LEADER 04263nam 22008295 450 001 9910983074703321 005 20250915135657.0 010 $a9783031747946 010 $a3031747941 024 7 $a10.1007/978-3-031-74794-6 035 $a(MiAaPQ)EBC31783853 035 $a(Au-PeEL)EBL31783853 035 $a(CKB)36583086000041 035 $a(DE-He213)978-3-031-74794-6 035 $a(EXLCZ)9936583086000041 100 $a20241115d2025 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAnalytical Methods in Applied Mathematics /$fby Edmundo Capelas de Oliveira, José Emílio Maiorino 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (395 pages) 225 1 $aProblem Books in Mathematics,$x2197-8506 311 08$a9783031747939 311 08$a3031747933 327 $aPreface -- 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. 330 $aThis book compiles an extensive list of solved and proposed problems in mathematical topics in analysis, aimed at students of mathematics, applied mathematics, physics, and engineering. The book begins with an exploration of simple linear and nonlinear ordinary differential equations in Chapter 1, advancing through topics such as power series and the Frobenius method for solving differential equations in Chapter 2. In subsequent chapters, the discussion expands to include functions of complex variables, special functions constructed through the hypergeometric function, and series solutions including Fourier, Fourier-Bessel, and Fourier-Legendre series. Problems in integral transforms, Sturm-Liouville systems, Green's function, linear partial differential equations are also included. The work finishes with a special chapter on fractional calculus and practical applications of the topics presented. With solved examples and step-by-step exercises, this book can be of value to undergraduate and graduate students seeking a hands-on approach on the listed topics, and as a bibliographical complement to STEM courses as well. 410 0$aProblem Books in Mathematics,$x2197-8506 606 $aDifferential equations 606 $aEngineering mathematics 606 $aEngineering$xData processing 606 $aSequences (Mathematics) 606 $aMathematical analysis 606 $aFunctions, Special 606 $aDifferential Equations 606 $aMathematical and Computational Engineering Applications 606 $aSequences, Series, Summability 606 $aIntegral Transforms and Operational Calculus 606 $aSpecial Functions 606 $aEquacions diferencials$2thub 606 $aSuccessions (Matemātica)$2thub 606 $aAnālisi matemātica$2thub 606 $aFuncions especials$2thub 608 $aLlibres electrōnics$2thub 615 0$aDifferential equations. 615 0$aEngineering mathematics. 615 0$aEngineering$xData processing. 615 0$aSequences (Mathematics) 615 0$aMathematical analysis. 615 0$aFunctions, Special. 615 14$aDifferential Equations. 615 24$aMathematical and Computational Engineering Applications. 615 24$aSequences, Series, Summability. 615 24$aIntegral Transforms and Operational Calculus. 615 24$aSpecial Functions. 615 7$aEquacions diferencials 615 7$aSuccessions (Matemātica) 615 7$aAnālisi matemātica 615 7$aFuncions especials 676 $a515.35 700 $aOliveira$b Edmundo Capelas de$0886489 701 $aMaiorino$b José Emílio$01785934 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910983074703321 996 $aAnalytical Methods in Applied Mathematics$94317373 997 $aUNINA