# Exercises and Problems in Mathematical Methods of Physics

## Benefits

• Satisfies the demand from students for a carefully structured book of exercises and problems in the mathematical methods of physics

• Offers an alternative way to understand the mathematical notions on which modern physics is based

• Proceeds from easier examples and exercises to more elaborate situations

• Avoids unnecessary difficulties and excessive formalism

Textbook

Part of the Undergraduate Lecture Notes in Physics book series (ULNP)

1. Front Matter
Pages i-x
2. Giampaolo Cicogna
Pages 1-55
3. Giampaolo Cicogna
Pages 57-71
4. Giampaolo Cicogna
Pages 73-125
5. Giampaolo Cicogna
Pages 127-144
6. Back Matter
Pages 145-182

### Introduction

This book presents exercises and problems in the mathematical methods of physics with the aim of offering undergraduate students an alternative way to explore and fully understand the mathematical notions on which modern physics is based. The exercises and problems are proposed not in a random order but rather in a sequence that maximizes their educational value. Each section and subsection starts with exercises based on first definitions, followed by groups of problems devoted to intermediate and, subsequently, more elaborate situations. Some of the problems are unavoidably "routine", but others bring to the forenontrivial properties that are often omitted or barely mentioned in textbooks. There are also problems where the reader is guided to obtain important results that are usually stated in textbooks without complete proofs. In all, some 350 solved problems covering all mathematical notions useful to physics are included. While the book is intended primarily for undergraduate students of physics, students of mathematics, chemistry, and engineering, as well as their teachers, will also find it of value.

### Keywords

Mathematical methods of Physics Fourier expansions Hilbert spaces and linear operators Complex variable methods Fourier and Laplace transforms Distributions Groups and symmetry in Physics Mathematical physics exercise book Solved problems in mathematical physics

#### Authors and affiliations

1. 1.Dipartimento di Fisica “Enrico Fermi”Università di PisaPisaItaly

Giampaolo Cicogna worked at the University of Pisa in Italy from 1966 to 2012, as Assistant Professor of Geometry for Physicists and of Complementary Mathematics for Engineers (1966–80) and as Associated Professor of Mathematical Methods of Physics (1967–2012). He joined the university’s staff shortly after graduating in Physics "magna cum laude" at the Department of Physics of Pisa University in 1964. He worked as a collaborator with the Italian Istituto Nazionale di Fisica Nucleare (INFN, National Institute for Nuclear Physics) until 2015. Author of more than 120 publications in international scientific journals, he has acted as a referee for various journals and as a reviewer for academic institutions and for CINECA (referee evaluation procedure), a nonprofit consortium comprising Italian universities, Italian research institutions, and the Italian Ministry of Education, Universities and Research (MIUR).

### Bibliographic information

• Book Title Exercises and Problems in Mathematical Methods of Physics
• Authors Giampaolo Cicogna
• Series Title Undergraduate Lecture Notes in Physics
• Series Abbreviated Title Undergraduate Lect. Notes Physics
• DOI https://doi.org/10.1007/978-3-319-76165-7
• Copyright Information Springer International Publishing AG, part of Springer Nature 2018
• Publisher Name Springer, Cham
• eBook Packages Physics and Astronomy Physics and Astronomy (R0)
• Softcover ISBN 978-3-319-76164-0
• eBook ISBN 978-3-319-76165-7
• Series ISSN 2192-4791
• Series E-ISSN 2192-4805
• Edition Number 1
• Number of Pages X, 182
• Number of Illustrations 8 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site
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