.8
  • Homework 6, Due Friday, December 16, 2016: p. 223 #15.10; p.241 #16.8; computational project 6

  • Disability Resource Services

    If you have a disability for which you are or may be requesting an accommodation, you are encouraged to contact both your instructor and Disability Resources and Services, 140 William Pitt Union, 412-648-7890 or 412-383-7355 (TTY) as early as possible in the term. DRS will verify your disability and determine reasonable accommodations for this course.

    Academic Integrity

    Cheating/plagiarism will not be tolerated. Students suspected of violating the University of Pittsburgh Policy on Academic Integrity will incur a minimum sanction of a zero score for the quiz, exam or paper in question. Additional sanctions may be imposed, depending on the severity of the infraction. On homework, you may work with other students or use library resources, but each student must write up his or her solutions independently. Copying solutions from other students will be considered cheating, and handled accordingly.

    Statement on Classroom Recording

    To address the issue of students recording a lecture or class session, the University's Senate Educational Policy Committee issued the recommended statement on May 4, 2010. "To ensure the free and open discussion of ideas, students may not record classroom lectures, discussion and/or activities without the advance written permission of the instructor, and any such recording properly approved in advance can be used solely for the student's own private use."