北京大学-应用偏微分方程

Applied PDEs II 要讲什么呢 ？
The "second" course in PDEs is much more problematic. It is not always clear at what level to pitch it, and since the subject is so vast, what cover. Possible texts for such a course are the ones by Fritz John, Folland, showalter, or approximately the first third of the book by Smol The book of Kevorkian is a valuable and welcome addition to this field. It is fast becoming the standard text on American campuses, being widely used in both senior and postgraduate level courses. It covers a great de classical material (Green's functions, transform methods), but this is n strength.
他山之石二
•Fall 2007: Applied Partial Differential Equations 1 (MATH 580). •http://www.math.mcgill.ca/~wihler/sy llabus.pdf
Poisson 方程 波动方程 热传导方程 特征线方法、非线性守恒律
Description The focus of this course are the concepts and techniques solving partial differential equations (PDE) that permea scientific disciplines. There will be an emphasis on non Applications include problems from fluid dynamics, elec and mechanical engineering, materials science, and quant mechanics.
他山之石三
•Applied Partial Differential Equations Fall Term 2005
Course webpage: www.math.ubc.ca/˜schoetzau/courses/math400.html Course contents: • The main equations • Method of characteristics for first-order problems • Sturm Liouville theory • Eigenfunction expansions • Fourier and Laplace transforms • Conformal mappings • Introduction to finite difference and finite element methods Text: There is no required text for this course. The material of the course will mos • R. Habermann: Applied differential equations, Pearson Prentice Hall, 2004. • E. Zauderer: Partial differential equations of applied Mathematics, Wiley, 1989. We will also cover material that is not in these texts.
P. Markowich 的书的介绍
This book presents selected topics in science and engineering from an applied-mathematics point of view. The described natural, socioeconomic, and engineering phenomena are modeled by partial differential equations that relate state variables such as mass, velocity, and energy to their spatial and temporal variations. Typically, these equations are highly nonlinear; in many cases they are systems, and they represent challenges even for the most modern
具体在下面一页
应用偏微y, one usually attempts to derive the (wave, heat) based on some reasonable-looking physical premises, and then to giv account of the mathematical (initial-value, boundary-value, etc.) problems that arise and of elementary methods for their solution (separation of variables, transform methods, Green's functions). It is not surprising that there exist numerous texts covering all t topics. I should only mention the excellent book by Boyce and Di Pr a favourite on many American campuses (in addition to the above top it also has an excellent treatment of Sturm-Liouville theory).
认识没有同一
Applied PDEs II 要讲的内容
The outstanding chapters in this book, in this reviewer's opinion, are the ones dealing with wave phenomena (chapters 3 - 5,7), nonlinear first order equations (chapter 6, my personal favourite) and perturbation techniques (chapter 8). Though there are very good books on asymptotic methods, it is very instructive to see them introduced and used for specific PDE purposes. After completing a course based on this book, a diligent student will have a good background in such important areas as shallow water waves, Hamilton-Jacobi equations, shock propagation, matched asymptotic expansions and the method of multiple scales. A highly recommended book, also competitively priced. M. GRINFIELD Department of Engineering Mathematics, Queen's Building, University Walk, Bristol BS8 ITR
Applied PDES I
还要讲什么呢？
Applied PDEs I 的内容
With computer technology available today, it is very easy to transform course notes into book form. The book by Trim is testimony to that, and another addition to the "first course in PDEs" genre. It covers all the material described above and more. Among the topics one would not expect in a course on this level is a thorough treatment of problems in various coordinate systems, a discussion of Hankel transforms, and a section on the inversion of the Laplace transform. One could objec that complex analysis should not be a prerequisite; on the other hand, this section could be used as a solid application of contour integration in a complex analysis course. I is a solid, well illustrated book, containing a wealth of exercises. A student supplement is available from the author. There are no particular reasons to choose this book over other contenders in the field, except that as an International Student Edition, it is competitively priced.