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 === Description ===   === Description === 
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−  == Chris Grant's Proposed Core Topics for Math 647/648 ==
 
−  <div style="mozcolumncount:2; columncount: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
 
−  #* AgmonDouglisNirenberg 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
 
−  # Secondorder linear elliptic operators
 
−  #* Weak Maximum Principle
 
−  #* Perron's Method
 
−  #* Uniqueness for the Dirichlet Problem
 
−  #* Hopf's bondarypoint lemma
 
−  #* Hopf's Strong Maximum Principle
 
−  #* Alexandroff Maximum Principle
 
−  #* GidasNiNirenberg
 
−  #* Uniqueness for the Neumann Problem
 
−  #* Harnack inequality
 
−  #* Finite difference methods
 
−  #* Interior regularity
 
−  #* Schauder estimates
 
−  #* Moser iteration
 
−  #* De Giorgi's theorem
 
−  #* Boundary/Global regularity
 
−  # Secondorder quasilinear equations in divergence form
 
−  #* Existence of weak solutions for the Dirichlet problem via the BrowderMinty theorem
 
−  #* Localintime existence for reactiondiffusion 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
 
−  </div>
 
   
 == Desired Learning Outcomes ==   == Desired Learning Outcomes == 
Revision as of 10:55, 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