Math 697 Applied Mathematics and Math Modeling

Instructor: Matthew Dobson
Class meeting: MWF 10:10am-11:00am LGRT 147
Course Text: Mathematics Applied to Deterministic Problems in the Natural Sciences by Lin and Segel
Office hours: Tu 3-4pm, Th 9:15-10:15, Fr 11a-12 or e-mail me to make an appointment.
Office: LGRT 1430 (Tower)
e-mail: dobson@math.umass.edu
Office phone: 545-7194

Course Structure and Grading Policies:

Reading

First week: Chapter 1
Rock-Paper-Scissors interactions in biology: Cyclic dominance in evolutionary games: a review

Second week: Chapter 2
Is the solar system stable?
Video about Orbital Instability and Planetary Collisions
Chapter 3.1


Third week: Chapter 3.3,3.4

Fourth week: Continuum limits in materials science, Snowball earth (Handout)

Fifth week: Chapter 6

Final week+ day:
Chapter 3 of Mathematics Applied to Continuum Mechanics by Segel

Homework

Homework 1: Due 2/14
1. Problem 1.3.2 from the text.
2. Problem 2.2.8 from the text.
3. Problem 2.2.10 from the text.
4. Determine the shape of orbits in a two-body system if gravitational force were proportional to r-a for 1 < a < ∞.

Homework 2: Due 2/28
From Lin and Segel: 3.1.2, 3.3.9, 3.3.11, 3.4.9.
From K.K Tung (handout): 8.9.1, 8.9.3 (Now moved to HW 3)
From class: Compute the linear elastic response for the square lattice.


Homework 3: 3/26
From K.K Tung (handout): 8.9.1, 8.9.3
More to be added.


Homework 4: Due 4/9
6.2.6, 6.3.8, 7.2.10, 8.2.6, 9.2.4
Inspired by the example in class, find the first two non-zero terms of a perturbative series approximation for each root of
eps^4 x^6 - eps x^4 - x^3 + 8 = 0, where eps is a small parameter.


Homework 5: Due 5/1
12.1.2, 13.3.4, 13.4.4b, 14.2.4, 15.1.7, 15.2.8