The Term Project will probably consist of either a 5-paged written presentation or a 15-minute oral presentation (your choice) which describes some topic involving complex variables which is of interest to the student. Please take a note of the Deadline and Requirements for the Project.

You can now access an archive of Spring 2004 Student Projects

You could choose to write about a particular interesting question on a quiz or problem set, write a computer program or talk about an application of complex variables to some other field.

The point is to communicate to me that at least one topic covered in the class was interesting enough to write about, and why. This is an important educational concept whereby not only are you presenting your understanding of a particular topic (i.e. the "what") but also your thoughts about your understanding of the topic and the significance to you (i.e. the "why").

One advantage of choosing the written version is that it may help you complete your Junior Writing portfolio.

Suggested topics

• Take a look at topics presented by students in Complex Analysis Fall 1996
• Mapping properties of other (more complicated) functions beyond w=e^z, w=zⁿ and w=(az+b)/(cz+d), such as w=sin (z) or tan (z). I have some ideas and you can find some interesting examples  in Appendix B of Saff and Snider..
• A computer program which finds and outputs all the values of z^c where z and c are Complex Numbers
• A computer program which solves complex algebraic equations, particularly quadratic equations like az²+bz=c=0 where a, b and c are Complex Numbers
• Discussion of Julia and Mandelbrot sets and functional iteration on complex functions of a complex variable and the resulting beautiful fractal images
• Produce webpages on some historical development (or current application) in Complex Analysis
• Introduction to Laplace or Fourier Transforms to solve simple ordinary differential equations
• Application of complex variables (particular contour integration or contour mapping) to Dirichlet-type boundary value problems
• Application of residues to improper integrals impossible to evaluate using real Cartesian coordinates
• Use of contour integrals with indented paths to evaluate real improper integrals

1. Mathematical Content
2. Comprehensibility
3. Effort
4. Degree of Difficulty
5. and Presentation.

Deadline and Requirements

You must give me a 100-250 word abstract and title of your project as well as the names of the group members by Friday April 2.

Last Updated May 21, 2007