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MATH 442
Numerical Solution of Differential Equations
TR 11-12:15 in Wilson 1-117


Announcements
Course Policy Statement: Course Policy Statement
Textbook: Numerical Mathematics and Computing, by W. Cheney and D. Kincaid (5th edition)

Topics for the Course
  1. Chapter 16: Optimization
  2. Chapter 4: Interpolation and Numerical Differentiation
  3. Chapter 9: Approximation by Spline Functions
  4. Chapter 10: Ordinary Differential Equations
  5. Chapter 11: Systems of Ordinary Differential Equations
  6. Chapter 14: Boundary Value Problems for ODEs
  7. Chapter 15: Partial Differential Equations
Assignments
Class Notes

Optimization 1
Optimization 2

Lagrange Interpolation
Newton Polynomials
Interpolation Error
Hermite Interpolation
Spline Approximation

Numerical Differentiation
Richardson Extrapolation

Numerical Quadrature
Composite Quadrature Rules

Romberg Integration
Adaptive Simpson's Rule
Gauss Quadrature

Existence/Uniqueness of Solns to IVPs
Euler's Formula
Taylor Series Methods
Error Analysis
Runge Kutta
RKF and ABM
Predictor-Correctors
Stability of Solutions of IVPs
Stability of Numerical Methods
Stability of Multistep Methods 1
Stability of Multistep Methods 2
Systems of ODEs

Supplementary Texts:
  1. An Introduction to Numerical Methods and Analysis (Wiley) by J.F. Epperson, 2002.
  2. Matrix Analysis and Applied Linear Algebra (SIAM) by C. Meyer
  3. Fundamentals of Matrix Computations (2nd edition) by David S. Watkins.
  4. Numerical Analysis (sixth edition) by R. Burden and J. Faires.
  5. Numerical Methods Using MatLab by J. Mathews and K. Fink
  6. Numerical Methods for Unconstrained Optimization and Nonlinear Equations (SIAM) by J. Dennis, R. Schnabel
  7. Numerical Optimization (Springer) by J. Nocedal, S.J. Wright

Students are NOT required to buy the supplementary texts. Occasionally, I will cover topics and include material from these texts that are not covered to my satisfaction in the required text.


Downloading Course Materials

Many of the Course Materials above must be downloaded in one of the given file formats (Postscript, PDF or DVI).

Acrobat Logo If you download the PDF version, you will need Adobe Acrobat Reader to view and print the document. Relax, the Reader is free and can be downloaded from the following site. Just click on the `Get Acrobat Reader' icon to the right, and follow the directions.

Ghostscript Logo If you prefer to download the PS (Postscript) version, you will need Ghostscript or GSView. This is also free software. Just click on the icon to the right and follow the directions. Note, I think you will need a version of WinZip or another program to decompress or `unzip' some of the downloaded files. Personally, I think the Acrobat Reader is a little easier to work with, but it is up to you. Note, if you are working on a UNIX machine, you can print Postscript files from the prompt. Check with your local computer guru or systems administrator before you download programs that are not needed.


Computer Resources

I will give you more information on computer assignments as the course progresses. In the meantime, there are some computer resources listed below. There are also a few listed on my `Useful Links' Page which can be accessed from the Navigation Bar above.
Davis