Sturm-Liouville Theory and its Applications

• Main Author: Al-Gwaiz, Mohammed
• Format: Book
• Language: English
• Published: Springer 2017
• Subjects: Sturm-Liouville Theory ; Sturm-Liouville equation.; Applications; Mathematics; 515.35
• Online Access: http://repository.vnu.edu.vn/handle/VNU_123/25398
• Institution: Vietnam National University, Hanoi

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.