What do you think?
Rate this book
PROBLEMS AND SOLUTIONS IN THEORETICAL AND MATHEMATICAL PHYSICS - VOLUME I: INTRODUCTORY LEVEL
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.
224 pages, Hardcover
First published June 1, 1996
16 people want to read
About the author
Willi-Hans Steeb
45 books1 followerWilli-Hans Steeb, Dept. of Physics, Raand Afrikaans U., Johannesburg, SA
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 of 1 review
July 22, 2021
I am surprised how unknown this book is. I started this book as part of my "rehabilitation" because my work involved so little pure brain power (more numerical stuff) that I lost touch with pen-and-paper skills. This book exceeded my expectations.
The book's exercises at this level is very manageable if you have seen the stuff before, some even look very easy. However, for some problems you need clever tricks and the solutions explained them really well. The problem I had with this book (perhaps it's actually a non-problem) is that the strike zone is so wide: it assumes that a typical theoretical and mathematical physics student would encounter very unusual special functions, familiar with functional analysis (for introductory book!), optimization, advanced complex analysis (meromorphic functions and the like), and differential equations (also difference equations).
My current judgment is that it's my weak foundation as a theoretical physics student that's to blame for my lack of background to completely conquer this book. But otherwise, this book's solutions (apart from some mistakes and typos) have things to learn from, especially when they approach the problem differently from what naturally comes to you. Also, if your background is only lacking for some topics, but sufficiently strong elsewhere, this book can easily serve its purpose by being selective; you don't have to do everything. I skipped things that I don't foresee I will working with in the next two years or so.
I would actually recommend this to anyone who wishes to pursue theoretical and mathematical physics in future, or during graduate school, just as a way to hone your skills. Even two pages a day would clear this book in 3 months, and for many problems two pages can be done in 15 minutes, certainly a timeframe that most busy people can afford to spare.
The book's exercises at this level is very manageable if you have seen the stuff before, some even look very easy. However, for some problems you need clever tricks and the solutions explained them really well. The problem I had with this book (perhaps it's actually a non-problem) is that the strike zone is so wide: it assumes that a typical theoretical and mathematical physics student would encounter very unusual special functions, familiar with functional analysis (for introductory book!), optimization, advanced complex analysis (meromorphic functions and the like), and differential equations (also difference equations).
My current judgment is that it's my weak foundation as a theoretical physics student that's to blame for my lack of background to completely conquer this book. But otherwise, this book's solutions (apart from some mistakes and typos) have things to learn from, especially when they approach the problem differently from what naturally comes to you. Also, if your background is only lacking for some topics, but sufficiently strong elsewhere, this book can easily serve its purpose by being selective; you don't have to do everything. I skipped things that I don't foresee I will working with in the next two years or so.
I would actually recommend this to anyone who wishes to pursue theoretical and mathematical physics in future, or during graduate school, just as a way to hone your skills. Even two pages a day would clear this book in 3 months, and for many problems two pages can be done in 15 minutes, certainly a timeframe that most busy people can afford to spare.
Displaying 1 of 1 review