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Mathematical Methods for Physics and Engineering
The third edition of this highly acclaimed undergraduate textbook is suitable for teaching all the mathematics for an undergraduate course in any of the physical sciences. As well as lucid descriptions of all the topics and many worked examples, it contains over 800 exercises. New stand alone chapters give a systematic account of the 'special functions' of physical science, cover an extended range of practical applications of complex variables. give an introduction to quantum operators. Further tabulations, of relevance in statistics and numerical integration, have been added. In this edition, half of the exercises are provided with hints and answers and, in a separate manual available to both students and their teachers, complete worked solutions. The remaining exercises have no hints, answers or worked solutions and can be used for unaided homework; full solutions are available to instructors on a password protected web site, www.cambridge.org/9780521679718.
1304 pages, Paperback
First published January 28, 1998
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Displaying 1 - 16 of 16 reviews
August 25, 2022
Pretty much all the applied/engineering maths you need for an undergraduate degree are contained within this book. This is a great review text or reference book for the following topics:
Complex numbers and hyperbolic functions
Series and limits
Partial differentiation
Multiple integrals
Vector algebra
Matrices and vector spaces
Normal modes
Vector calculus
Special functions
Quantum operators
Calculus of variations
Integral equations
Complex variables
Applications of complex variables
Line surface and volume integrals
Fourier series
Integral transforms
First-order ordinary differential equations
Higher-order ordinary differential equations
Series solutions of ordinary differential equations
Eigenfunction methods for differential equations
Tensors
Numerical methods
Group theory
Representation theory
Probability
The solutions manual is also pretty comprehensive and actually explains how to arrive at the denoted answers.
Complex numbers and hyperbolic functions
Series and limits
Partial differentiation
Multiple integrals
Vector algebra
Matrices and vector spaces
Normal modes
Vector calculus
Special functions
Quantum operators
Calculus of variations
Integral equations
Complex variables
Applications of complex variables
Line surface and volume integrals
Fourier series
Integral transforms
First-order ordinary differential equations
Higher-order ordinary differential equations
Series solutions of ordinary differential equations
Eigenfunction methods for differential equations
Tensors
Numerical methods
Group theory
Representation theory
Probability
The solutions manual is also pretty comprehensive and actually explains how to arrive at the denoted answers.
June 26, 2019
Indispensable to anyone wanting to learn a bit more about applied mathematics, with a focus on applications in physics and engineering. This took nearly two months to read, taking notes. I can only imagine how much longer you could spend with this book if you wanted to tackle every suggested exercise. Years probably. You can get a lot out of it just working through the theorems and derivations though, just because there are so many, and because they are explained in so much detail. I won't pretend that I understand and thus can derive everything in this book, but I now feel like I could study this if I wanted to. Good teachers give you the confidence to go further and study even more.
(A personal note. This book is also all the maths I learned - and didn’t learn- while studying engineering. It corresponds to the mathematics courses delivered in the first two years of the Cambridge degree, and the authors appear to be Cambridge mathmos or similar. If I had listened when my lecturers had recommended this book, and then read and absorbed the material, then maybe I would have got a degree after all. Although now it makes more sense, and back then it all was too much to take in, too quickly. Oh well. Pick your own moral of the story: listen to experienced people giving you good advice, read more, people learn in different ways. Sometimes things don't make sense in the moment, but then one day they do. Or Von Neumann's quote: “In mathematics you don't understand things. You just get used to them.�)
(A personal note. This book is also all the maths I learned - and didn’t learn- while studying engineering. It corresponds to the mathematics courses delivered in the first two years of the Cambridge degree, and the authors appear to be Cambridge mathmos or similar. If I had listened when my lecturers had recommended this book, and then read and absorbed the material, then maybe I would have got a degree after all. Although now it makes more sense, and back then it all was too much to take in, too quickly. Oh well. Pick your own moral of the story: listen to experienced people giving you good advice, read more, people learn in different ways. Sometimes things don't make sense in the moment, but then one day they do. Or Von Neumann's quote: “In mathematics you don't understand things. You just get used to them.�)
January 12, 2020
This is a terrific resource. I self-studied a lot of higher maths using this book, and it remains a handy reference. The chapters are well structured and easy to navigate, and, as an added benefit, I've found the exercises to be well varied requiring a good use of one's skills.
November 5, 2019
I read parts of it (I'd say about 1/3rd. Read the chapters on infinite series, vector algebra, univariate, multivariate, and vector calculus, linear algebra, ordinary differential equations, Fourier series, Fourier transforms and probably Laplace transforms) some 5 years ago, so I don't clearly remember all its pluses and minuses. But as far as I remember, the topics are well-covered, but exercises are few compared to the chapter sizes. The standard undergrad text on mathematical physics is Mary Boas' Mathematical Methods in the Physical Sciences, but Boas covers some things too briefly (for example, group theory). Boas does, however, have some topics dealt better than this book. Also, it's studded with exercises. (On average though, Boas goes much less deeper than Riley so if you want extra stuff, refer to Riley or any standard math text on that topic. You can also go through Arfken but I haven't read that and I hear it's great and daunting.) So I'd say buy or borrow both if you're a physics or engineering major. They complement each other really well.
