Problems and Solutions in Theoretical and Mathematical Physics, Introductory Level, Vol. 1, 2nd Edition 2nd Edition by Willi-Hans Steeb (PDF)

Description

This book is a collection of problems with detailed solutions which will prove valuable to students and research workers in mathematics, physics, engineering and other sciences. The topics range in difficulty from elementary to advanced level. Almost all the problems are solved in detail and most of them are self-contained. All relevant definitions are given. Students can learn important principles and strategies required for problem solving. Teachers will find this text useful as a supplement, since important concepts and techniques are developed through the problems. The material has been 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 detailed solutions, are collected, to meet the needs of graduate students and researchers. The 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, the Hirota technique, the Painlevé test, the Bethe ansatz, the Yang-Baxter relation, chaos, fractals, complexity, etc.

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⭐Table of Contents follows:Volume 1: Introductory/Undergraduate Level1 Complex Numbers2 Sums and Product3 Discrete Fourier Transform4 Algebraic and Transcendental Equations5 Matrix Calculations6 Matrices and Groups7 Matrices and Eigenvalue Problems8 Transformations9 L’Hospital’s Rule10 Lagrange Multiplier Method11 Linear Difference Equations12 Linear Differential Equations13 Integration14 Continuous Fourier Transform15 Complex Analysis16 Special Functions17 Inequalities18 Functional Analysis19 Combinatorics20 Convex Sets and Functions21 Optimization

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