Project Guidelines
As stated in the syllabus, there is a Term Project in this course.
It should consist of either a 5-page written presentation or a 15-minute oral presentation (your choice) which describes some topic involving complex variables which is of interest to you. This term poject is due on April 24 1998.
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 var
iables to some other field. If you choose an item or topic already discussed in class then you must be sure you indicate what new work you put into producing your project. Your project should either be an expansion of a previously-understood topic or a brief look at an entirely new topic.
Suggested topics
- Mapping properties of other (more complicated) functions beyond w=ez, 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 on pages 370-377 in Appendix 2 of Brown and Churchill.
- A computer program which finds and outputs all the values of zc where z and c are Complex Numbers
- A program which solves complex algebraic equations, particularly quadratic equations like az2+bz=c=0 where a, b and c are Complex Numbers
- 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) to dirichlet 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
Projects will be graded on 5 different scales:
- Mathematical Content
- Comprehensibility
- Effort
- Degree of Difficulty
- and Presentation.
Deadline and Requirements
Projects must be completed by Friday April 24. I expect that you will have to meet with me atleast once to discuss your topic. You may work in small groups but I will have proportionally increased expectations from group projects. 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 10.