Differential Equations, Fourier Series, and Hilbert Spaces

Lecture Notes at the University of Siena
1. Auflage 2023
ISBN: 978-3-11-129485-8
Verlag: De Gruyter

Buch, Englisch, 204 Seiten, Format (B × H): 170 mm x 240 mm, Gewicht: 382 g

Reihe: De Gruyter graduate

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

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

Zielgruppe

Graduate and advanced undergraduate students interested in applic

Autoren/Hrsg.

Chiappinelli, Raffaele

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Über Autor(innen)

Raffaele Chiappinelli obtained his Laurea in Physics at the University of Naples, Italy (1974) and then his Ph.D. at the University of Sussex, UK (1986) under the advice of D.E. Edmunds. He has been Associate Professor of Mathematical Analysis for more than 30 years, first at the University of Calabria (1986-1994) and then at the University of Siena (1994-2018), where he is remained in activity as a Senior Professor. His research interests focus on Eigenvalue problems and spectral theory for nonlinear operators acting in Banach spaces and on the related Bifurcation theory, with applications to ordinary and partial differential equations. He is author of more than 40 publication.