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Analytical methods in applied mathematics

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Analytical methods in applied mathematicsby Edmundo Capelas de Oliveira, José Emílio Maiorino.
作者:	Oliveira, Edmundo Capelas de.
其他作者:	Maiorino, José Emílio.
出版者:	Cham :Springer Nature Switzerland :2025.
面頁冊數:	xiii, 388 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Mathematical analysis.
電子資源:	https://doi.org/10.1007/978-3-031-74794-6
ISBN:	9783031747946$q(electronic bk.)

Analytical methods in applied mathematics
Oliveira, Edmundo Capelas de.

Analytical methods in applied mathematics[electronic resource] /by Edmundo Capelas de Oliveira, José Emílio Maiorino. - Cham :Springer Nature Switzerland :2025. - xiii, 388 p. :ill., digital ;24 cm. - Problem books in mathematics,2197-8506. - Problem books in mathematics..

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.

ISBN: 9783031747946$q(electronic bk.)

Standard No.: 10.1007/978-3-031-74794-6doiSubjects--Topical Terms:

186133
Mathematical analysis.

LC Class. No.: QA300

Dewey Class. No.: 515

Analytical methods in applied mathematics
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505 0 $a 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.
520 $a 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.
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650 2 4 $a Integral Transforms and Operational Calculus. $3 913382
650 2 4 $a Special Functions. $3 274846
700 1 $a Maiorino, José Emílio. $3 992296
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