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Sturm-Liouville Theory and its Applications / Al-Gwaiz, Mohammed

Tác giả : Al-Gwaiz, Mohammed

Nhà xuất bản : Springer

Năm xuất bản : 2008

Mô tả vật lý : 270 p.

Số phân loại : 515.35

Chủ đề : 1. Applications. 2. Mathematics. 3. Sturm-Liouville Theory ; Sturm-Liouville equation.. 4. Book.

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Tóm tắt :

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.

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