Analytical methods in applied mathematics

• Verfasst von: Oliveira, Edmundo Capelas de [VerfasserIn]
• Verfasst von: Maiorino, José Emílio [VerfasserIn]
• Titel: Analytical methods in applied mathematics
• Verf.angabe: Edmundo Capelas de Oliveira, José Emílio Maiorino
• Verlagsort: Cham
• Verlag: Springer
• E-Jahr: 2025
• Jahr: [2025]
• Umfang: 1 Online-Ressource (xiii, 388 Seiten)
• Gesamttitel/Reihe: Problem books in mathematics
• ISBN: 978-3-031-74794-6
• DOI: doi:10.1007/978-3-031-74794-6
• Datenträger: Online-Ressource
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe: Oliveira, Edmundo Capelas de: Analytical methods in applied mathematics. - Cham : Springer Nature, 2025. - xiii, 388 Seiten
• K10plus-PPN: 1908972378
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

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.

Abstract

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.