December 6, 2021
Any undergraduate mathematical methods for scientists is behond essential for every human. Even without knowing how to solve problems at least the general ideas are fundamental tools and technologies that underlie our world.
January 19, 2021
great mathematics textbook
August 21, 2023
Notes on this book, by chapter:
Chapters 1-20, from preliminary algebra through linear algebra, analysis, and ordinary differential equations, is written very well and is great for learning or reviewing the material. Perhaps one of the best presentations of the material I've seen.
Chapters 20-25, on partial differential equations, the calculus of variations, and complex variables, was markedly worse than the first twenty chapters and most readers would probably benefit from going through those topics in another book.
Chapters 26 & 27, on tensors and numerical methods, is fine but a little too concise. Would be worth reading other books on the topic just for getting a good sense of them, which the book sadly didn't do a great job of doing.
Chapters 28 & 29, on group theory and representation theory, suffers from being both too long and difficult to follow because it relies on verbal descriptions rather than introducing a system of symbolic logic and discussing the topics within it using that system. There were easy 10, 15 page sections in those chapters that could have been replaced by a half page of logical statements.
Chapters 30 & 31, on probability and statistics, are a bit disappointing. They start from very low levels (Venn Diagrams) and introduce a symbolic logic system for translating those Venn diagrams into the level that people can understand things like Bayes' Rule. However, it lacked some things that would be good for probability students to learn, like a rigorous discussion of the Kolmogorov axioms, various conceptions of probability, and the underlying assumptions behind statisticial procedure.
Nonetheless this book is a masterwork, the first 2/3rds are an essential read and the last 1/3 provides some information on the topics that would be better supplemented with other works. For anyone considering reading more into the higher mathematics and their application in the sciences, this book is well-worth picking up.
Chapters 1-20, from preliminary algebra through linear algebra, analysis, and ordinary differential equations, is written very well and is great for learning or reviewing the material. Perhaps one of the best presentations of the material I've seen.
Chapters 20-25, on partial differential equations, the calculus of variations, and complex variables, was markedly worse than the first twenty chapters and most readers would probably benefit from going through those topics in another book.
Chapters 26 & 27, on tensors and numerical methods, is fine but a little too concise. Would be worth reading other books on the topic just for getting a good sense of them, which the book sadly didn't do a great job of doing.
Chapters 28 & 29, on group theory and representation theory, suffers from being both too long and difficult to follow because it relies on verbal descriptions rather than introducing a system of symbolic logic and discussing the topics within it using that system. There were easy 10, 15 page sections in those chapters that could have been replaced by a half page of logical statements.
Chapters 30 & 31, on probability and statistics, are a bit disappointing. They start from very low levels (Venn Diagrams) and introduce a symbolic logic system for translating those Venn diagrams into the level that people can understand things like Bayes' Rule. However, it lacked some things that would be good for probability students to learn, like a rigorous discussion of the Kolmogorov axioms, various conceptions of probability, and the underlying assumptions behind statisticial procedure.
Nonetheless this book is a masterwork, the first 2/3rds are an essential read and the last 1/3 provides some information on the topics that would be better supplemented with other works. For anyone considering reading more into the higher mathematics and their application in the sciences, this book is well-worth picking up.
November 20, 2024
A comprehensive math methods book!
Students seeking to begin their studies can consider this text or Mary L. Boas' book. While Boas' book has a friendly tone and detailed explanations, this book offers a concise, thought-provoking approach that covers a broader range of topics.
Although primarily tailored for undergraduate students, graduate students can also benefit from its comprehensive coverage and maintained mathematical rigor. The book effectively bridges gaps between undergraduate and graduate studies (like Griffith's ED).
A notable strength of this text is its problem sets, which include both direct application exercises to reinforce concepts and conceptual questions that test deeper understanding. It also includes answers to odd numbered problems, thud making it a complete resource for self study.
Students seeking to begin their studies can consider this text or Mary L. Boas' book. While Boas' book has a friendly tone and detailed explanations, this book offers a concise, thought-provoking approach that covers a broader range of topics.
Although primarily tailored for undergraduate students, graduate students can also benefit from its comprehensive coverage and maintained mathematical rigor. The book effectively bridges gaps between undergraduate and graduate studies (like Griffith's ED).
A notable strength of this text is its problem sets, which include both direct application exercises to reinforce concepts and conceptual questions that test deeper understanding. It also includes answers to odd numbered problems, thud making it a complete resource for self study.
November 24, 2023
This is a really good textbook for learning the mathematical foundations of theoretical physics. I've especially liked how tensors and tensor analysis were explained - this was the clearest explanation by far in literature on this level.
January 4, 2025
Great book for learning vector calculus and solving ODEs/PDEs. Great selection of problems as well. Terrible treatment of group/representation theory and tensors however, but not surprising since its written for physicists and engineers.
November 8, 2022
It's a very good quick reference guide, but not so great for learning brand new material.
December 22, 2022
A very nice reference text for physicists. It was recommended as the textbook for a class in my undergraduate days and I'm still using it almost 20 years later.
March 28, 2024
By far one of the best books on mathematical methods you need to know as a physics engineer major!
January 7, 2025
Decent.
January 8, 2025
Written for a brookes student
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August 12, 2014CONCEPT OF VECTOR MATHEMATICS
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