Introduction to Partial Differential Equations and Hilbert Space Methods (Dover Books on Mathematics) 3rd Edition by Karl E. Gustafson (PDF)

Description

Easy-to-use text examines principal method of solving partial differential equations, 1st-order systems, computation methods, and much more. Over 600 exercises, with answers for many. Ideal for a 1-semester or full-year course.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Mainly used this as an additional reference to another text in my PDE course. Instructionally very decent. Half the text shouldn’t be appendices…

⭐I do not think that this is a good first book on the subject (I have completed a course on Boundary Value Problems and am very familiar with PDEs). The author moves very quickly in this text by attempting to give theory, background, motivation, etc. but then asks you to solve problems (like what you would find in a typical math textbook). It’s very odd, Evans is better than this text in that regard. He explains the thought process, then gives you theory problems to solve to push your understanding.The field is in fact very accessible to beginners, but that being said you wouldn’t get that idea from reading this book. I remember trying to pick it up a few years ago and thinking that it was an unnecessarily complicated book that was lacking. With my experience in math now I would say it’s tremendously outdated by the abundance of quality PDE texts.The author does provide solutions to the problems but I believe that there are many other good books on the subject that I would start with instead of this one. I believe that this book is better as a second text, as it is lacking in examples but it does offer some theory. The text also makes much use of the geometrical meaning behind solutions and problems, which some other books might breeze by. I do appreciate this as this was something that I had not ever really understood.Note to the beginner: if you’ve completed ODE then you can complete PDE (at the undergraduate level).I recommend Bleecker (has an introductory ODE section), Asmar, and/or Debnath. But there are many many more.

⭐There are newer editions than this one, and they come cheaper as well.

⭐The book is of PDE topics, with the understanding that you have a well mastered trig through calculus 3, and can recall them from memory.The book requores some on-line studying to find worked examples of the concepts instead of brief overviews.

⭐This is an excellent book for the beginning engineer/scientist as well as the more experienced technical person. I will use this as a reference in the class I teach on Mathematical Methods for Electromagnetic Theory.

⭐Not a good introduction. It does not go through all of the standard PDE material, and seemed to me to have a somewhat circular structure – none of it made much sense until I already understood the topics (I even tried reading it backwards as Gustafson often does with books). I agree with the other reviewer, “An overview of PDE’s for the advanced student, and interesting applications.” would be a better title.

⭐not helpful at all

⭐Having just taken this course from Professor Gustafson, I can say, with complete support from everyone in every PDEs class he’s taught as of yet, that this book leaves a lot to be desired. There is absolutely no mention of separation of variables, the section on greens functions forgets to mention at all what they’re used for, and further how to do anything with them, and numerous other grave omissions. I feel a more apt title would be: “An overview of PDE’s for the advanced student, and interesting applications.” So perhaps, for the right teacher this will be a fine book, but beware, you are going to have a lot of work filling in the large gaps the book leaves.Also, thought this has no bearing on the quality of the book, he has a strange obsession with the number 3.

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