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Mathematics for Physicists (Dover Books on Physics) Paperback – 20 Dec 1996
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dipping into both as a mathematical dictionary for use in solving
problems and for general background reading.
I would rate the book as being useful for both students (graduate level and probably below as well) and professionals. It is well
laid out, the exposition is clear and the examples are carefully chosen.
It is an excellent guide with good worked examples of many mathematical situations that crop up on a day to day basis for physics students.
You'll be perfectly aware if you need this sort of thing or not - it isn't the kind of book you're likely to buy on a whim out of idle curiosity!
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Now, for the important question of rigour. This book is wholly about Mathematics, not Physics (there are, however, a section of 4 pages on applications of conformal mapping to Electrostatics and a few other such sections), and its level of rigour is probably higher than the typical Mathematical Physics text. But how does it compare with the requirements of a Mathematics text? I think that it lacks in some areas (e.g. contour integration and operators in infinite-dimensional spaces) which is not suprising given that the book's prerequisites are only Calculus, Vector Analysis, and systems of Algebraic Equations (e.g. not including plane set topology). Nevertheless, it will serve well any undergraduate theoretical physicist who needs to know the necessary mathematics yet has little time to study the topics in their most general and rigorous form (though I strongly believe that no theoretical physicist should be content with a semi-rigorous understanding of the mathematics they use, though the rigorous understanding may very unfortunately have to wait).
As for the style of presentation, I say it is slightly too brief, but I no longer view this as a defect. Furthermore, there are a few typographical errors in this edition, but they are tolerable. All in all, this is a great book at a great price (typical of Dover Publications, I realize).