Analytical Methods in Applied Mathematics
Series: Problem Books in Mathematics;
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Product details:
- Edition number 2024
- Publisher Springer Nature Switzerland
- Date of Publication 15 November 2024
- Number of Volumes 1 pieces, Book
- ISBN 9783031747939
- Binding Hardback
- No. of pages388 pages
- Size 235x155 mm
- Language English
- Illustrations XIII, 388 p. 15 illus. Illustrations, black & white 731
Categories
Long description:
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.
MoreTable of Contents:
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.
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