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:
-
The course covers classical methods in applied mathematics and math modeling, including dimensional analysis, asymptotics, regular and singular perturbation theory for ordinary differential equations, random walks and the diffusion limit, and classical solution techiques for PDE. The techniques will be applied to applications throughout the natural sciences.
- There will be five assignments during the semester, including
homework problems and more open-ended projects.
You are encouraged to work together.
- There will be a final exam on May 9th.
- The ideas will be illustrated using numerical schemes and students
are expected to participate and present results in class
- The course grade will be a combination of course participation (10%),
homework assignments (60%), and final (30%).
- Please speak to me at least one week in advance if you need special
exam accommodation or if you need a make-up exam.
- Late policy: Homework is due at the beginning of class on the due date.
Late homework is not accepted except: each student may submit one homework
assignment up to one week late. This is meant to cover any unforeseen absence
from class. If you will miss class for a religious observance or for a
university activity on the day of an exam or homework due date, you must
contact me one week before the missed class to arrange for making up the work.
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