Exercises and Problems in Mathematical Methods of Physics

1. Front Matter

   Pages i-x

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2. Hilbert Spaces

   • Giampaolo Cicogna

   Pages 1-55

3. Functions of a Complex Variable

   • Giampaolo Cicogna

   Pages 57-71

4. Fourier and Laplace Transforms. Distributions

   • Giampaolo Cicogna

   Pages 73-125

5. Groups, Lie Algebras, Symmetries in Physics

   • Giampaolo Cicogna

   Pages 127-144

6. Back Matter

   Pages 145-182

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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 fore nontrivial 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. 

• 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

• Dipartimento di Fisica “Enrico Fermi”, Università di Pisa, Pisa, Italy

  Giampaolo Cicogna

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).

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