Difference between revisions of "Math 647: Theory of Partial Differential Equations 1"

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(Minimal learning outcomes)
(Chris Grant's Proposed Core Topics for Math 647/648)
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=== Description ===
 
=== Description ===
 
== Chris Grant's Proposed Core Topics for Math 647/648 ==
 
<div style="-moz-column-count:2; column-count:2;">
 
#  Linear elliptic operators of order ''n''
 
#* Classification
 
#* Strong and weak solutions
 
#* Gårding's inequality
 
#* Existence of weak solutions for the Dirichlet and Neumann problems
 
#* Agmon-Douglis-Nirenberg regularity
 
#* Green's formula
 
#  Fundamental solutions for general linear differential operators
 
#  Green's functions for general linear BVPs
 
#  Dirichlet's Principle for Laplace’s equation in '''R'''<sup>''n''</sup>
 
#  Poisson's Equation
 
#* Newtonian Potential
 
#* Local existence for the Dirichlet Problem with locally Hölder boundary data
 
#* Interior Hölder estimates
 
#* Kellogg's Theorem
 
#  Second-order linear elliptic operators
 
#* Weak Maximum Principle
 
#* Perron's Method
 
#* Uniqueness for the Dirichlet Problem
 
#* Hopf's bondary-point lemma
 
#* Hopf's Strong Maximum Principle
 
#* Alexandroff Maximum Principle
 
#* Gidas-Ni-Nirenberg
 
#* Uniqueness for the Neumann Problem
 
#* Harnack inequality
 
#* Finite difference methods
 
#* Interior regularity
 
#* Schauder estimates
 
#* Moser iteration
 
#* De Giorgi's theorem
 
#* Boundary/Global regularity
 
#  Second-order quasilinear equations in divergence form
 
#* Existence of weak solutions for the Dirichlet problem via the Browder-Minty theorem
 
#* Local-in-time existence for reaction-diffusion IBVPs and systems using the contraction mapping principle
 
#  Abstract evolution equations
 
#* General theory
 
#* Existence and reqularity for parabolic IVPs
 
#* Existence for hyperbolic IVPs
 
#  Viscosity solutions
 
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== Desired Learning Outcomes ==
 
== Desired Learning Outcomes ==

Revision as of 09:55, 31 May 2011

Catalog Information

Title

Theory of Partial Differential Equations 1.

Credit Hours

3

Prerequisite

Math 541, 547.

Description

Desired Learning Outcomes

Prerequisites

Minimal learning outcomes

Textbooks

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

Additional topics

Courses for which this course is prerequisite