Mathematical Modeling and Methods of Applied Mathematics

Math 8401 - 8402

Fall, 2021 - Spring, 2022

MWF 1:25-2:15

Vincent Hall 1

Instructor for Math 8401-2: Mitchell Luskin

The goal of this course is to develop the basic mathematical concepts needed to model physical and biological problems. Topics will include ordinary and partial differential equations, integral equations, calculus of variations, Fourier analysis, asymptotic expansions, perturbation theory, and Gaussian processes for machine learning. Both deterministic and stochastic methods will be presented.

The prerequisites are undergraduate courses in 4xxx linear algebra, multivariable calculus, and ordinary differential equations or the equivalent. Prospective students should contact the instructor about questions concerning their preparation for this course.

Main text (PDF can be downloaded free from SpringerLink through the UoM Library):
Partial Differential Equations in Action: From Modelling to Theory, Salsa, Springer, third edition, 2015.
We will cover the first 5 chapters. Solutions to exercises can be found in the companion text:
Partial Differential Equations in Action: Complements and Exercises, Salsa and Verzini, Springer, 2015.

Supplementary Texts (PDF can be downloaded free from SpringerLink through the UoM Library):
Multiscale methods: averaging and homogenization, Pavliotis and Stuart, 2008, Springer.
Introduction to Perturbation Methods, Holmes, second edition, 2014, Springer.
Stochastic Tools in Mathematics and Science, Chorin and Hald, third edition, 2013, Springer.

You can also download the additional supplementary text from the link:
Gaussian Processes for Machine Learning, Rasmussen and Williams, 2006, MIT Press.

Random Walks in Biology, Howard Berg, Princeton University Press, expanded edition, 1993.

Homework will be given to develop modeling and analytic skills.

For more information or questions, please contact

Mitchell Luskin