Exercises and Problems in Mathematical Methods of Physics

✍ Scribed by Giampaolo Cicogna

• Publisher: Springer International Publishing
• Year: 2018
• Tongue: English
• Leaves: 188
• Series: Undergraduate Lecture Notes in Physics
• Edition: 1st ed.
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-x
Hilbert Spaces (Giampaolo Cicogna)....Pages 1-55
Functions of a Complex Variable (Giampaolo Cicogna)....Pages 57-71
Fourier and Laplace Transforms. Distributions (Giampaolo Cicogna)....Pages 73-125
Groups, Lie Algebras, Symmetries in Physics (Giampaolo Cicogna)....Pages 127-144
Back Matter ....Pages 145-182

✦ Subjects

Physics; Mathematical Methods in Physics; Fourier Analysis; Operator Theory; Functions of a Complex Variable; Integral Transforms, Operational Calculus; Group Theory and Generalizations