一、課程說明(Course Description) 
<br>本課程主要是介紹基本的偏微分方程:一階偏微分方程及二階線性偏微分方程。我們將學習一些解偏微分方程
<br>的方法，如特徵線方法、分離變數法、傅立葉轉換法、拉普拉斯轉換法、格林函數方法。
<br>
<br>
<br>This course is an introduction to the theory of partial differential equations intended for students 
<br>majoring in mathematics. Our aim is to introduce basic concepts and techniques of partial 
<br>differential equations. Throughout the course we will illustrate by some important mathematical 
<br>models for problems from physics, such as wave propagation, diffusion, potential theory, etc. 
<br>Students registering to this course should have some background knowledge on advanced 
<br>calculus, linear algebra, and elementary differential equations. 
<br>
<br>Topics to be covered include:
<br>
<br>Separation of variables, Fourier series,  Eigenvalue problems , Harmonic functions and 
<br>superposition, Duhamel's principle, characteristic method. Green's function, generalized functions 
<br>and fundamental solutions. Maximum principle, existence, uniqueness and continuous 
<br>dependence on data. If time permits, we will cover  Variational method, Cauchy-Kowalevski 
<br>theorem and nonlinear partial differential equations.
<br>
<br>
<br>二、指定用書(TextBook) 
<br>
<br>Walter Strauss: Partial Differential Equations, An Introduction, Second Edition, 2008 
<br>
<br>
<br>三、參考書籍(References) 
<br>Brown Chruchill, Fourier Series and boundary value problems, Eighth Edition, 2012
<br> 
<br>
<br>四、教學方式(Teaching Method) 
<br>Traditional. 
<br>習題課時間 Wed (7-9pm) 教室 (綜三館201) 
<br>
<br>
<br>五 、 成績考核(Evaluation) 
<br>25% quizzes and homework+ 35% midterm (to be scheduled)+ 40%final (to be scheduled). 
<br>
<br>Homework assignments will be mostly selected from the textbook. Some of them will be collected 
<br>and graded. Quizzes will be based on homework assignments and taken place during discussion 
<br>sessions. Details are to be announced during the first week of classes. 
<br>
<br>
<br>六、可連結之網頁位址 
<br>http://www.math.nthu.edu.tw 
<br>