Math 651: Modeling and Mechanics                             Fall 2021
Meetings: Randall 4404, Mon/Wed 10-11:20 a.m.
Instructor: Prof. Silas Alben
Email: alben at
Office: East Hall 4858, tel. 734-647-5518
Office hours: Mon/Tues 3-4 or by appointment.

Course outline:
This course will develop mathematical modeling techniques which are useful in many areas of science and engineering, particularly those described by (partial) differential equations.

Pre-requisities: An advanced undergrad course in PDE at the level of Math 450 or 454. Some exposure to functions of a complex variable.

About 4-5 HW assignments and a short presentation (~10-15 slides) of a mathematical model from your own research area. Presentation could include: Motivating experiments/data, relevant equations, nondimensionalization and scaling of variables, simplifications/approximations of equations and corresponding assumptions made, identification of important parameter ranges/limits, analytical or numerical solutions, comparisons with experiments/data.

The grade will be based on these assignments as well as class attendance and participation.

Dimensional analysis (LS, H)
Scaling (LS, H)
Tensors (S)
Continuum mechanics of solids and fluids (S, LL, F)
Elasticity (S, LL, F)
Potential theory (LS, T)
Organismal locomotion (C)
Fluid-structure interactions (papers)

Main references:
* indicates freely available through the UM library web site.

*(LS) Lin and Segel, Mathematics Applied to Deterministic Problems in the Natural Sciences
*(S) Segel, Mathematics Applied to Continuum Mechanics
*(LL) Landau and Lifschitz, Elasticity
*(H) Howison, Practical Applied Mathematics

Additional sources:

(AP) Audoly and Pomeau, Elasticity and Geometry
(C) Childress, Mechanics of Swimming and Flying
*(vGM) van Groesen and Molenaar, Continuum Modeling in the Physical Sciences
(M) Middleman, An Introduction to Fluid Dynamics
(T) Tayler, Mathematical Models in Applied Mechanics
(F) Fowler, Mathematical Models in the Applied Sciences

The Principle of Similitude by Lord Rayleigh
Dimensional Analysis notes by Douglas Hundley
Tadashi Tokieda, Toys in Applied Mathematics
Fluid Dynamics videos