By Sadri Hassani

The aim of this ebook is to reveal the reader to the critical function that arithmetic performs in glossy physics. beginning with the concept of vector areas, the 1st 1/2 the e-book develops themes as diversified as algebras, classical orthogonal polynomials, Fourier research, advanced research, differential and fundamental equations, operator conception, and multi-dimensional Green's services. the second one half the booklet introduces teams, manifolds, Lie teams and their representations, Clifford algebras and their representations, and fibre bundles and their purposes to differential geometry and gauge theories.

This moment version is a considerable revision with an entire rewriting of many chapters and the addition of latest ones, together with chapters on algebras, illustration of Clifford algebras, fibre bundles, and gauge theories. The spirit of the 1st version, specifically the stability among rigour and actual software, has been maintained, as is the abundance of old notes and labored out examples that exhibit the "unreasonable effectiveness of arithmetic" in glossy physics.

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