Differential Equations, Fourier Series, and Hilbert Spaces : : Lecture Notes at the University of Siena / / Raffaele Chiappinelli.
This book is intended to be used as a rather informal, and surely not complete, textbook on the subjects indicated in the title. It collects my Lecture Notes held during three academic years at the University of Siena for a one semester course on "Basic Mathematical Physics", and is organi...
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Superior document: | Title is part of eBook package: De Gruyter DG Plus DeG Package 2023 Part 1 |
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2023] ©2023 |
Year of Publication: | 2023 |
Language: | English |
Series: | De Gruyter Textbook
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Online Access: | |
Physical Description: | 1 online resource (XVI, 204 p.) |
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Other title: | Frontmatter -- Introduction -- Contents -- Preliminaries -- Notations -- 1 Ordinary differential equations -- 2 Metric and normed spaces -- 3 Fourier series and Hilbert spaces -- 4 Partial differential equations -- Bibliography -- Index |
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Summary: | This book is intended to be used as a rather informal, and surely not complete, textbook on the subjects indicated in the title. It collects my Lecture Notes held during three academic years at the University of Siena for a one semester course on "Basic Mathematical Physics", and is organized as a short presentation of few important points on the arguments indicated in the title. It aims at completing the students' basic knowledge on Ordinary Differential Equations (ODE) - dealing in particular with those of higher order - and at providing an elementary presentation of the Partial Differential Equations (PDE) of Mathematical Physics, by means of the classical methods of separation of variables and Fourier series. For a reasonable and consistent discussion of the latter argument, some elementary results on Hilbert spaces and series expansion in othonormal vectors are treated with some detail in Chapter 2. Prerequisites for a satisfactory reading of the present Notes are not only a course of Calculus for functions of one or several variables, but also a course in Mathematical Analysis where - among others - some basic knowledge of the topology of normed spaces is supposed to be included. For the reader's convenience some notions in this context are explicitly recalled here and there, and in particular as an Appendix in Section 1.4. An excellent reference for this general background material is W. Rudin's classic Principles of Mathematical Analysis. On the other hand, a complete discussion of the results on ODE and PDE that are here just sketched are to be found in other books, specifically and more deeply devoted to these subjects, some of which are listed in the Bibliography. In conclusion and in brief, my hope is that the present Notes can serve as a second quick reading on the theme of ODE, and as a first introductory reading on Fourier series, Hilbert spaces, and PDE |
Format: | Mode of access: Internet via World Wide Web. |
ISBN: | 9783111302522 9783111175782 9783111319292 9783111318912 9783111319209 9783111318608 |
DOI: | 10.1515/9783111302522 |
Access: | restricted access |
Hierarchical level: | Monograph |
Statement of Responsibility: | Raffaele Chiappinelli. |