Titlebook: Mathematical Physics; A Modern Introductio Sadri Hassani Textbook 2013Latest edition The Editor(s) (if applicable) and The Author(s), under

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Textbook 2013Latest editionspaces, the first half of the book develops topics as diverse as algebras, classical orthogonal polynomials, Fourier analysis, complex analysis, differential and integral equations, operator theory, and multi-dimensional Green‘s functions. The second half of the book introduces groups, manifolds, Li

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Complex Analysis of SOLDEsyticity of the coefficient functions? If so, how? Are the singular points of the coefficients also singular points of the solution? Is the nature of the singularities the same? This chapter answers some of these questions.

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Hilbert Spaceshing is crucially different in the new situation, and this difference makes the study of infinite-dimensional vector spaces both richer and more nontrivial: In a finite-dimensional vector space we dealt with finite sums; in infinite dimensions we encounter infinite sums. Thus, we have to investigate the convergence of such sums.

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Calculus of Residueschapter. In the preceding chapter we saw examples in which integrals were related to expansion coefficients of Laurent series. Here we will develop a systematic way of evaluating both real and complex integrals.

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Separation of Variables in Spherical Coordinatesiations with respect to position are also important. Partial derivatives with respect to coordinate variables show up in the differential equations, which are therefore called partial differential equations (PDEs). We list the most common PDEs of mathematical physics in the following.

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Matricesconcrete representations of vectors and operators are necessary in most applications. Such representations are obtained by choosing a basis and expressing all operations in terms of components of vectors and matrix representations of operators.

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