Lecture Notes on Functional Analysis: With Applications to Linear Partial Differential Equations (Graduate Studies in Mathematics) by Alberto Bressan (PDF)

Description

This textbook is addressed to graduate students in mathematics or other disciplines who wish to understand the essential concepts of functional analysis and their applications to partial differential equations. The book is intentionally concise, presenting all the fundamental concepts and results but omitting the more specialized topics. Enough of the theory of Sobolev spaces and semigroups of linear operators is included as needed to develop significant applications to elliptic, parabolic, and hyperbolic PDEs. Throughout the book, care has been taken to explain the connections between theorems in functional analysis and familiar results of finite-dimensional linear algebra. The main concepts and ideas used in the proofs are illustrated with a large number of figures. A rich collection of homework problems is included at the end of most chapters. The book is suitable as a text for a one-semester graduate course.

User’s Reviews

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

⭐Nice book, it develops the fundamental tools of functional analysis in order to study the main linear PDEs. This book is very similar to that of Brezis, but it is shorter and it has a faster development of the theory. In addition, there are many exercises at the end of each chapter. My only negative observation is that it is a little bit expensive, probably because it is hardcover. Maybe a softcover edition would get a perfect price for this textbook.

⭐A truly well written text. The author achieves a lot in under 300 pages. Presentation is detailed, and problems are suitable. Includes a few applications to partial differential equations. Appendices contain the necessary background material. Highly recommended.

⭐(la parte di PDE non la ho affrontata e non esprimo un parere riguardo quella)buono come libro introduttivo ma, allo stesso prezzo, si trovano libri più completi che trattano lo stesso programma nel dettaglio. Mi ha colpito negativamente la parte di Topologia Debole: è assente, solo qualche riferimento alla convergenza. Anche per quanto concerne gli spazi riflessivi e le loro proprietà.Purtroppo un acquisto che non ripeterei.(Consigli il libro di Brezis, Functional Analysis..)CONSEGNA: rapidissima ed efficiente come sempre

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