All inquiries about our graduate program are warmly welcomed and answered daily:
grad@math.lsu.edu
All inquiries about our graduate program are warmly welcomed and answered daily:
grad@math.lsu.edu
We will mostly follow the book by Folland. We will also hand out notes as needed. There are several other very good books on analysis and measure theory:
The material in this course builds toward open problems in mathematical physics centered around wave dynamics and scattering in electromagnetics and acoustics. The mathematical topics form a coherent body of theory and techniques. The main components are the partial differential equations (PDE) of electromagnetics and acoustics and other derived phenomena in complex media; integral equations and boundary-integral representations of solutions to PDE; Fourier analysis and the residue calculus for the study of scattering and resonance; spectral theory of differential and integral operators illustrated and motivated by examples; and asymptotic analysis. The second semester of the course will concentrate on specific problems that are motivated by modern scientific and mathematical research. A goal is that students will be able to understand open problems in this area and be equipped with the basic mathematical tools to begin trying to solve them.
(1) Hyperbolic, Parabolic, and Elliptic Partial Differential Equations
(2) Examples: The Wave Equation, The Heat Equation, The Laplace Equation
(3) Sobelev spaces and existence and uniqueness of solution.
(4) Spectral theory
(5) Banach fixed point theorem
(6) Subdifferentials and nonlinear semigroups
(7) Hamilton Jacobi Equations