Titlebook: Advanced Mathematics for Engineers and Physicists; Sever Angel Popescu,Marilena Jianu Textbook 2022 The Editor(s) (if applicable) and The

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Professionalisierungstheoretische Einbettungtions are presented, together with the techniques for obtaining their solutions (either in implicit or explicit form). The last section is dedicated to the Theorem of existence and uniqueness of the solution of the Cauchy problem for first-order differential equations.

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Kasseler Edition Soziale Arbeitcients are placed in the foreground, because in this case we have a closed-form solution for homogeneous equations, as well as for a wide class of non-homogeneous equations. We also present the Euler-type equations which have variable coefficients but can be transformed into linear equations with constant coefficients.

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Kasseler Edition Soziale Arbeit order linear equation. Autonomous systems are also studied, and, since first-order partial differential equations are closely related to autonomous systems, we present them in the last section of this chapter.

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https://doi.org/10.1007/978-3-658-24305-0f non-periodic functions defined on the whole set of real numbers. We present the properties and some applications of the Fourier transform. Finally, we introduce the discrete Fourier transform which can be used when a function is given only in terms of values at a finite number of points.

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https://doi.org/10.1007/978-3-658-24305-0in Chap. . we use the Laplace transform for the solution of the finite vibrating string equation. By using the Heaviside step function or the Dirac delta function, the Laplace transform can be applied in problems where the free term has some discontinuities or represents short impulses.

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https://doi.org/10.1007/978-3-031-21502-5Fourier Transform; Laplace Transform; Equations of Physics; Hilbert Spaces; Complex Functions; Ordinary D

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978-3-031-21504-9The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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