Analytical Methods in Applied Mathematics [Hardcover]

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.

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 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 tlS+