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PROBLEMS AND SOLUTIONS IN THEORETICAL AND MATHEMATICAL PHYSICS
Volume I: Introductory Level
Volume II: Advanced Level
by Willi-Hans Steeb (Rand Afrikaans University)
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. Bäcklund transformation, soliton equations, Lie algebra valued differential forms, Hirota technique, Painlevé test, the Bethe ansatz, the Yang–Baxter relation, chaos, fractals, complexity, etc.
Contents:
- Volume I:
- Complex Numbers and Functions
- Sums and
Product
- Discrete Fourier Transform
- Algebraic and Transcendental Equations
- Matrix Calculations
- Matrices and Groups
- Matrices and Eigenvalue Problems
- Transformations
- L'Hospital Rule
- Lagrange Multiplier Method
- Linear Difference Equations
- Linear Differential Equations
- Integration
- Continuous Fourier Transform
- Complex Analysis
- Special Functions
- Inequalities
- Functional Analysis
- Combinatorics
- Convex Sets and Functions
- Optimalization
- Volume II:
- Lax Representation in Classical Mechanics
- Kronecker and Tensor Product
- Nambu Mechanics
- Gateaux and Fréchet Derivative
- Stability and Bifurcations
- Nonlinear Ordinary Difference Equations
- Nonlinear Ordinary Differential Equations
- Groups
- Generalized Functions
- Linear Partial Differential Equations
- Nonlinear Partial Differential Equations
- Group Theoretical Reduction
- Bäcklund Transformation
- Soliton Equations
- Lax Pairs for Partial Differential Equations
- Hirota Technique
- Painlevé Test
- Lie Algebra
- Differential Forms
- Lie Derivative
- Metric Tensor Fields
- Killing Vector Fields
- Inequalities
- Ising Model and Heisenberg Model
- Number Theory
- Combinatorical Problems
- Fermi Operators
- Bose Operators
- Lax Representation and Bethe Ansatz
- Gauge Transformation
- Chaos, Fractals and Complexity
Readership: Theoretical physicists, mathematical physicists and nonlinear
scientists.
Vol. II | |
| 336pp |
Pub. date: Jun 1996 |
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