Math 4Q03 Numerical Methods for Ordinary
and Partial Differential Equations Winter 2000
Office: BSB-246E, Tel: x23412
Office hours: Monday 14:30-15:30, Thursday 13:30-14:30 and by appointment
Purpose of the course
Most mathematical problems that arise from applications in science and
engineering are difficult or, more often, impossible to solve using techniques
from algebra or analysis courses. However, approximate solutions are almost
always possible using numerical techniques implemented on a computer.
The convergence and stability of these methods can be calculated and thus
the solution can be found to a specified precision.
The objective of this course is to teach a variety of numerical methods
(e.g., spline interpolation, numerical integration and differentiation,
numerical linear algebra and root finding) by applying them to the solution
of ordinary and partial differential equations. This approach shows how
these methods can be combined to solve a particular practical problem:
the solution of ODE's and PDE's.
An introduction to numerical methods and their application to the numerical
solution of initial and boundary value problems of ODEs and PDEs. More
specifically, topics to be covered include:
Introduction to numerical methods: interpolation, numerical differentiation
Ordinary differential equations.
Initial value problems: Euler's method, predictor-corrector, Runge-Kutta
methods, linear multistep, convergence and stability, techniques for stiff
Boundary value problems: finite differences, Galerkin method, collocation,
finite elements (interpolation and splines).
Numerical solution of algebraic equations: iterative methods, Jacobi, Gauss-Seidel,
SOR, Newton's method.
Partial differential equations:
Introduction to PDE's: classification and characteristics.
Parabolic equations: spatial discretization by finite differences, explicit
and implicit methods for time stepping, numerical instabilities and physical
Convergence theory: consistency, stability and convergence, Lax's equivalence
Hyperbolic equations: finite differences, convergence analysis.
Elliptic equations (steady-state equations): finite differences and finite
The primary texts for the course are:
Optional texts include:
Mathews, J. H. & Fink, K. D. 1999 Numerical methods using MATLAB
(3rd edition). Prentice Hall.
The Student edition of MATLAB, Version 4 for Microsoft Windows,
Pratap, R. 1999 Getting started with MATLAB 5. Oxford University
Press, W. H., Flannery, B. P., Teukolsky S. A. & Vetterling, W. T.
1992 Numerical Recipes in C/Fortran, Cambridge University Press,
(QA76.783.C15N865, QA 297.N866).
Sewell, G. 1988 The Numerical solution of Ordinary and Partial Differential
equations. Academic Press (QA 372.S4148).
Five problem sheets will be given and marked for credit. Assignments are
to be dropped into the Math 4Q03 locker in the basement of the Burke Sciences
Building by 15:00 on the due date. No late assignments will be accepted.
Solutions to assignments and tests will be put on reserve in the Thode
Library. In addition, there will be one project where a single problem
is investigated in depth.
Assignment given Assignment due
January 7 January 21
January 21 February 4
February 4 February 21
March 10 March 27
March 24 April 7
Project given Project due
February 18 March 20
There will be one 50 minute test, held in a location to be announced, during
the regularly scheduled class hour on the following date:
Monday 28 February.
of topics for test (pdf)
Review session for test: Friday 18 February 13:30-15:20
at my office
Test room: A-L PC B127 (normal room)
M-Z BSB B154
Special Office hour: 9:30-10:30 Friday 25 February.
There will be a three-hour final examination during the April examination
of topics for Final Exam (pdf)
I have posted course marks on my
door (BSB 246E). Please check your marks and report any problems
to me before the final exam.
The final mark will be calculated as follows:
I reserve the right to change the weight of any portion of this marking
scheme. If changes are made, your grade will be calculated using the original
weightings and the new weightings, and you will be given the higher of
the two grades. At the end of the course the grades may be adjusted but
this can only increase your grade and will be done uniformly. I will use
the grade equivalence chart in the university calendar to convert between
letter grades, grade points and percentages.
MATLAB is installed on the computers in the lab on the 2nd floor of the
Burke Science Building. A package is also available on diskettes bound
in the book The student edition of MATLAB.
More information about MATLAB can be found at The Math Works Inc. Web site
www.mathworks.com. The book Getting started with Matlab 5
is a good guide to programming in MATLAB.
Statement on academic ethics
Attention is drawn to the ``Statement on Academic Ethics'' and ``Senate
Resolutions on Academic Dishonesty'' as found in the Senate Policy Statements
distributed at Registration and available in the Senate Office. Any student
who infringes on one of these resolutions will be treated according to
the published policy. In particular, it is expected that the assignments
and project shall be done and submitted as individual work. Students may
discuss general problems or approaches, but the final solution must be
a result of the student's own effort.
The Faculty of Engineering is concerned with ensuring an environment
that is free of all adverse discrimination. If there is a problem that
cannot be resolved by discussion among the persons concerned, individuals
are reminded that they should contact their Department Chair, the Sexual
Harassment Office or the Human Rights Consultant, as soon as possible.
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