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by W. Strauss

  • ISBN: 0471573647
  • Category: Math & Science
  • Author: W. Strauss
  • Subcategory: Mathematics
  • Other formats: mobi azw lit doc
  • Language: English
  • Publisher: John Wiley and Sons (WIE); International Ed edition (June 9, 1992)
  • Pages: 464 pages
  • FB2 size: 1565 kb
  • EPUB size: 1902 kb
  • Rating: 4.3
  • Votes: 926
Download Partial Differential Equations: An Introduction fb2

It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs, the wave, heat and Lapace equations. Advanced concepts are introduced frequently.

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However, if you have never studied partial differential equations before, you will never learn the subject merely by reading this book. Yes, the style is comprehensible and conversational, but the derivations leave out many important steps, and you will never be able to work the excellent problems at the end of each section merely by reading and understanding each section of this book.

Partial differential equations also play a central role in modern mathematics, especially in geometry and analysis. The availability of powerful computers is gradually shifting the emphasis in partial differential equations away from the analytical computation of solutions and toward both their numerical analysis and the qualitative theory. This book provides an introduction to the basic properties of partial dif- ferential equations (PDEs) and to the techniques that have proved useful in analyzing them.

Covers the fundamental properties of partial differential equations (PDEs) and proven techniques useful in analyzing them. Uses a broad approach to illustrate the rich diversity of phenomena such as vibrations of solids, fluid flow, molecular structure, photon and electron interactions, radiation of electromagnetic waves encompassed by this subject as well as the role PDEs play in modern mathematics, especially geometry and analysis.

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Partial Differential Equations presents a balanced and comprehensive introduction to the concepts and techniques required to solve problems containing unknown functions of multiple variables. While focusing on the three most classical partial differential equations (PDEs)-the wave, heat, and Laplace equations-this detailed text also presents a broad practical perspective that merges mathematical concepts with real-world application in diverse areas including molecular structure, photon and electron interactions, radiation of electromagnetic waves, vibrations of a solid, and many more.

It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations.

Dr. Walter A. Strauss is a professor of mathematics at Brown University. He has published numerous journal articles and papers. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Dr.

from some of these books. Ordinary and partial dierential equations occur in many applications. Chapter 1. Introduction. An. ordinary dierential equation is a special case of a partial dierential equa-. tion but the behaviour of solutions is quite dierent in general. A large class of solutions is given by. u H(v(x, y))

Containing both realistic exercises and advanced topics, this undergraduate introduction to the field provides an analysis of the Robin boundary condition and the need for Fourier expansions. Schrodinger equations are also discussed, to illustrate the connection with chemistry and physics.
Reviews about Partial Differential Equations: An Introduction (7):
Just_paw
I used this book for an undergraduate level course on Partial Differential Equations. The book clearly states that it is meant for undergraduates, but my class had a healthy number of graduate students, and my professor noted that much of the book's material lands squarely in graduate territory. Depending on the sections that you study, I would suggest developing a strong background in analysis before delving into this book.

The book really isn't bad, and I learned a lot from it, but I had two major gripes:

Firstly, the author tried to pack so many supplemental (Graduate level!) chapters into the book, that the actual core material was neglected. The core chapters are very scant, and typically average only a few pages. Many important proofs are left as exercises, as well, which makes it difficult to understand the objectives of each sub-chapter. The book would be a lot better if the author had cut out four or five of the late chapters, and made the first five more detailed.

Secondly, there is a somewhat heavy emphasis on physics in this book. I'm well aware that physics and PDE are closely linked topics, but a math textbook should favor mathematical treatment of the subject matter, rather than assume that I know all about the physical meaning of equations from physics.
Malaunitly
Like another reviewer said, if you persevere and log the long hours in the earlier chapters of this book, it pays off in dividends in later chapters and exercises. My senior PDEs class covered Chapters 1-7, 9 and 12. This is a tough book but many of the ideas and exercises are interlaced in such a way that a really diligent student will be able to follow. The key here is perseverance against all frustration; for you will be frustrated with this book in the first several chapters and with the exposition. Keep a pencil in hand and work through every step of every proof and example (including all of the intermediate steps that Strauss leaves out) and you will eventually get there.
Mash
In the introduction of this book the author says the text was meant for an undergraduate level course... we are currently using the text for my graduate level class. The text is vague and there are virtually no examples. Many of the proofs normally spelled out in a text book are actually exercises. There is a solutions manual, but the manual does not contain all the solutions--just the work for the ones which already have the answers in the back of the book. If you are looking for a challenge or perhaps a review of PDEs this is the book you want. However, if this is the first time you've ever seen PDEs or you are unsure of your math capabilities you might want to have another back up text for clarification like "Applied Partial Differential Equations" by Haberman or "Partial Differential Equations for Scientists and Engineers" by Farlow.
Armin
This text is probably quite useful if you already understand partial differential equations and just need to review topics that you have already covered and grasped in the past. It outlines all aspects of introductory PDE's well, and in the appropriate order. There are well-thought out problems at the end of each chapter with answers to selected exercises that will reinforce your recall of the material. However, if you have never studied partial differential equations before, you will never learn the subject merely by reading this book. Yes, the style is comprehensible and conversational, but the derivations leave out many important steps, and you will never be able to work the excellent problems at the end of each section merely by reading and understanding each section of this book. Instead, if you are a newby to this subject and you are forced to use this book as the result of taking a course in which it is the assigned textbook, I recommend that you use "Partial Differential Equations : An Introduction" by David Colton (ISBN 0486438341) in conjunction with this text. Colton's book does a pretty good job of mopping up after Strauss, in that Colton's text takes the time to show adequate proofs and examples of sufficient complexity that you can understand the material. In addition, it pretty much covers the same subjects as Strauss in the same order only with much more detail. In addition, Colton also has good exercises for each chapter and also has answers to selected exercises. In summary, read Strauss as an outline for review and problem sets, read Colton's book for a good explanation.
Snowseeker
Easy and clear to understand. Proofs are a bit light on the rigor, but it doesn't get in the way of understanding and the exercise selection is excellent. Book arrived a little more beat up than anticipated.
Gavinrage
This textbook is really brief, not a very good textbook at all. But you are probably buying it for a course so you don't have a choice. Rental from Amazon is good as always.
Hi_Jacker
Written in a rather terse style. He glosses over many steps in derivations of equations, theorems, etc. This can make learning purely from the text difficult, but with a decent professor to fill in the gaps it's an ideal text. The skipped detail makes coming back to the text later in your career much more productive.
First: This is a very small book!!! Only about 450 pages and pages are very small. Not much materials inside.

I have five other text books on PDE include books by Nakhle Asmar, Bleecher, Haberman, Pinsky and Powers. This got to be the worst worst one. I finished studying PDE and work out a lot of problems in both Asmar and Bleecker books already and I still have a hard time following this book. I was just studying extras on PDE and looking at this book hoping to find something useful, I am so annoyed with this book I have to stop and come here to write this review!!!

This is a very difficult subject, you want to have as much explainations and examples as possible. You want detail derivation of formulas. This is what this books is particularly weak. The preface actually said it does not want to put in a lot of derivation!!!! Great!!!

If your school use it as a text book, either you have to have a very good instructor that provide very good notes or you better get another book like Asmar for supplimental reading material.

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