Mathematics for Physicists: Introductory Concepts and Methods

I bought this textbook in order to brush up analytically on my single variable calculus, multiple variable calculus, and linear algebra. What I got from reading this textbook was an alternative viewpoint unlike that of a mathematician regarding these 3 mathematical subjects. I was able to gain further insight and a physical point of view regarding these subjects, this alone has helped me out tremendously furthermore my background in mathematics consists of your regular single/multi variable calculus, ordinary differential equations and linear algebra, partial differential equations & complex analysis, and signals analysis and some real analysis.I would highly recommend this text to other physicists, really, any scientist in general that needs a concise brush up or introduction, the reason why is that one is able to relearn their calculus and linear algebra and touch upon some topics within the text that may have never been covered in their university courses, I never recalled learning multilinear algebra, differential geometry, hermiticity & symmetry and various other peculiar/special functions during undergrad calculus and engineering mathematics (with engineering math being just a concise introduction and combination of ordinary differential equations and linear algebra for time purposes). The 3-D diagrams within the textbook are extremely helpful in representing what is going on, also, the various problems within this textbook are helpful as well because they really do make you think (this isn't an exaggeration, some really make you think) and represent the core of the material being taught, no dilly dallying in learning what are the core concepts that one needs to be able work with the mathematics, it also helps out a lot that the text contains solutions to half of the problems.Now for the bad news. One major thing that irks me a lot is that there is no table/list of symbols/greek alphabet which displays in english the mathematical notations/symbols used (pic related), this also isn't helped by the fact that some of the symbology isn't named? Maybe this is the only exception but the reason why I said the previous sentence is that in section C6.1 the dirac delta function is introduced but isn't even called the dirac delta function, it's just referred to as "function" no joke. I don't recall this occuring regularly, or maybe it's because it's such a famous function that it just caught me completely off guard, I had to google the function name to see if i wasn't going crazy in not recognizing the dirac delta function.The very first section of the linear algebra section L1.1 Sets and maps & L1.2 Groups, is no joke. I would find it very hard to believe that a student who has never taken an introductory course on proofs and group theory would fully understand this section, seeing as how I've taken a proofs course followed by a group theory course with Book of Proof by Hammack and Discovering Group Theory: A Transition to Advanced Mathematics by Barnard (two of the absolute best introductory mathematical analysis texts I've ever used). I really don't see how one who is new to those two subjects would fully digest those two extremely condensed and concise sub sections, and the problems that go along with said sub sections are no joke (bad).Of course if you already have some mathematical maturity then going through that part of the text would be a complete breeze, a cakewalk even, but i'm talking about this from the theoretical perspective of a brand new undergrad who bought this textbook to learn from scratch calculus, linear algebra, and some various mathematical methods, who has never seen this stuff before, of course they will have problems with such a short introduction to those two sub section, personally I think that the authors should just reform those two subsections into full chapters or just into bigger subsections in general and explain with more detail about sets and groups (maybe like 15-20 pages each), I mean, come on, the entire book is built using said information from those two subsections in order to understand what is going on in the rest of the text, I can see how that can be a problem for the uninitiated. If you're reading this and decide to buy the book, go for it, it's a really great text to do problems in and relearn or for the first time ever, learn CALC and LINALG and other side stuff that's very useful, also one can easily use this as a reference.But yeah, just expand those two subsections and make a table of symbols used throughout the text.

This is a book for a university course, in Germany, to prepare students for mastering undergrad physics. It's entirely written in English, the language of physics journal papers. The intent of this book is to teach the mathematical concepts necessary to understand modern physics concepts rather than the student having to learn the mathematics in a rushed manner in modern physics courses, possibly inadequately. The authors explain the concepts, while maintaining a good degree of mathematical rigor, rather than merely presenting them. That makes learning the concepts from scratch from this book entirely possible and enjoyable. There are problems to fortify your understanding and worked-out solutions to the odd-numbered problems for self-study. This book builds on basics and walks the reader through advance math concepts and problems. The book starts with set theory and proceeds to linear algebra, with tensors at the final section of linear algebra. Next, it moves onto calculus of a single variable, explaining the derivative and integral. It moves onto multivariable calculus, Taylor series, and differential equations. The book finishes with vector calculus. I believe one really could learn quite well all these topics from scratch from this book, and that's the authors' intent. I've never read a book quite like this that presents so much mathematical material in a progressive manner that's actually very easy and enjoyable to read without relying on a bunch of theorems and lemmas and not much explanation. The authors went through the trouble to explain everything as succinctly as they could without cutting out too much detail, and I think they did a good job. I highly recommend this outstanding book.

This book is great! I'm able to actually learn about the mathematics machinery needed in physics from the ground up. I'd highly recommend for anyone that is currently in undergrad and above

This is an excellent textbook for learning math fundamentals for physics! Certainly, one of the best, if not best.

The authors say that this book is meant to be a bridge between the rigor of math and a math methods book. However they spend too much time on linear maps and too little on differential equations, which are the math heart of physics. I think Riley or Boas are better options, especially for advanced undergrads and beginning grad students.