The target of this booklet is to show the reader to the imperative position that mathematics---often very abstract---plays in sleek physics. beginning with the idea of vector areas, the 1st half the ebook develops issues as varied as algebras, classical orthogonal polynomials, Fourier research, complicated research, differential and indispensable equations, operator idea, and multi-dimensional Green's services. the second one 1/2 the e-book introduces teams, manifolds, Lie teams and their representations, Clifford algebras and their representations, and fiber bundles and their purposes to differential geometry and gauge theories.

This moment variation is a considerable revision of the 1st one with an entire rewriting of many chapters and the addition of latest ones, together with chapters on algebras, illustration of Clifford algebras and spinors, fiber bundles, and gauge theories. The spirit of the 1st variation, particularly the stability among rigor and actual program, has been maintained, as is the abundance of ancient notes and labored out examples that reveal the "unreasonable effectiveness of arithmetic" in glossy physics.

Einstein has famously stated, "The so much incomprehensible factor approximately nature is that it truly is comprehensible." What he had in brain used to be reiterated in one other one in all his recognized fees about the query of the way " ... arithmetic, being in the end a manufactured from human inspiration, is so admirably applicable to the gadgets of reality." it's a query that involves everyone's brain whilst encountering the hugely summary arithmetic required for a deep figuring out of contemporary physics. it's the adventure that Eugene Wigner so profoundly defined as "the unreasonable effectiveness of arithmetic within the common sciences."

Some compliment for the former edition:

PAGEOPH [Pure and utilized Geophysics]

Review by means of Daniel Wojcik, collage of Maryland

"This quantity may be a welcome boost to any assortment. The ebook is definitely written and factors tend to be transparent. Lives of well-known mathematicians and physicists are scattered in the e-book. they're really prolonged, usually fun, making great interludes. quite a few workouts aid the coed perform the equipment brought. … i've got lately been utilizing this booklet for a longer time and bought a liking for it. between all of the to be had books treating mathematical equipment of physics this one definitely stands proud and skillfully it should go well with the desires of many physics readers."

ZENTRALBLATT MATH

Review by way of G.Roepstorff, collage of Aachen, Germany

"… not like such a lot current texts with an identical emphasis and viewers, that are simply collections of evidence and formulation, the current publication is extra systematic, self-contained, with a degree of presentation that has a tendency to be extra formal and summary. This involves proving a great number of theorems, lemmas, and corollaries, deferring many of the functions that physics scholars should be drawn to to the instance sections in details. certainly, there are 350 worked-out examples and approximately 850 difficulties. … a truly great function is the best way the writer intertwines the formalism with the existence tales and anecdotes of a few mathematicians and physicists, prime at their instances. As is usually the case, the ancient view aspect is helping to appreciate and have fun with the guidelines provided within the textual content. … For the physics scholar in the course of his education, it's going to definitely turn out to be super useful."

THE PHYSICIST

Review by way of Paul Davies, Orion Productions, Adelaide, Australia

"I am happy to have such a lot of issues gathered in one quantity. the entire methods are there in fact, yet supported by way of adequate rigour and substantiation to make the devoted mathematical physicist sigh with delight."

EMS [EUROPEAN MATHEMATICAL SOCIETY] NEWSLETTER

"This publication is a condensed exposition of the maths that's met in so much components of physics. The presentation attains an outstanding stability among the formal advent of thoughts, theorems and proofs on one hand, and the utilized procedure at the different, with many examples, absolutely or in part solved difficulties, and historic feedback. a magnificent volume of arithmetic is roofed. … This publication could be warmly urged as a uncomplicated resource for the examine of arithmetic for complex undergraduates or starting graduate scholars in physics and utilized arithmetic, and likewise as a reference ebook for all operating mathematicians and physicists ."