Possible Research Topics

Below is a list of possible subjects for your research project. You can propose your own subject as well and check with me whether it is OK. In parentheses are the sections in Arfken and Weber where you can read a little bit about the subjects but I expect that you will use additional references for your research (you can check wikipedia but do not use it as a reference; valid references are scientific journals and books). As soon as people tell me that they are interested in one of the subjects I will write their names next to it so that it is clear what subjects are still available.

  1. Gauss' Theorem and its applications (1.11) -
  2. Stokes' Theorem and its applications (1.12) - Michelle Neeley
  3. Helmholtz's Theorem and its applications (1.16) - Allison Reagan
  4. Pseudotensors. Physical Examples (2.9) - Andrew Ayres
  5. Applications of Eigenvector and Eigenvalue Theory (3.5) - Shengnan Li
  6. Group Theory I: Discrete Groups and their applications. (4.7) - Deborah Penchoff
  7. Group Theory II: Continuous Groups and their Applications (4.2) - Jessica White
  8. Taylor's Expansion and its applications (5.6) - Jacob Fosso Tande
  9. Bernouilli Numbers and their applications (5.9) -
  10. Conformal Mapping and its applications (6.8) - Suman Ganguli
  11. Method of Steepest Descent and its applications (7.3) - Xu Wang
  12. The Gamma function and its applications (8.1)
  13. The Beta Function and its applications (8.5) - Riddhi Dave
  14. Separation of Variables and its applications (9.3) -
  15. Green's Functions and their applications (9.7 and 10.5) - Erik Olsen
  16. Hermitian Operators and their applications (10.2) - Andy Hicks
  17. Bessel Functions and their applications (Chapter 11) - Jen Niedziela
  18. Legendre Functions and their applications (Chapter 12) -
  19. Hermite Functions and their applications (13.1) 
  20. Laguerre Functions and their applications (13.2)
  21. Chebyshev Functions and their applications (13.3)
  22.  Mathieu Functions and their applications (13.6)
  23. Applications of Fourier Series (14.3) - Matt Hollingsworth
  24. Fourier Transforms and their Applications  (15.3) - Allyn Milojevich
  25. Laplace Transforms and their Applications (15.8) - Sarina Adhikari
  26. Convolution Theorem and its Applications (15.11)
  27. Lagrangian Multipliers and their Applications (17.6) - Huijuan Li
  28. Poisson Distribution and its Applications (19.4) - Hao Hu
  29. Gauss' Normal Distribution and its Applications (19.5) - Gyu Tae Kim
  30. Finite Element Methods and its application for solving PDEs. - Haihang You