Math 646 Applied Mathematics and Math Modeling
Instructor: Matthew Dobson
Class meeting: MWF 9:05am-9:55am LGRT 1322
Course Text:
Applied Mathematics by David Logan (3rd edition preferred, others
permitted).
Office hours: Mo 10:10-11:00am, Tu 3-4pm, Fr 11:10am-12pm 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, PDE, and continuum mechanics. The techniques will be applied
to applications throughout the natural sciences.
- There will be six assignments during the semester, including
homework problems and more open-ended projects.
You are encouraged to work together, but you must acknowledge sources of help.
- There will be a final exam (date TBA).
- The course grade will be a combination of course participation (15%),
homework assignments (50%), and final (35%).
- There will be weekly reading assignments for the course. As part
of your participation grade, each week you will send questions about the
reading by midnight on Saturday
- 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 Assignments
Week 1: Sections 1.3 and 2.1 (3rd edition) Sections 1.3 and 3.1 (4th edition). Send your questions to me by midnight on 1/25.
Week 2: Sections 2.2-2.5 (3rd edition) Sections 3.2-3.5 (4th edition). Send your questions to me by midnight on 2/1.
Week 3: Sections 3.1-3.3 (3rd edition) Sections 4.1-4.3 (4th edition). Send your questions to me by midnight on 2/8.
Week 4: Sections 3.4-3.5 (3rd edition) Sections 4.4-4.5 (4th edition). Send your questions to me by midnight on 2/15.
Week 5: Snowball Earth and Global Warming, from K. K. Tung's
Topics in Mathematical Modeling. (Printed copy provided in class.) Send your questions to me by midnight on 2/22.
Week 6: Sections 5.1-5.3 (3rd edition) Sections 9.1-9.3 (4th edition). Send your questions to me by midnight on 2/29.
Week 7: Section 5.4 (3rd edition), Section 9.4 (4th edition). Also:
An Algorithmic
Introduction to SDEs by D. Higham.
Send your questions to me by midnight on 3/7.
Week 8: Readings from
Introduction to Stochastic Differential Equations for Finance
by Andrew Papnicolaou
Chapter 1, Sections 2.1-2.3, Sections 3.1-3.5. Please send your questions
by midnight on 3/22.
Week 9: Sections 6.1 and 6.2 (both editions). Please send your questions by
midnight 3/31.
Week 10: Sections 6.3-6.6 (both editions). Please send your questions by
midnight 4/4.
Week 11: Sections 7.1-7.2. Please send your questions by midnight 4/14.
Week 12: Chapter 8. Please send your questions by midnight 4/21.
Additional Resources
An additional resource on random walks: Durret, Probability: Theory and Examples
Demo code for March 25th:
Random Walk Codes. The code is written in
Scilab, which is a free software alternative to Matlab. The syntax is similar
to Matlab, so it should be easy to convert if you choose.
Demo code for March 27th:
Heat Map Generation.
Homework Assignments
Problem numbers are listed for each edition. Please carefully note the subsection and subsubsection number for each problem, since subsections can have multiple sets of exercises.
Homework 1: Due 2/10
Sec 1.1.4: 6, 11; Sec 1.2.3: 3; Sec 2.1.4: 2; Sec 2.2.3: 1a,c; Sec 2.3.4: 4. (3rd edition)
Sec 1.1.4: 6, 11; Sec 1.2.3: 3; Sec 3.1.4: 2; Sec 3.2.3: 1a,c; Sec 3.3.4: 4. (4th edition)
Homework 2: 2/26
Section 2.4.2: 4; Sec 2.5.2: 5; Sec 3.1.2: 2; Sec 3.2.3: 13; Sec 3.3.3: 13;
3.5.3: 3, 8. (3rd Edition)
Section 3.4.2: 4; Sec 3.5.2: 5; Sec 4.1.2: 2; Sec 4.2.3: 5; Sec 4.3.3: 13;
4.5.3: 3, 8. (4th edition)
Homework 3: 3/13
Tung Handout: 6, 9
Section 5.1.2: 5; Sec 5.3.2: 4, 5; 5.3.3: 3, 5. (3rd Edition)
Section 9.1.2: 4; Sec 9.3.2: 4, 5; 9.3.3: 3, 5. (4th Edition)
Homework 4: 4/3
Homework 4
Homework 5: 4/17
Section 6.1.1: 4, 6
Section 6.2.5: 3, 13
Section 6.3.2: 7 (There is a typo in both editions. Please take n = 3.)
Section 6.4.2: 1b
Section 6.6.2: 2, 3
Homework 6: 5/1
Section 7.1.2: 1; Section 7.2.1: 2; Section 8.1.4: 4,6;
Section 8.3.3: 6, 20, 21, 22 (3rd Edition)
Section 7.1.1: 1; Section 7.2.1: 2; Section 8.1.2: 1, 11
Section 8.4.3: 6, 21, 22, 23 (4th Edition)