Problems and Solutions in Theoretical and Mathematical Physics. Introductory Level

Willi-Hans Steeb9789810229436, 9810229437

The purpose of this book is to supply a collection of problems together with their detailed solution which will prove to be valuable to students as well as to research workers in the fields of mathematics, physics, engineering and other sciences. The topics range in difficulty from elementary to advanced. Almost all problems are solved in detail and most of the problems are self-contained. All relevant definitions are given. Students can learn important principles and strategies required for problem solving. Teachers will also find this text useful as a supplement, since important concepts and techniques are developed in the problems. The material was tested in the author’s lectures given around the world.
The book is divided into two volumes. Volume I presents the introductory problems for undergraduate and advanced undergraduate students. In volume II, the more advanced problems, together with their detailed solutions are collected, to meet the needs of graduate students and researchers. Problems included cover most of the new fields in theoretical and mathematical physics such as Lax representation. Bocklund transformation, soliton equations, Lie algebra valued differential forms, Hirota technique, Painleve test, the Bethe ansatz, the Yang-Baxter relation, chaos, fractals, complexity, etc.

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Table of contents :
Front cover……Page 1
Title page……Page 3
Date-line……Page 4
Preface……Page 5
Contents……Page 7
Notation……Page 9
1 Complex Numbers and Functions……Page 11
2 Sums and Product……Page 15
3 Discrete Fourier Transform……Page 29
4 Algebraic and Transcendental Equations……Page 33
5 Matrix Calculations……Page 39
6 Matrices and Groups……Page 63
7 Matrices and Eigenvalue Problems……Page 67
8 Transformations……Page 87
9 L’Hospital Rule……Page 113
10 Lagrange Multiplier Method……Page 117
11 Linear Difference Equations……Page 121
12 Linear Differential Equations……Page 133
13 Integration……Page 151
14 Continuous Fourier Transform……Page 167
15 Complex Analysis……Page 173
16 Special Functions……Page 189
17 Inequalities……Page 201
18 Functional Analysis……Page 207
19 Combinatorics……Page 219
20 Convex Sets and Functions……Page 225
21 Optimalization……Page 231
References……Page 235
Index……Page 237
Back cover……Page 239