Physical Mathematics

The book covers a broad spectrum of topics and tries to give the young physicist all possible sort of tools she needs for her research. It covers lots of topics and in my opinion is far better than Arfken since it covers more up to date research related topics. It can be used by undergrad and grad students with different lines of interest from string theory and quantum optics to experimental biophysics and finance. As a graduate student in Biophysics / Optics, i find this book more relevant to today's way of thinking rather than any other book available.

Cahill's work evinces a great insight and passion for teaching mathematical methods and theoretical physics. His decades of classroom experience are evident in his command of the foundational topics in this overlap of mathematics and physics. The pace is brisk and the presentation is complete and economic. The choice of topics is fresh which makes the book a pleasure to read. The examples and exercises reveal a skilled explicator who has helped to train a generation of physicists. This tome is a welcome and modern addition to even the most crowded bookshelf.

The only thing I could think would make this book any worse would be to make the formulas and derivations incorrect in this book. From a mathematician's perspective, we need to stop relegating a physicist's mathematical education to books like these once they get past basic Differential Equations and Linear Algebra. It's a huge mistake to teach like this. in fact, I think it goes even deeper. Why teach calculus twice? First you take basic calculus, then you take real analysis, if you are smart. This book is in that Freshman-Calculus style of mathematics that doesn't really get to the root of the issues of why the mathematics works. It's very ugly, but this is what physicists are used to, not thinking deeply about mathematics. I remember the first time I took a graduate quantum class. Physicists love to just swing their mathematics around like baseball bats breaking things. Mathematicians are like the ones behind a laser guided missile system, precisely coordinating the attack for striking. It's a huge difference. This book illustrates that very well. Don't use books like these written by physicists without even an Undergraduate's training in mathematics. It's bad style. Not only that, but if you ever get into the deeper aspects of physics, via mathematical physics such as what Michael Atiyah does, then you'll have to become acquainted with the mathematicians respect for rigor and structure. If you want to be a physicist, please stay away from books like these. These sorts of books are sacrilege to the science of mathematics.

We used to read Courant-Hilbert and some others years ago. Those books are still relevant. But Cahill's book is a very modern treatment of the subject and with it one can go deeply into the mathematical background of much of modern physics. I would say, as a professional mathematician (retired professor) that Cahill's style is somewhat different from a mathematician's in subjects I am familiar with, but with effort one can go deeply into many topics: tensor analysis and gravitation, Sturm-Liouville methods just to name two. Cahill constantly illuminates his discussion with examples from current research. Anthony Zee recommends this book and so I think that is sufficient.

I bought it with only one reason in mind: learn the mathematical foundations of General Relativity. The book is complete and very good, but really to complicated for those, like me, know few more than calculus. I had to return to more basic books before taking it again. It's excellent, but really far from basic.

Cahill covers the origin of gauge theory in a unique way not covered in almost any other mathematical physics book. Cahill always writes very clearly. A must have for physicists..

This book is half the price of Elsevier's math-methods book and better. Loaded with physics and math. Concise clear prose. Great graphics.

Physical Mathematics explains as simply as possible the mathematics that graduate students and professional physicists need in their courses and research. I probably should have paid more attention to that sentence in the description. I have a BS in Engineering and much of it is over my head. Yet, I still enjoyed thumbing through this book and reading the parts I could. If you are included in "graduate students and professional physicists", I think you'll find this book 5 stars.