Topics in Differential Equations (Partial Differential Equations)

MAGN 610

Spring 1996, 9:30-10:45 Tuesday and Thursday, Green Center 252

Instructor: Erik S. Van Vleck, Stratton 216, x3553


Topics

Examples of Partial Differential Equations (PDEs)
Single PDEs
Systems of PDEs
Strategies for studying PDEs
Well-posed problems; classical solutions
Weak solutions and regularity
Explicit formulas for certain linear PDEs
Transport equation
Laplace's equation
Heat equation
Wave equation
First order nonlinear PDEs
Characteristics
Hamilton-Jacobi equations
Conservation laws
Second-order Elliptic PDEs
Sobolev spaces
Weak solutions
Regularity
Maximum principles
Eigenvalues and eigenfunctions
Linear evolution equations
Second-order parabolic PDEs
Second-order hyperbolic PDEs
Systems of first-order hyperbolic PDEs
Semigroup theory

Texts

1. M. Renardy and R. C. Rogers, ``An Introduction to Partial
Differential Equations,'' Springer-Verlag (1993).
2. L. C. Evans , ``Partial Differential Equations,''
Berkeley Mathematics Lecture Notes (1994).