Differential Equations, Fourier Series, and Hilbert Spaces: Lecture Notes at the University of Siena
Differential Equations, Fourier Series, and Hilbert Spaces: Lecture Notes at the University of Siena by Raffaele Chiappinelli
English | September 18, 2023 | ISBN: 3111294854 | 220 pages | MOBI | 1.20 Mb
English | September 18, 2023 | ISBN: 3111294854 | 220 pages | MOBI | 1.20 Mb
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.
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