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Thorough yet practical treatment, with carefully documented collection of MATLAB programs implementing the ideas presented.

Undergraduate courses on partial differential equations (PDEs) have traditionally been based on the Fourier series method for analysing and solving PDEs. What this textbook offers is a fresh approach; the traditional method taught alongside the modern finite element method. Both powerful methods are introduced to the reader and emphasised equally. A further beneficial feature of the book is that it uses the language of linear algebra, in particular in emphasising the role of best approximation in function spaces and the idea of an eigenfunction expansion. Its inclusion of realistic physical...

This text provides a broad foundation for the study of advanced mathematics and applications of linear algebra to other areas of mathematics. Featured application areas include linear ordinal differential equations, polynomial approximation, and finite element methods. It offers numerous exercises covering a range of difficulties.

Tikhonov regularization is the most popular general-purpose method for regularization, a mathematical technique to suppress the effect of noise in data, and uses much of the machinery of Hilbert space theory. This book develops the theory of Tikhonov regularization for a certain class of linear inverse problems which are defined on Hilbert spaces. To explain why and how Tikhonov regularization works, the singular value expansion for compact operators is introduced. Tikhonov regularization with seminorms is also analyzed and for this purpose, densely defined unbounded operators are addressed...