Methods in Applied Math I

   Fall Semester 2006                Eric Olson
   MWF 12:00-12:50pm AB205           ejolson at unr.edu
   Office hours MW 2pm and F 1pm in AB614

This course is part one of a two semester sequence of courses aimed at beginning graduate students in both pure and applied mathematical sciences. The goal of this course sequence is to provide a thorough introduction to the advanced study of partial differential equations. We shall read a standard graduate level text giving a modern mathematical treatment of partial differential equations.

Methods in Applied Math I will cover chapters 1-4 from the text including Laplace, heat, and wave equations, characteristics, Cauchy-Kovaleskaya Theorem, Holmgren's Uniqueness Theorem, conservation laws and shocks, Rankine-Hugoniot condition, Lax shock condition, maximum principles, and the Arzela-Ascoli Theorem.

Next semester methods in Applied Math II will cover chapters 5-7 from the text including distributions, fundamental solutions, the Fourier transform, Green's functions, Banach and Hilbert spaces, Hahn-Banach Theorem, Sobolev spaces, Sobolev Imbedding Theorem, trace theorems, Open Mapping Theorem, Sturm-Liouville boundary-value problems, and the Freedholm index.

Texts:

1. Michael Renardy, Robert C. Rogers, An Introduction to Partial Differential Equations, Texts in Applied Mathematics 13, Springer-Verlag, 1993.

Course Web Page: http://fractal.math.unr.edu/~ejolson/761/

Prerequisites: It is recommended that the student be currently enrolled in Math 713 or have already taken it. The text is suitable for first-year graduate students. A student should already have complete a course in advanced calculus such as Math 310/311 or equivalent.