AMATH 383: Introduction to Continuous Mathematical Modeling

TTh 2:30-3:50, MOR 230
(Prerequisites: AMATH 351 or MATH 307)

Instructor:

Professor Hong Qian
Lewis Hall 319
tel: 543-2584
fax: 685-1440
office hours: W: 10:00-12:00
and

Teaching Assistants:

Mr. Lowell Thompson
tel: 685-
fax: 685-
office hours: M: 2:00-4:00 PM
Lewis Hall 129


Course description Textbook Syllabus Schedule

Course Description

Introductory survey of applied mathematics with emphasis on modeling of physical and biological problems in terms of differential equations. Formulation, solution, and interpretation of the results.

Textbook

Topics in Mathematical Modeling, by K.K. Tung, Princeton University Press, Hardcover. (It is available at the University Book Store.)

Syllabus

Schedule and Homework

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Homework and Exams Homework Due Date Homework Problem Sets Homework Solutions
First day of classes Thursday, Sept. 26
1st Homework, Thursday, Oct. 3 due Thu. Oct. 10 Homework # 1
Thursday, Oct. 10 due Thu. Oct. 17 Homework # 2 Solution
Thursday, Oct 17 due Thu. Oct. 24 Homework # 3
Thursday, Oct. 24 due Thu. Oct. 31 Homework # 4
Thursday, Oct. 31 due Thu. Nov. 7 Homework # 5
Thursday, Nov. 14 Term paper proposal due
Thanksgiving Thursday, November 28 No class
Last day of lectures Thursday, Dec. 5
Friday, Dec. 6 Term paper Due

Grading

There will be no exams. There will be 5 homework assignments, each counting 10% towards the final grade. There is a term paper (40% of the final grade). The remaining 10% is for class participation.

Additional Course Materials, Notes, etc.

Week 1: Lecture 1: Introduction

Lecture 2: Mechanistic stochastic model

Week 2: Lecture 3: Discrete population with age strucutre

Lecture 4: Per capita growth rate with independent subpopulations

Week 3: Lecture 5: Degree distribution of networks

Lecture 6: Mechanical motion and Kepler's law

Week 4: Lecture 7, 8: Stochastic population dynamics

Week 5: Lecture 9, 10: Nonlinear population dynamics of a single species, bifurcation and linear stability analysis (Chapters 6 and 9)

Week 6: Lecture 11: Nonlinear population dynamics of two interacting species

Week 7: Chaotic dynamics in Lorenz system

Stochastic population dynamics

Week 8: State transition and bifurcation, of a molecule and the Earth

Diffusion and rando walk


Tue Dec 7 16:30:37 PST 2015