Lectures: MTWR 9:30-11:45, S&T I, Room 242.

Textbook: No textbook, but a good reference is Evans, Blackledge, and Yardley, Numerical Methods for Partial Differential Equations, Springer Verlag.

Office hours: The lecturer of the day will be available for questions for an hour after the end of the lecture.

Lab: There is a computer lab session every afternoon. This is not a beginning lab to learn how to use basic commands. It is a high level self-paced program in how to do large scale numerical computations across a variety of platforms. It is an excellent opportunity to improve your skills. The lab is mandatory if you are an URCM student.

Grading: The grade is based on weekly homework (75%) and a final (25%).

Course Web Page: http://math.gmu.edu/~sander/courses/m493s09/

Homework There will be four homework assignments, which will be available on the website.

Topics List: Here is a list of topics. Be sure to read the appropriate sections and solve problems in the textbook.

• 5/19, Week 1: Introduction to PDEs
  1. Mathematical background.
  2. Derivation of some standard partial differential equations.
  3. Classification and characteristics.
  4. Orthogonal functions.
  5. Numerical linear algebra.
  6. Sturm-Liouville boundary value problems.
• 5/26, Week 2: Numerics of finite differences.
• 6/2, Week 3:
  1. Numerics of hyperbolic equations.
  2. Separation of variables
• 6/9, Week 4:
  1. Numerics of elliptic equations.
  2. Finite element method for ODEs.
• 6/16, Week 5:
  1. Numerical methods for PDEs.
  2. The last two days are reserved for some special topics.
  3. Final day Final exam.

• Daily practice problems
• Previous Year Homework Assignments
• Practice Final.

Homework:

• Homework 1 (assigned week 1, collected week 2)
• Homework 2 (assigned week 2, collected week 3)
• Homework 3a (assigned week 3, collected week 4)
• Homework 3b (assigned week 3, collected week 4)
• Homework 4a(assigned week 4, collected week 5)
• Homework 4b(assigned week 4, collected week 5)

• Course notes
  
• A real world example: Musical Acoustics:
  • Musical Acoustics Lecture
  • banjoA.wav
  • basin10sec.wav
  • lownoteclarinet.wav
  • lownoteflute.wav
  • lookingatsound.m

• beuler.m
• bvp_fd.m
• euler.m
• feuler.m
• fun_lorenz.m
• heat_mol_RHS.m
• heat_mol.m
• lorenz.m
• Spectral Theory specdiff1.m, specdiff2.m, specdiff3.m, spectralPa.m, spectralPb.m
• Collocation colloc1.m, colloc2.m, colloc3.m, colloc3scr1.m, colloc3scr2.m, colloc4.m, colloc5.m
• Least squares leastsquares1.m, leastsquares2.m, galerkin1.m, Matlab diary
• Finite element fem1.m, fem2.m, fem3.m
• AUTO lecture code (post class)
  Matlab: logistic.m, logisticper6.m, and iterating.m.
  AUTO: logistic.c (find the period doublings up to period 16), c.logistic, logistic2.c (finds the saddle-node and period-doubling cascades in the period 6 window), c.logistic2, and logistic.auto (These are the commands to use in AUTO.)

Participants