Significantly revised and expanded, this new Second Edition provides readers at all levels---from beginning students to practicing analysts---with the basic concepts and standard tools necessary to solve problems of analysis, and how to apply these concepts to research in a variety of areas.
Authors Elliott Lieb and Michael Loss take you quickly from basic topics to methods that work successfully in mathematics and its applications. While omitting many usual typical textbook topics, Analysis includes all necessary definitions, proofs, explanations, examples, and exercises to bring the reader to an advanced level of understanding with a minimum of fuss, and, at the same time, doing so in a rigorous and pedagogical way. Many topics that are useful and important, but usually left to advanced monographs, are presented in Analysis, and these give the beginner a sense that the subject is alive and growing.
This new Second Edition incorporates numerous changes since the publication of the original 1997 edition and includes:
Features:
new chapter on eigenvalues that covers the min-max principle, semi-classical approximation, coherent states, Lieb-Thirring inequalities, and more
extensive additions to chapters covering Sobolev Inequalities, including the Nash and Log Sobolev inequalities
new material on Measure and Integration
many new exercises
and much more ...
The Second Edition continues its no-nonsense approach to the topic that has made it one of the best selling books on the subject. It is an authoritative, straight-forward volume that readers---from the graduate student, to the professional mathematician, to the physicist or engineer using analytical methods---will find useful both as a reference and as a guide to real problem solving.
3 有用 蒜子袋鼠 2021-01-03 11:14:25
我实在不太能get到为什么有人认为这本书很连贯……可能是我没怎么读透。。 我反而觉得这本书很“离散”,一个又一个小的topic。 这书不适合做教材,但也不全然没有参考价值,有许多东西在其他书很难找到,很多内容也很硬。 尽管我觉得大多数读者读这本书会很不顺畅,但莫名感觉lieb自己写的时候觉得很流畅…
0 有用 Fetalian 2015-08-21 03:15:36
读过几章
1 有用 滴滴 2018-08-11 08:43:33
对pde方向的学生很友好,参照sobolev space那本书一起。整本书思路非常连贯,门槛不高
3 有用 蒜子袋鼠 2021-01-03 11:14:25
我实在不太能get到为什么有人认为这本书很连贯……可能是我没怎么读透。。 我反而觉得这本书很“离散”,一个又一个小的topic。 这书不适合做教材,但也不全然没有参考价值,有许多东西在其他书很难找到,很多内容也很硬。 尽管我觉得大多数读者读这本书会很不顺畅,但莫名感觉lieb自己写的时候觉得很流畅…
1 有用 滴滴 2018-08-11 08:43:33
对pde方向的学生很友好,参照sobolev space那本书一起。整本书思路非常连贯,门槛不高
0 有用 Fetalian 2015-08-21 03:15:36
读过几章