{"product_id":"applied-functional-analysis-dover-books-on-mathematics","title":"Applied Functional Analysis (Dover Books on Mathematics) (Spiral Bound)","description":"\n\u003ctable align=\"center\" border=\"0\" cellpadding=\"2\" cellspacing=\"0\" width=\"100%\"\u003e\n\u003ctr\u003e\n\u003ctd class=\"productDetailSmallElements\"\u003e\n\u003cp\u003e\n\u003cstrong\u003eMarc Notes\u003c\/strong\u003e:\u003cbr\u003e\n\t\t\t\t\t\t\t\tOriginally published: Chichester, W. Sussex: E. Horwood;New York: Halsted Press, 1981.;Includes bibliographical references (p. [382]-386) and indexes.\u003cbr\u003e\u003cbr\u003e\n\u003cstrong\u003eTable of Contents\u003c\/strong\u003e:\u003cbr\u003e\n\t\t\t\t\t\t\t\tPreface \n\u003cbr\u003ePart I. Distribution Theory and Green's Functions \n\u003cbr\u003e Chapter 1. Generalised Functions \n\u003cbr\u003e 1.1 The Delta function \n\u003cbr\u003e 1.2 Basic distribution theory \n\u003cbr\u003e 1.3 Operations on distributions \n\u003cbr\u003e 1.4 Convergence of distributions \n\u003cbr\u003e 1.5 Further developments \n\u003cbr\u003e 1.6 Fourier Series and the Poisson Sum formula \n\u003cbr\u003e 1.7 Summary and References \n\u003cbr\u003e Problems \n\u003cbr\u003e Chapter 2. Differential Equations and Green's Functions \n\u003cbr\u003e 2.1 The Integral of a distribution \n\u003cbr\u003e 2.2 Linear differential equations \n\u003cbr\u003e 2.3 Fundamental solutions of differential equations \n\u003cbr\u003e 2.4 Green's functions \n\u003cbr\u003e 2.5 Applications of Green's functions \n\u003cbr\u003e 2.6 Summary and References \n\u003cbr\u003e Problems \n\u003cbr\u003e Chapter 3. Fourier Transforms and Partial differential Equations \n\u003cbr\u003e 3.1 The classical Fourier transform \n\u003cbr\u003e 3.2 Distributions of slow growth \n\u003cbr\u003e 3.3 Generalised Fourier transforms \n\u003cbr\u003e 3.4 Generalised functions of several variables \n\u003cbr\u003e 3.5 Green's function for the Laplacian \n\u003cbr\u003e 3.6 Green's function for the Three-dimensional wave equation \n\u003cbr\u003e 3.7 Summary and References \n\u003cbr\u003e Problems \n\u003cbr\u003ePart II. Banach spaces and fixed point theorems \n\u003cbr\u003e Chapter 4. Normed spaces \n\u003cbr\u003e 4.1 Vector spaces \n\u003cbr\u003e 4.2 Normed spaces \n\u003cbr\u003e 4.3 Convergence \n\u003cbr\u003e 4.4 Open and closed sets \n\u003cbr\u003e 4.5 Completeness \n\u003cbr\u003e 4.6 Equivalent norms \n\u003cbr\u003e 4.7 Summary and References \n\u003cbr\u003e Problems \n\u003cbr\u003e Chapter 5. The contraction mapping theorem \n\u003cbr\u003e 5.1 Operators on Vector spaces \n\u003cbr\u003e 5.2 The contraction mapping theorem \n\u003cbr\u003e 5.3 Application to differential and integral equations \n\u003cbr\u003e 5.4 Nonlinear diffusive equilibrium \n\u003cbr\u003e 5.5 Nonlinear diffusive equilibrium in three dimensions \n\u003cbr\u003e 5.6 Summary and References \n\u003cbr\u003e Problems \n\u003cbr\u003e Chapter 6. Compactness and Schauder's theorem \n\u003cbr\u003e 6.1 Continuous operators \n\u003cbr\u003e 