北京大学-应用偏微分方程
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应用偏微分方程
卢朓 北京大学数学科学学院 tlu@math.pku.edu.cn
Applied Partial Differential Equations
•内容是什么？ •怎样选择？ •我们的选择
他山之石之一
• MIT 公开课件 Advanced Partial Differential Equations with Applications, Spring 2004
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.
他山之石二
•Fall 2007: Applied PartiaLeabharlann Baidu 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.
书评，也是对 Applied PDEs 的 思考
第一本书： Applied partial differential equations, by D. W. Trim. Pp 521. £ 15-95. 1990. ISBN 0-534-98243-3 (Chapman and Hall) 第二本书 : Partial differential equations: analytical solution techniques, by J. Kelvorkian. Pp 547. £14-95. 1990. ISBN 0-534-98180-1 (Chapman and Hall) 摘要： 偏微分方程要分两部分，第一部分主要是三个线性方程 ;
具体在下面一页
应用偏微分方程 I 要讲的
More specifically, 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).
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.
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
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.
好看的书
•P. Markowich, "Applied Partial Differential Equation: A Visual Approach" Springer | ISBN 3540346457 | Year 2006 | 206 pages |
书中有很多漂亮的图片 介绍了应用偏微分方程的好几个应用领域 http://hi.baidu.com/motioo 给出了下载地址
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
卢朓 北京大学数学科学学院 tlu@math.pku.edu.cn
Applied Partial Differential Equations
•内容是什么？ •怎样选择？ •我们的选择
他山之石之一
• MIT 公开课件 Advanced Partial Differential Equations with Applications, Spring 2004
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.
他山之石二
•Fall 2007: Applied PartiaLeabharlann Baidu 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.
书评，也是对 Applied PDEs 的 思考
第一本书： Applied partial differential equations, by D. W. Trim. Pp 521. £ 15-95. 1990. ISBN 0-534-98243-3 (Chapman and Hall) 第二本书 : Partial differential equations: analytical solution techniques, by J. Kelvorkian. Pp 547. £14-95. 1990. ISBN 0-534-98180-1 (Chapman and Hall) 摘要： 偏微分方程要分两部分，第一部分主要是三个线性方程 ;
具体在下面一页
应用偏微分方程 I 要讲的
More specifically, 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).
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.
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
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.
好看的书
•P. Markowich, "Applied Partial Differential Equation: A Visual Approach" Springer | ISBN 3540346457 | Year 2006 | 206 pages |
书中有很多漂亮的图片 介绍了应用偏微分方程的好几个应用领域 http://hi.baidu.com/motioo 给出了下载地址
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