Instructor: Prof. Hans De Sterck, office: MC5016, email: hdesterck@uwaterloo.ca
Lectures: 9:30-10:20MWF (MC 4042)
Office hours: 4:00-5:00Th (MC5016)
TA: Paul Ullrich, office: MC5133, email: paullric@math.uwaterloo.ca
Office hours: 12:30-1:30W (MC5133)
Course Objectives:
Systems of ordinary differential equations (ODEs) are widely used to model processes in a variety of application domains, including weather forecasting, control engineering, biology and finance. This computational mathematics course gives a solid introduction to the numerical methods used to solve systems of ordinary differential equations on computers.
The goal of the course is threefold. You will receive a solid introduction to the theory of numerical methods for differential equations (with derivations of the methods and some proofs). You will learn to implement the computational methods efficiently in Matlab, and you will apply the methods to realistic problems in several fields.
Prerequisites: CM 271 / CS 371 / AMATH 341 or permission of the instructor (N.B. this will require good grades in CS 370 or both MATH 237/247 and MATH 235/245)
Tentative Outline:
I. Introduction to ODEs and Numerical Methods (12 lectures)
II. Linear Multistep Methods for Scalar Initial Value Problems (8 lectures)
III. Nonlinear One-step Methods for Scalar Initial Value Problems (3 lectures)
IV. Methods for Systems of Initial Value Problems (4 lectures)
V. Adaptive methods (3 lectures)
VI. Methods for Boundary Value Problems (4 lectures)
VII. Stochastic ODE Methods (2 lectures)
Course Material: Class lectures are the primary source of material for the course. Course notes are available for part of the course.
Course Website: the ACE system will be used extensively for all course communications.
Reference Material:
Books on reserve in library:
1. Introduction to numerical computation : analysis and MATLAB¨ illustrations, Lars Elden et al., Studentlitteratur, 2004. (on 1-day reserve in Davis library) (Chapter 10 covers part of what we will learn in this class. This book is also a recommended general reference book for Computational Mathematics methods; available in UW bookstore, and CDN$ 41 or US$39 online.)
2. A first course in the numerical analysis of differential equations, Iserles, Cambridge University Press, 1997. (Chapters 1-6) (on 1-day reserve in Davis library)
3. Numerical analysis, Burden and Faires, Thomson Brooks/Cole, 2003-2004-2005. (Chapters 5, 11) (on 1-day reserve in Davis library)
4. An introduction to numerical analysis, Atkinson, Wiley, 1989. (Chapter 6) (on 1-day reserve in Davis library)
Online resources:
5. Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations, Trefethen. (Chapter 1) (download course notes pdf from http://web.comlab.ox.ac.uk/oucl/work/nick.trefethen/pdetext.html)
Reference material on ODEs:
6. Introduction to (ordinary) differential equations, Wainwright, Course Notes for AM250 (good general background resource for ODEs; available in MC2018, and on 1-day reserve in Davis library)
Assignments: There will be three Computational Assignments of project nature (22% weight in final grade, programming in Matlab), and four smaller Theoretical Assignments (8% weight in final grade). Tentative topics for the computational projects are Chaos in Fluid Dynamics, Pendulum Motion, and Flame Propagation. There will be an optional Matlab tutorial in the first week of the term. Assignments will generally be due on Fridays.
Academic Honesty: You are allowed to discuss theoretical and computational assignment problems and your solution strategies with your classmates, but you are not allowed to copy any material. All assignment material that you submit (including written documents, program code and graphical output) should be strictly your own work. Compliance will be actively monitored.
Exams: Sample practice exams will be provided before the midterm and final exams. Formula sheets will be available for midterm and final exams.
Final Grade: 20% Midterm Exam, 50% Final Exam, 8% Theoretical Assignments (4), 22% Computational Assignments (3).