MS650 – Methods of Applied Mathematics II

Professor's Assistant (PED-B), University of Campinas, Institute of Mathematics, Statistics and Scientific Computing, 2020

Course Information - Class A

Role

I served as a Professor’s Assistant (PED-B) for this course. My work included leading weekly problem-solving sessions, assisting with grading, and holding student support hours outside regular class time.

At Unicamp, PED (Programa de Estágio Docente) is a graduate teaching internship program through which graduate students support undergraduate instruction under faculty supervision.

Course Overview

This course covers advanced topics in applied mathematics, including a review of complex variables, integral transforms, partial differential equations, integral equations, and the calculus of variations.

Syllabus

Functions of a complex variable (review). Integral transforms (Fourier and Laplace). Inverse transforms. Integral representations of functions. Partial differential equations. Classification and well-posed problems. Wave, heat, and Laplace equations. Separation of variables. Introduction to integral equations. Calculus of variations.

References

  • Butkov, E. Física Matemática. Livros Técnicos e Científicos, 1988.
  • Vaz Jr., J.; Capelas de Oliveira, E. Métodos Matemáticos. Vol. II. Editora da UNICAMP, 2016.
  • Arfken, G. B.; Weber, H.-J.; Harris, F. E. Mathematical Methods for Physicists. 7th ed. Academic Press, 2012.
  • Capelas de Oliveira, E. Funções Especiais com Aplicações. Livraria da Física, 2005.
  • Courant, R.; Hilbert, D. Methods of Mathematical Physics. Vols. I-II. Wiley, 1989.

My Contributions

My main contributions to the course included:

  • leading two hours of problem-solving sessions per week under the supervision of the course professor;
  • assisting with grading;
  • holding two one-hour student support sessions each week outside regular class time.

Lecture Notes

The following lecture notes were prepared for the problem-solving sessions I taught in this course: