Analytical Methods in Applied Mathematics
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Beschreibung
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.
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.
Covers essential topics for students of mathematics, applied mathematics, physics, and engineering Offers a hands-on approach, providing step-by-step exercises and hints to the proposed problems Functions as both a textbook supplement and a reference for solving problems
Autor*in
Edmundo Capelas de Oliveira
Themen in »Analytical Methods in Applied Mathematics«
applied mathematics analytical methods solved problems ordinary differential equations partial differential equations power series Frobenius method Laurent series special functions Fourier series Fourier-Bessel series Fourier-Legendre series Laplace and Fourier transforms Sturms-Liouville systems fractional calculus
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“This book is a mainly problem-based textbook addressed to advanced undergraduate and graduate students in mathematics, applied mathematics, physics, and engineering. The book emphasizes a hands-on, learning-by-doing approach, offering numerous solved examples and proposed exercises with answers to reinforce theoretical concepts. … The book is organized into 11 chapters, each one based on the content of the previous one in such a way that the reader can increase the level of complexity and depth … .” (Jaime Burgos Garca, Mathematical Reviews, February, 2026)
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