Titlebook: Analytical Methods in Applied Mathematics; Edmundo Capelas de Oliveira,José Emílio Maiorino Textbook 2025 The Editor(s) (if applicable) an

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https://doi.org/10.1007/978-3-031-74794-6applied mathematics; analytical methods; solved problems; ordinary differential equations; partial diffe

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978-3-031-74796-0The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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0941-3502 undergraduate and graduate students seeking a hands-on approach on the listed topics, and as a bibliographical complement to STEM courses as well..978-3-031-74796-0978-3-031-74794-6Series ISSN 0941-3502 Series E-ISSN 2197-8506

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Ordinary Differential Equations,by step, concluding with a list of proposed exercises, among which some interesting applications are left to the reader—Legendre equation, harmonic oscillator, Whittaker equation, .-circuit, and the Green function—all of them with the corresponding anwser and/or suggestion.

cataract

Laurent Series and Residues,ises; among them, some interesting applications are left to the reader, particularly the ones involving different contours to evaluate real integrals by means of complex functions, all of them with the answer and/or suggestion.

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,Fourier, Fourier-Bessel, and Fourier–Legendre Series,aplace equations in cartesian coordinates. As applications we evaluate some infinite sums. We conclude with a list of proposed exercises; among them, some interesting applications involving Legendre polynomials and Bessel functions are left to the reader, all of them with the correspondint answer an

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Laplace and Fourier Transforms,rsion problem involving the modified Bromwich contour. As an application we evaluate the Fourier transform of the Dirac delta function and obtain an integral representation for the Bessel function. We conclude with a list of proposed exercises; among them, some interesting applications involving Gre

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Partial Differential Equations, the two-dimensional Laplace equation written in Cartesian coordinates and in polar coordinates. We conclude with a list of proposed exercises, among them some interesting applications are left to the reader; one of them is the Tricomi equation, which has non constant coefficients; all of them with