MAE 290B

Numerical Methods for Differential Equations

This course discusses numerical methods for ordinary and partial differential equations with particular emphasis on the equations encountered in mathematical physics and engineering.

Instructor:

C. Pozrikidis
Office: 2209 EBU1, Email: cpozrikidis AT ucsd.edu

Teaching Assistant:

TBA

Time and place:

Tuesdays and Thursdays, 8:00-9:20 am, TBA.

Office hours:

After each lecture and by appointment.

Prerequisites:

You must have taken MAE290A or equivalent. Essential prerequisites are:

Ability to program in a low- or mid-level scientific language
such as FORTRAN, C, C++, or Pascal.
Familiarity with a flavor of Unix.
A strong background in differential and integral calculus.
A strong background in numerical linear algebra and matrix calculus,
including the algebraic eigenvalue problem.
A good knowledge of numerical function differentiation and integration.
General knowledge of elementary numerical methods.

Topics:

This course covers the following main topics:

Ordinary differential equations; initial-value problems.
Ordinary differential equations; boundary-value problems.
Ordinary differential equations; eigenvalue problems.
Finite-difference methods for partial differential equations.
Boundary-element methods for partial differential equations.
Finite-element methods for partial differential equations.

Text:

Pozrikidis, C., Numerical Computation in Science and Engineering. Oxford University Press (1998).

Important restrictions on Matlab and Mathematica:

The use of advanced languages and applications such as MAPLE, MATLAB, and MATHEMATICA are acceptable only at the level of a low level language such as FORTRAN, C or C++ with regard to the use of intrinsic subroutines, or else for the purposes of plotting and verification.

Assignments:

Five problem sets involving a combination of theoretical and programming projects will be assigned and will be due every two weeks at the beginning of the lecture. Discussion of the homework problems is permitted, but cooperation is strictly prohibited. When you sit down to write solutions and programs, please be alone. Each student is expected to write his/her own programs and produce her/his own solutions. Duplicate solutions and slightly different computer codes will be discarded with no regard to original authorship. Even if one problem of a set if found duplicate, the whole set will be zeroed.

First problem set Due on Tuesday, Jan 22

Second problem set Due on Tuesday, Feb 05

Third problem set Due on Tuesday, Feb 19

Fourth problem set Due on Tuesday, March 04

Fifth problem set Due on the last class

Exams:

Final exam.

Grade:

The final course grade will be based on the homework problem solutions (50%) and final exam (50%).

Books on reserve:

Pozrikidis, C. 2008 Numerical Computation in Science and Engineering. II. Numerical Methods Oxford University Press.
Atkinson, K. E. 1989 An Introduction to Numerical Analysis. Wiley.
Press, W. H., Flannery, B. P., Teukolsky, S. A., Vetterling, W. T., 1992 Numerical Recipes in FORTRAN: The Art of Scientific Computing. Second Edition, Cambridge University Press.