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Methods of Mathematical Physics Volume 1: v. 1 (Wiley Classics Library) [Paperback]

R Courant

Price: £109.00 & FREE Delivery in the UK. Details
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Book Description

4 Jan 1989 0471504475 978-0471504474 Volume 1
Since the first volume of this work came out in Germany in 1924, this book, together with its second volume, has remained standard in the field. Courant and Hilbert′s treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant′s second and final revision of 1953.

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David Hilbert (1862 ¿ 1943) received his PhD from the University of Königsberg, Prussia (now Kaliningrad, Russia) in 1884. He remained there until 1895, after which he was appointed Professor of Mathematics at the University of Göttingen. He held this professorship for most of his life. Hilbert is recognized as one of the most influential mathematicians of the 19th and early 20th centuries. His own discoveries alone would have given him that honour, yet it was his leadership in the field of mathematics throughout his later life that distinguishes him. Hilbert′s name is given to Infinite–Dimensional space, called Hilbert space, used as a conception for the mathematical analysis of the kinetic gas theory and the theory of radiations. Richard Courant (1888 ¿ 1972) obtained his doctorate at the University of Göttingen in 1910. Here, he became Hilbert¿s assistant. He returned to Göttingen to continue his research after World War I, and founded and headed the university¿s Mathematical Institute. In 1933, Courant left Germany for England, from whence he went on to the United States after a year. In 1936, he became a professor at the New York University. Here, he headed the Department of Mathematics and was Director of the Institute of Mathematical Sciences – which was subsequently renamed the Courant Institute of Mathematical Sciences. Among other things, Courant is well remembered for his achievement regarding the finite element method, which he set on a solid mathematical basis and which is nowadays the most important way to solve partial differential equations numerically.

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In the present volume we shall be concerned with many topics in mathematical analysis which are intimately related to the theory of linear transformations and quadratic forms. Read the first page
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Amazon.com: 4.3 out of 5 stars  6 reviews
12 of 13 people found the following review helpful
4.0 out of 5 stars Theory of advanced mathematics (not physics). 5 July 2010
By A. I. Haque - Published on Amazon.com
Format:Paperback|Verified Purchase
This book is intended for mathematicians and not for physicists. All of the mathematics is developed through proofs of theorems. The chapter on approximation of functions is the best in the book. There is also a short introduction to Lebesgue integration which is the best explanation of what it actually means that I have ever seen! (i.e. not having to develop the messy business of measure theory that fills up 10s of pages in most books).

If you want to learn graduate level mathematics (i.e. analysis and PDEs) in gorey detail then this is the book for you. If you want to understand applications, then it is not. I don't like the term "mathematical physics." It depend on which department teaches it. A mathematician will focus on the topics in this book. A physicist would focus on methods and not on proofs.
11 of 14 people found the following review helpful
5.0 out of 5 stars The best book available 29 April 2009
By P. Mohanamuraly - Published on Amazon.com
I would definitely not agree with any bad comments to this book. There are millions of books out there for you to workout problems and help you pass exams. But there is only one who actually teaches the subject and it's Courant. I don't expect literary genius out of a Mathematics book but clear development of the topics. The translation does a good job at it. Believe me if you really want to know the subject and get a feel for it read this book.This is not for the feckless as you will start defacing its stature with your comments. But the price tag is exorbitant and not many can afford to read this wonderful text. I had to borrow from my library as I cannot afford to buy one. 230+$ for two volumes is no joke especially for a student !!
5.0 out of 5 stars In reply to 'theory of advance mathematics(not physics)'. On what I have read so far. 25 Nov 2013
By Hari Rau-Murthy - Published on Amazon.com
I will not claim to have read the whole book . But I have read his brief stint on lebesgue integration(after seeing the comment 'theory of advance mathematics(not physics)' and his chapter on integral equations and on that in volume two giving a rigorous ground on generalized functions carefully. I give this book 5 stars based on what I have read.

The material on lebesgue integration being two pages long is clear because it is mostly formulation. It does not give proofs. However proofs are found in a great many places and there is no point in a book meant to be read, especially one like this, being encyclopedic. This is mainly useful as motivation(why do we need a new integral, how we end up needing the inverse image of the partitions of the range to be sets we can find a useful area of, and why we need the measure to be countably additive. His motivation for dominated convergence theorem is great, giving a weaker version that is easy to understand. Then he formulates what he means by the hilbert space being closed and how it implies completeness.(if you forgot what this means this is formulated in the couple pages where he talks about it too).

This motivation that courant and hibert have given is very important and missing in standard measure theory and integration texts (even the ones with flowery introductions to each theorem and chapter like STEIN and SHAKARCHI) because otherwise, this all feels like unnecessary complications.

The section on integral equations was very clear to me. Maybe it is because I struggled on it for so long and let it sit before picking up this section. I think it is because it was straight after the section on lebesgue integration and right before he talks about what are today called 'good'' kernels and approximations to the identity. Thus this gives motivation for trying to formalize what exactly the limit to the identity. In any pde where one needs to take derivatives and ends up with generalized functions(e.g.dirac delta), the equation needs to be written in terms of an integral equations. This(placement) principally motivates his study of integral equations. His elaboration on generalized functions in volume two are equally admirable.
11 of 20 people found the following review helpful
4.0 out of 5 stars This book is a classics, but perhaps not exhaustive 27 July 2003
By A Customer - Published on Amazon.com
I think that this book is better in its original german than in english langauge. As to its content, it may perhaps not include all items of this thema, but the items include are treated with genius. The lack of problems to solve may be a draw back, but for me that is not much trouble because there are many books with many problems to solve. The interest of this book lies in its being a source book, though historically written down in 1924, it still mantains its beauty and its present mathematical value.
23 of 50 people found the following review helpful
3.0 out of 5 stars This book is famous, but cannnot be described as classics. 5 Aug 2001
By Wan Koon Yat - Published on Amazon.com
I brought this book ( volume 2 also as well ) because of its " fame ", but when I read it, it has several draw backs. First, may be the original vesion is in German, so even with good translation, it seem does not fit in the usual English style we get used to .Also the topics it choose is too few and also the area covered is too narrow and not well co-ordinated. For example, the whole volumme I is almost dedicated to Calculus of variation only. In volume 2, the whole book is dedicted to differentiation equations. But that is not the greatest drawback. The most bad point is that the book just presents formulae after formulae, equations after equations, without giving examples of how to use it,and also no exercise for me to practice. Compared the the timeless classic " A course of mordern analysis " by Whittaker and Watson, it is definitely at a lower level. This book cannot be described as " classics ".
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