偏微分方程導論

The goal of this course is to introduce students to subjects such as: Laplace equation, heat equation, and wave equations. We will stress the importance of boundary value problem, as well as initial boundary value problem for time-dependent partial differential equations. Since we will NOT strictly follow the material of the reference book, it is important for a student to take his or her own lecture notes in class. Without taking the lecture notes on your own, the course is hard to follow.

Calculus I, Calculus II, Vector Calculus, Linear Algebra.

We will plan cover the following chapters in the order: Chapter 5 Fourier Series Chapter 6 Harmonic Functions. Chapter 2: Waves and Diffusions Chapter 3: Reflections and Sources Chapter 7: Green's Identity and Green's Functions Chapter 9: Waves in Spaces Chapter 4: Boundary problems,

Homework assignments 20% (your lecture notes taking count 10 % out of the homework.) Quiz 20% Mid-Term 1 , 30 % Final Exam, 30%

Reference textbook: Partial Differential Equations, an Introduction, by Walter A. Strauss, second Edition, publisher: John Wiley & Sons, Ltd. (Wiley). This book is NOT absolutely necessary for the course. I will NOT strictly follow this book. However, we will take it as a reference. Other useful references are: Partial Differential Equations by L.C.Evans, published by AMS Elliptic Partial Differential Equations of Second Order by David Gilbarg and Neil S. Trudinger, published by Springer.