Difference between revisions of "Math 438: Modeling with Dynamics and Control 2"
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m (moved Math 438 to Math 438: Differential and Integral Equations 2) 
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Revision as of 16:11, 3 April 2013
Contents
Catalog Information
Title
Differential and Integral Equations 2
(Credit Hours:Lecture Hours:Lab Hours)
(3:3:0)
Offered
W
Prerequisite
Math 436, Math 402; concurrent with Math 439, Math 404
Description
An introduction to the theory of integral equations, of the calculus of variations, of stochastic differential equations and of optimal stochastic control. An introduction to the algorithms that are commonly used to study these systems
Desired Learning Outcomes
Prerequisites
Math 436, Math 402; concurrent with Math 439, Math 404
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 understand the model specifications for the algorithms, and be able to recognize whether they apply to a given application or not. They will be able to perform the relevant computations on small, simple problems. They will have a basic knowledge of the capabilities of commercial software that available for these problems.
 Integral Equations
 Classification and Origins
 Relationship to Differential Equations
 Fredholm Equations
 Symmetric Kernels
 Volterra Equations
 General Integral Equations
 Calculus of Variations
 Variational Problems
 EulerLagrange Condition
 Second Variation
 Generalizations of the Variational Problem
 Hamiltonian Theory
 Optimal Control
 Problem Formulation
 HamiltonJacobiBellman Equation
 The Adjoint Equation
 Sufficient Conditions
 Linear Quadratic Regulator (LQR)
 Stochastic Differential Equations
 Brownian Motion and Diffusion
 Weiner Processes
 Itô Processes and Itô's Lemma
 BlackScholes Equation
 Stochastic Optimal Control
 Problem Formulation
 HamiltonJacobiBellman Equation
 Optimal Stopping Times
 Linear Quadratic Gaussian (LQG)
 InvestmentConsumption Problems
Textbooks
Possible textbooks for this course include (but are not limited to):