TY - BOOK ID - 8654290 TI - Distributions : Theory and Applications AU - Duistermaat, J. J. AU - Kolk, Johan A.C. PY - 2010 SN - 0817646728 0817646752 PB - Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, DB - UniCat KW - Electronic books. -- local. KW - Theory of distributions (Functional analysis). KW - Theory of distributions (Functional analysis) KW - Fourier transformations KW - Civil & Environmental Engineering KW - Mathematics KW - Physical Sciences & Mathematics KW - Engineering & Applied Sciences KW - Operations Research KW - Calculus KW - Distribution (Functional analysis) KW - Distributions, Theory of (Functional analysis) KW - Functions, Generalized KW - Generalized functions KW - Mathematics. KW - Approximation theory. KW - Fourier analysis. KW - Functional analysis. KW - Differential equations. KW - Partial differential equations. KW - Applied mathematics. KW - Engineering mathematics. KW - Functional Analysis. KW - Approximations and Expansions. KW - Applications of Mathematics. KW - Partial Differential Equations. KW - Fourier Analysis. KW - Ordinary Differential Equations. KW - Engineering KW - Engineering analysis KW - Mathematical analysis KW - Partial differential equations KW - 517.91 Differential equations KW - Differential equations KW - Functional calculus KW - Calculus of variations KW - Functional equations KW - Integral equations KW - Analysis, Fourier KW - Theory of approximation KW - Functional analysis KW - Functions KW - Polynomials KW - Chebyshev systems KW - Math KW - Science KW - Differential equations, partial. KW - Differential Equations. KW - Differential equations, Partial. UR - https://www.unicat.be/uniCat?func=search&query=sysid:8654290 AB - This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. Throughout the book, methods are developed to deal with formal calculations involving functions, series, and integrals that cannot be mathematically justified within the classical framework. Key features: • Many examples, exercises, hints, and solutions guide the reader throughout the text. • Includes an introduction to distributions, differentiation, convergence, convolution, the Fourier transform, and spaces of distributions having special properties. • Original proofs, which may be difficult to locate elsewhere, are given for many well-known results. • The Fourier transform is transparently treated and applied to provide a new proof of the Kernel Theorem, which in turn is used to efficiently derive numerous important results. • The systematic use of pullback and pushforward introduces concise notation. • Emphasizes the role of symmetry in obtaining short arguments and investigates distributions that are invariant under the actions of various groups of transformations. Distributions: Theory and Applications is aimed at advanced undergraduates and graduate students in mathematics, theoretical physics, and engineering, who will find this textbook a welcome introduction to the subject, requiring only a minimal mathematical background. The work may also serve as an excellent self-study guide for researchers who use distributions in various fields. ER -