Mathematics 645: Numerical Analysis II

Class Times Tuesday and Thursday 7:00-8:15pm
Locations Maybank 223, and sometimes in the Maybank 200 computer classroom
Instructor Brenton leMesurier
Office Room 103, 4 Greenway (enter from behind Randolph Hall)
Phone 953-5917
Electronic Mail lemesurierb@cofc.edu
Course Web Site http://math.cofc.edu/faculty/lemesurier/math645/
Office Hours Before classes and others TBA

A collection of handouts, programs and such is being compiled at http://math.cofc.edu/faculty/lemesurier/math645/docs/

NEW! There is also a page describing Assignments and other sugested exercises (including Due Dates) NEW!
 

Texts and Other materials

The main text is
Computational Differential Equations by K Eriksson, D Estep, P Hansbro and C Johnson (Cambridge University Press)
A recommended supplementary source, for background topics and the finite difference method, is the text use for Math 545,
Numerical Analysis  by Richard Burden and J Douglas Faires (Brooks/Cole)
A few other useful references are
Scientific Computing and Differential Equations: An Introduction to Numerical Methods by G Golub and J Ortega (Academic Press)

Numerical Solution of Partial Differential Equations: Finite Difference Methods by G D Smith (Clarendon Press)

Matrix Computations by G H Golub and C F Van Loan (Johns Hopkins University Press)

I will also distribute handouts on a few topics not covered in the text, and provide various materials and links to other resources through the course web site.

Course Description

This course will deal mainly with methods for the numerical solutions of partial differential equations, with an emphasis on the finite element method. Examples will include numerical solution of equations modeling mechanical, thermal and electrical equilibrium, heat conduction, vibration, wave motion and convection, and the stationary Schrodinger Equation.

Solving such problems numerically often involves solving large systems of simultaneous linear equations and sometimes computing eigenvalues and eigenvectors of large matrices, and so we will consider iterative methods for these problems of numerical linear algebra. It often helps to consider both the partial diffential equation and the related linear algebra problems as minimization problems, and so if there is time we will look at some related numerical methods for optimization  problems.

Computational work will be done principally with the Matlab package for interactive computation and graphics and programming. We will also consider the use of Fortran 90 and a variety of widely used, high quality, public domain computational libraries. Matlab is available on the Macintoshes in the Maybank 200 computer classroom, on some Macintoshes in the J C Long computer lab, and for remote acccess on a UNIX server, where Fortran and the related libraries and software will also be available.

There will be an emphasis on understanding and evaluating the methods used in such software and libraries, in order to choose the right tool for a particular task.  This involves considering the accuracy, reliability, robustness and efficiency of various alternative methods for solving a given problem.

Assessment

Assignments

Assessment will be based mostly on assignments combining written work and programming tasks.  These will typically involve devising, implementing, testing and comparing methods for numerical solution of various problems.

I expect considerable discussion and work in class on assigments, particularly with the programming parts, and to emphasise that, drafts of programming work will be due one week before the deadline for each assignment.

Mid-semester Take-home Test

I propose to have only one test, a weekend take-home at mid-semester.

Grading

The assignments will count for 80% of the total grade, with the mid-semester test counting for the other 20%.

All work will be given a score on a scale of ``points lost'', from 0 for perfection down to 15, with letter grade interpretations as below. The scores will then be averaged, rounded to an integer and converted to final course grades as shown on the last row of the table.
 

Point score 0 1 2 3 4 5 6 7 8 9  to 15
Equivalent Letter Grade A+ A A- B+ B B- C+ C C- F
Conversion for Final Grade A B+ B C+ C F

Missing drafts will be penalized two points, and late work, if accepted, will also be penalised.

Attendance

Regular, punctual attendance is important, especially due to the ``hands-on'' work that will be done at times.

You are responsible for knowing what happens in each class, so if you miss one, get notes and find out about any assignments or other announcements; either from a classmate or from me. To help with this, there will be a brief diary on the course website.

Help Outside Classes

I am free immediately before and after classes, so you can ask questions in the classroom or come to my office.  I will also be available for posted office hours once these times are arranged, and at most other times.  However, if you want to see me outside of office hours it is best to check (call) before coming to my office.