Credits -- 3 (3-0-0)
Term Offered -- Fall, odd numbered years
Prerequisite -- M340
- Description
-- -
Introduction to the theory of linear partial differential equations;
representations of solutions; qualitative properties of solutions.
Topics --
Mathematical Models & Origins of PDE
Integral Cons. Laws Æ PDE Cons. Laws
Laplace Equation
Diffusion Equation
Second Order Wave Equation
First Order Wave Equation
Auxiliary Conditions; Well Posedeness
Classification and Characteristics (2)
Dimensional Analysis and Similarity Solutions (2)
Linearity and superposition
Applications of Superposition (2)
Product Law and DuHumel's Principle
Fourier Series (4)
Separation of Variables
Diffusion Equation
Laplace Equation
Second Order Wave Equation
Harmonic Þ Mean Value Property
Mean Value Property Þ Maximum Principle
Harmonic ¤ Mean Value Property
Subharmonic and Superharmonic
Extended Maximum Principles (2)
Uniqueness Results -- Laplace Equation
Dirichlet; Neumann; Exterior
A Priori Extimates -- Laplace Equation
Maximum Principle for Diffusion Equation
Uniqueness Results -- Diffusion Equation
Dirichlet; Neumann; Exterior
A Priori Estimates -- Diffusion Equation
D'Alembert Solution -- Second Order Wave Eq.
Uniqueness Results -- Second Order Wave Eq.
(About 38 days to cover these topics.
Remainder for testing and discussion.)