Download Sturm-Liouville theory and its applications eBook in PDF

(By Mohammed Abdelrahman Al-Gwaiz)



Click here to Download and Read Sturm-Liouville theory and its applications eBook

Format: PDF

Language: English

Publisher: Springer



Undergraduate textbooks on Fourier series which follow a pointwise approach to convergence miss the rich geometric content which comes with treating the subject within the inner product space L2. This book, developed from a course taught to senior undergraduates, provides a unified introduction to Fourier analysis and special functions based on the Sturm-Liouville theory in L2. The basic results of this theory, namely the orthogonality and completeness of its eigenfunctions, are established in Chapter 2; the remaining chapters present examples and applications. The last two chapters, on Fourier and Laplace transformations, while not part of the Sturm-Liouville theory, extend the Fourier series method for representing functions to integral representations. The treatment relies heavily on the convergence properties of sequences and series of numbers as well as functions, and assumes a solid background in advanced calculus and an acquaintance with ordinary differential equations and linear algebra. Familiarity with the relevant theorems of real analysis, such as the Ascoli�Arzela theorem, is also useful for following the proofs. The presentation follows a clear and rigorous mathematical style that is both readable and well motivated, with many examples and applications used to illustrate the theory. Although addressed primarily to undergraduate students of mathematics, the book will also be of interest to students in related disciplines, such as physics and engineering, where Fourier analysis and special functions are used extensively for solving linear differential equations.�



More ebooks:
Gap and density theorems ebook
Qualitative Analysis and Synthesis of Recurrent Neural Networks ebook
Advances in discrete tomography and its applications ebook
Theory of functions of real variable and theory of Fourier series ebook
Lie algebras and Lie groups ebook
Properties of complex inorganic solids ebook
Complex algebraic geometry ebook

Download Sturm-Liouville theory and its applications ebook
Download Sturm-Liouville theory and its applications ebook pdf
Download Sturm-Liouville theory and its applications ebook djvu
Download Sturm-Liouville theory and its applications ebook chm
Sturm-Liouville theory and its applications ebook
Sturm-Liouville theory and its applications ebook pdf
Sturm-Liouville theory and its applications ebook djvu
Sturm-Liouville theory and its applications ebook chm
Mohammed Abdelrahman Al-Gwaiz ebooks