Difference between revisions of "Math 436: Modeling with Dynamics and Control 1"

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(Desired Learning Outcomes)
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=== Offered ===
=== Offered ===
Sp Su
The course runs through both Spring and Summer.
=== Prerequisite ===
=== Prerequisite ===

Revision as of 13:56, 13 June 2012

Catalog Information


Differential and Integral Equations 1

(Credit Hours:Lecture Hours:Lab Hours)



The course runs through both Spring and Summer.


Math 322, Math 341, Math 346; concurrent with Math 437


The theory and applications of dynamic systems and partial differential equations. Specific topics include dynamic systems, bifurcation theory, control theory, and Hyperbolic, Parabolic and Elliptic partial differential equations. We will study several commonly-used algorithms.

Desired Learning Outcomes


Math 322, Math 341, Math 346; concurrent with Math 437

Minimal learning outcomes

Students will have a solid understanding of the concepts listed below. They will be able to prove theorems that are central to this material, including theorems that they have not seen before. They will be able to recognize whether differential equation models apply in the context of a given application or not. They will be able to perform the relevant computations on small, simple problems.

  1. Dynamical Systems
    • Matrix Exponentiation
    • Linear Stability
    • Variation of Constants Formula
    • Lyapunov Matrices
    • Nonlinear Stability
    • Stable, Center, and Unstable Manifolds
    • Poincare-Bendixson Theorem
    • Chaotic Dynamics
  2. Bifurcation Theory
    • Saddle-Node Bifurcation
    • Trans-critical Bifurcation
    • Pitchfork Bifurcation
    • Hopf Bifurcation
  3. Control Theory
    • State-Space Models and Realizations
    • Observability and Controllability
    • Transfer Functions and Minimal Realizations
    • State Feedback
  4. Hyperbolic PDE
    • Method of Characteristics
    • Shock Waves and Rarefactions
    • Wave Equation
    • Fourier Transform
    • Separation of Variables
  5. Parabolic PDE
    • Heat Equation
    • Maximum Principle
    • Separation of Variables
    • Convolution and the Gaussian Kernel
  6. Elliptic PDE
    • Laplace equation
    • Separation of Variables
    • Green’s Function


Possible textbooks for this course include (but are not limited to):

Additional topics

Courses for which this course is prerequisite