Math 441 Analysis and Dynamics of Differential Equations (Spring 2017)
# All Materials from Spring 2017 Semester

# Class content and policy

Syllabus and Class Policy
# Handouts

Summary of topics covered in class: Topics
# Exams

#### Midterm Exam

Midterm pdf.
#### Final Exam

Final pdf.
# Assignments

#### Assignment 1

Assignment 1.
#### Assignment 2

Assignment 2.
#### Assignment 3

Assignment 3.
#### Assignment 4

Assignment 4.
#### Assignment 5

Assignment 5.
#### Assignment 6

Assignment 6.
#### Spring 2017 Student presentations

- Ergodic Theory and Statistical Mechanics slides.
- The Rossler System slides.
- Dynamical Billiards slides.
- Introduction to Chaos of Financial Markets slides.
- Calculating the Lorenz System Lyapunov Exponents slides.
- Chaos Economics slides.
- Difference Between Chaos and Randomness slides.
- Chaos and Strange Attractors slides.

# All Materials from Spring 2016 Semester

#### Spring 2016 Class Content and Policy

Syllabus and Class Policy

#### Spring 2016 Handouts

Summary of topics covered in class: Topics
#### Spring 2016 Exams

#### Midterm exam on Tuesday March 15

pdf
#### Final exam on Tuesday May 3

pdf
#### Spring 2016 Assignments

#### Assignment 1

Read chapters 1 and 2.

Submit Problems: 2.1.3, 2.2.1, 2.2.7, 2.2.10, 2.2.13, 2.3.1, 2.4.4, 2.4.9, 2.5.2, 2.5.5, 2.7.1, 2.8.2 (d), 2.8.3.
#### Assignment 2

Assignment 2 on existence and uniqueness.
#### Assignment 3

Assignment 3 on bifurcation, dimensional analysis, singular perturbation.
#### Assignment 4

Assignment 4 on two dimensional flows, linear systems, nonlinear systems and phase portraits.
#### Assignment 5

Assignment 5 on two dimensional flows: alpha and omega limit sets, Poincare Bendixson Theorem, no chaos in two dimensions, limit cycles, Hopf bifurcations..
#### Assignment 6

Assignment 6 on three dimensional flows: Chaos, strange attractors, fractals, Liapunov exponent.
#### Spring 2016 Student presentations

- The logistic map and chaos slides.
- Theoretical model of cancer growth slides.
- Introduction to mass action kinetics and chemical reaction networking modeling slides.
- Nonlinear dynamical system in humanoid robots slides.
- Navier-Stokes equation: Theory and applications slides.
- The structure of chaos slides.

#### Spring 2016 Photos