- Paperback: 236 pages
- Publisher: World Scientific Publishing Co Pte Ltd (25 July 2003)
- Language English
- ISBN-10: 9812384308
- ISBN-13: 978-9812384300
- Product Dimensions: 23.3 x 14.7 x 1.5 cm
- Average Customer Review: 5.0 out of 5 stars See all reviews (1 customer review)
- Amazon Bestsellers Rank: 827,148 in Books (See Top 100 in Books)
- See Complete Table of Contents
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Product Description
Product Description
Providing a concise exposition of the basic ideas of the theory of distribution and Fourier transforms and its application to partial differential equations, this book clearly presents the ideas, precise statements of theorems, and explanations of ideas behind the proofs. Methods in which techniques are used in applications are illustrated, and many problems are included. The book also introduces several significant recent topics, including pseudodifferential operators, wave front sets, wavelets, and quasicrystals. Background mathematical prerequisites have been kept to a minimum, with only a knowledge of multidimensional calculus and basic complex variables needed to fully understand the concepts in the book.
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First Sentence
You have often been asked to consider a function f (x) as representing the value of a physical variable at a particular point x in space (or space-time). Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
You have often been asked to consider a function f (x) as representing the value of a physical variable at a particular point x in space (or space-time). Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Customer Reviews
Most Helpful Customer Reviews
1 of 1 people found the following review helpful
Format:Hardcover
The book is written very well. From the start it gives you very clear view of what the distributions are. In the next part of the book you are thaught very well how to deal with calculations using distributions. The examples are picked in a very didactic way, simple but they show you the crucial points of calculations and the material is treated indepth. You should know, dustribution theory is not a simple theory, it is based on Lebesque theory of measureable sets, so try read the basics of this theory first and then return to the book. If you are accustomed to Fubini theorem, Fourier transforms, a set measure then you may start reading this book. The next might be Zemanian "Distribution Theory and Transform Analysis" - old but still very good for the practical use. There are given many examples in this book hardly met in other ones like Fourier transform of special functions from a beginner point of view, direct solutions of differential equations via Fourier transforms - there are distribution additions yet etc. The exercises are of medium difficulty, but feasible for a student and they are very didactic. In addition to that there given many physical examples of distribution and Fourier transform using, very clearly explained. Thus, finally, this is the very good book for an advanced student.
Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com:
2 reviews
11 of 11 people found the following review helpful
Excellent
17 Sep 2007
Format:Hardcover
Distributions are objects most physicists will frequently encounter during their career, but, surprinsingly, the subject is not given the place it deserves in the current ordinary science curriculum.
I would particularly recommend this book to physics students willing to learn the foundation of distribution theory and its close ties to Fourier transforms. Distribution theory is, basically speaking, a way of making rigorous the operations physicists find Ok to carry on functions, that otherwise wouldn't rigorously make sense. Distribution theory therefore provides a useful way of checking, in the process of a calculation, if it is allowed (according to the extended rules of distribution theory), or if it is definitely dubious (e.g. current distribution theory doesn't provide a mean of making sense of a product of Dirac delta functions, while such expressions sometimes pop out in the context of quantum field theory ; nevertheless, there exist other formal theories, such as Colombo calculus that aim at justifying this ; yet, for some reason, they seem to bear less power than the original distribution theory).
This work is an easy, gentle, pedagogical piece of mathematical exposition.
The subject is wonderfully motivated.
As such, this book is suited to self-study.
It could also be used as a textbook for an introductory course on the subject, or as an introductory reading to more advanced texts (Aizenman, for instance).
Highly recommended.
I would particularly recommend this book to physics students willing to learn the foundation of distribution theory and its close ties to Fourier transforms. Distribution theory is, basically speaking, a way of making rigorous the operations physicists find Ok to carry on functions, that otherwise wouldn't rigorously make sense. Distribution theory therefore provides a useful way of checking, in the process of a calculation, if it is allowed (according to the extended rules of distribution theory), or if it is definitely dubious (e.g. current distribution theory doesn't provide a mean of making sense of a product of Dirac delta functions, while such expressions sometimes pop out in the context of quantum field theory ; nevertheless, there exist other formal theories, such as Colombo calculus that aim at justifying this ; yet, for some reason, they seem to bear less power than the original distribution theory).
This work is an easy, gentle, pedagogical piece of mathematical exposition.
The subject is wonderfully motivated.
As such, this book is suited to self-study.
It could also be used as a textbook for an introductory course on the subject, or as an introductory reading to more advanced texts (Aizenman, for instance).
Highly recommended.
Introductory textbook
14 May 2012
Format:Paperback|Amazon Verified Purchase
I like this book as an introductory distribution theory book. It has plenty of examples and the language form makes it easy to not fall asleep when reading. However, if you're digging in to the subject deeply (looking for specific theorems etc.) you will notice that some things are missing, and some details in proofs are missing.
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