數學建模之物理應用 (Mathematical Modeling in Physics)
 

Instructor: 郭鴻基   Email:  kuo@as.ntu.edu.tw            Office: 理學大樓 313

Class time: Wednesdays, 12:10-15:00        Location: (Tentative) S201

Grading Policy: based on in class discussions, homeworks, examinations and/or presentations

Syllabus:

Wk

Dates

Topics

Readings/Notes

1

9/17

Introduction to Mathematical Modeling

 

2

9/24

Exponential Growth, Dimensional Analysis and Introduction to Differential Equations (DEs)

 

3

10/1

Stability in a One-Component System and Systems of First-Order DEs

 

4

10/8

Phase Plane Analysis and Equilibrium in Two-Component, Linear Systems

 

5

10/15

Multiple Equilibriums and Stability in Nonlinear Systems

 

6

10/22

Matrix Notation and Nonlinear Stability Revisited

 

7

10/29

The Australian Predators and Examples of Dynamical System

 

8

11/5

Introduction to Vectors and Vector Calculus

 

9

11/12

Midterm Examination

Midterm exam week

10

11/19

Introduction to Advection and Diffusion Equations

 

11

11/26

Two Key Properties of the Advection and Diffusion Equations

 

12

12/3

PDE solutions and Pattern Formation

 

13

12/10

Traveling Waves and Traveling Wave Velocities

 

14

12/17

Advection/Diffusion in Atmosphere and Ocean (I)

 

15

12/24

Advection/Diffusion in Atmosphere and Ocean (II)

 

16

12/31

Periodic Solutions; Fast and Slow; Estimating Elapsed Time and Switches

 

17

1/7

Testing for Periodicity and Causes of Chaos

 

18

1/14

Final exam

Final exam week

 
Reference Books:
(1) Topics in Mathematical Modeling, K.K. Tung, Princeton University Press.
(2) Modeling Differential Equations in Biology, C. H. Taubes, Cambridge Press