04263nam 22008295 450 991098307470332120250704133122.09783031747946303174794110.1007/978-3-031-74794-6(MiAaPQ)EBC31783853(Au-PeEL)EBL31783853(CKB)36583086000041(DE-He213)978-3-031-74794-6(EXLCZ)993658308600004120241115d2025 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierAnalytical Methods in Applied Mathematics /by Edmundo Capelas de Oliveira, José Emílio Maiorino1st ed. 2025.Cham :Springer Nature Switzerland :Imprint: Springer,2025.1 online resource (395 pages)Problem Books in Mathematics,2197-85069783031747939 3031747933 Preface -- Ordinary Differential Equations -- Power Series and the Frobenius Method -- Laurent Series and Residues -- Special Functions -- Fourier, Fourier-Bessel and Fourier-Legendre Series -- Laplace and Fourier Transforms -- Sturm-Liouville Systems -- Partial Differential Equations -- Separation of Variables -- Fractional Calculus -- Applications -- Answers and Hints -- Index.This book compiles an extensive list of solved and proposed problems in mathematical topics in analysis, aimed at students of mathematics, applied mathematics, physics, and engineering. The book begins with an exploration of simple linear and nonlinear ordinary differential equations in Chapter 1, advancing through topics such as power series and the Frobenius method for solving differential equations in Chapter 2. In subsequent chapters, the discussion expands to include functions of complex variables, special functions constructed through the hypergeometric function, and series solutions including Fourier, Fourier-Bessel, and Fourier-Legendre series. Problems in integral transforms, Sturm-Liouville systems, Green's function, linear partial differential equations are also included. The work finishes with a special chapter on fractional calculus and practical applications of the topics presented. With solved examples and step-by-step exercises, this book can be of value to undergraduate and graduate students seeking a hands-on approach on the listed topics, and as a bibliographical complement to STEM courses as well.Problem Books in Mathematics,2197-8506Differential equationsEngineering mathematicsEngineeringData processingSequences (Mathematics)Mathematical analysisFunctions, SpecialDifferential EquationsMathematical and Computational Engineering ApplicationsSequences, Series, SummabilityIntegral Transforms and Operational CalculusSpecial FunctionsEquacions diferencialsthubSuccessions (Matemàtica)thubAnàlisi matemàticathubFuncions especialsthubLlibres electrònicsthubDifferential equations.Engineering mathematics.EngineeringData processing.Sequences (Mathematics)Mathematical analysis.Functions, Special.Differential Equations.Mathematical and Computational Engineering Applications.Sequences, Series, Summability.Integral Transforms and Operational Calculus.Special Functions.Equacions diferencialsSuccessions (Matemàtica)Anàlisi matemàticaFuncions especials515.35Capelas de Oliveira Edmundo886489Maiorino José Emílio1785934MiAaPQMiAaPQMiAaPQBOOK9910983074703321Analytical Methods in Applied Mathematics4317373UNINA