Math 441 Analysis and Dynamics of Differential Equations (Spring 2017)

# Class content and policy

Syllabus and Class Policy

# Handouts

Summary of topics covered in class: Topics

Midterm pdf.

Final pdf.

# Assignments

Assignment 1.

Assignment 2.

Assignment 3.

Assignment 4.

Assignment 5.

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

pdf

pdf

#### Assignment 1

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.