Fall 2017

Lecture: TuTh: 5-6:40 PC 211

Instructor: Dr. Yuanchang Sun

Office Hours: TuTh 2-3

Office Location: 437C, DM

Phone and E-mail: (305)348-4959, yuasun@fiu.edu


Textbook: Topics in Mathematical Modeling, by K.K. Tung


Recommended references: 

  1. Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry, and Engineering, by Steven H. Strogatz.
  2. Modeling Differential Equations in Biology, by C.H. Taubes.
  3. Differential Equation Models, by Braun, Coleman, and Drew.
  4. Mathematical Models: Mechanical Vibrations, Population Dynamics and Traffic Flow, By R. Haberman.

Prerequisites: Calculus and differential equations, computer programming experiences in Matlab.

Course Introduction:  Learn how simple mathematics can help formulate and solve real problems of current research interests in a variety of fields, including biology, ecology, computer sciences, geophysics, engineering, and the social sciences.

Course topics : (maybe updated or added, and the topics are not necessarily in order)

Course Schedule (subject to change)

week planned topics
1-2 Introductions, Chapter 1.

Homework: hw1

3-4 Chapter 2, 2.1-2.7. 3

Homework:hw2  due Sep 20

3 Chapter 4: 4.1-4.6.

Homework: 4.7: 4, 5

4 Chapter 5: 5.1-5.6

Homework: 5.7: 1, 4, 5

5 Chapter 6:

Homework: 4,5

6 Chapter 7, Logistic map, periodic and chaotic solutions.

Homework: 2,3

7.8 Chapter 8, supplemental materials

Homework, 6

9,10 Chapter 10?


11 Chapter 11
12 Chapter 12
13 Chapter 13
14 Additional materials
The last week Student presentations

Homework:   (see the table above)   Finished homework should be sent to yuasun (at)fiu.edu, NO hard copy of the homework is accepted.

Grade :   0% exam + 75% homework + 25% project and presentation

Projects and Presentations:  Teams should consist <= 3 students.  Topics will be selected on Nov 1.  A brief presentation will be due at the end of the semester.  Longer papers or combinations of related papers could serve as a project. In addition, groups of related problems from Tung or the recommended references may also serve as bases of projects. Reproduction of computational results from the papers is highly encouraged.

Possible topics and references for team projects and reports will be sent to you later this semester .