6.2 Brouwer's theorem \n\u003cbr\u003e 6.3 Compactness \n\u003cbr\u003e 6.4 Relative compactness \n\u003cbr\u003e 6.5 Arzelà's theorem \n\u003cbr\u003e 6.6 Schauder's theorems \n\u003cbr\u003e 6.7 Forced nonlinear oscillations \n\u003cbr\u003e 6.8 Swirling flow \n\u003cbr\u003e 6.9 Summary and References \n\u003cbr\u003e Problems \n\u003cbr\u003ePart III. Operators in Hilbert Space \n\u003cbr\u003e Chapter 7. Hilbert space \n\u003cbr\u003e 7.1 Inner product spaces \n\u003cbr\u003e 7.2 Orthogonal bases \n\u003cbr\u003e 7.3 Orthogonal expansions \n\u003cbr\u003e 7.4 The Bessel, Parseval, and Riesz-Fischer theorems \n\u003cbr\u003e 7.5 Orthogonal decomposition \n\u003cbr\u003e 7.6 Functionals on normed spaces \n\u003cbr\u003e 7.7 Functionals in Hilbert space \n\u003cbr\u003e 7.8 Weak convergence \n\u003cbr\u003e 7.9 Summary and References \n\u003cbr\u003e Problems \n\u003cbr\u003e Chapter 8. The Theory of operators \n\u003cbr\u003e 8.1 Bounded operators on normed spaces \n\u003cbr\u003e 8.2 The algebra of bounded operators \n\u003cbr\u003e 8.3 Self-adjoint operators \n\u003cbr\u003e 8.4 Eigenvalue problems for self-adjoint operators \n\u003cbr\u003e 8.5 Compact operators \n\u003cbr\u003e 8.6 Summary and References \n\u003cbr\u003e Problems \n\u003cbr\u003e Chapter 9. The Spectral theorem \n\u003cbr\u003e 9.1 The spectral theorem \n\u003cbr\u003e 9.2 Sturm-Liouville systems \n\u003cbr\u003e 9.3 Partial differential equations \n\u003cbr\u003e 9.4 The Fredholm alternative \n\u003cbr\u003e 9.5 Projection operators \n\u003cbr\u003e 9.6 Summary and References \n\u003cbr\u003e Problems \n\u003cbr\u003e Chapter 10. Variational methods \n\u003cbr\u003e 10.1 Positive operators \n\u003cbr\u003e 10.2 Approximation to the first eigenvalue \n\u003cbr\u003e 10.3 The Rayleigh-Ritz method for eigenvalues \n\u003cbr\u003e 10.4 The theory of the Rayleigh-Ritz method \n\u003cbr\u003e 10.5 Inhomogeneous Equations \n\u003cbr\u003e 10.6 Complementary bounds \n\u003cbr\u003e 10.7 Summary and References \n\u003cbr\u003e Problems \n\u003cbr\u003ePart IV. Further developments \n\u003cbr\u003e Chapter 11. The differential calculus of operators and its applications \n\u003cbr\u003e 11.1 The Fréchet derivative \n\u003cbr\u003e 11.2 Higher derivatives \n\u003cbr\u003e 11.3 Maxima and Minima \n\u003cbr\u003e 11.4 Linear stability theory \n\u003cbr\u003e 11.5. Nonlinear stability \n\u003cbr\u003e 11.6 Bifurcation theory \n\u003cbr\u003e 11.7 Bifurcation and stability \n\u003cbr\u003e 11.8 Summary and References \n\u003cbr\u003e Chapter 12. Distributional Hilbert spaces \n\u003cbr\u003e 12.1 The space of square-integrable distributions \n\u003cbr\u003e 12.2 Sobolev spaces \n\u003cbr\u003e 12.3 Application to partial differential equations \n\u003cbr\u003e 12.4 Summary and References \n\u003cbr\u003eAppendix A. Sets and mappings \n\u003cbr\u003eAppendix B. Sequences, series, and uniform convergence \n\u003cbr\u003eAppendix C. Sup and inf \n\u003cbr\u003eAppendix D. Countability \n\u003cbr\u003eAppendix E. Equivalence relations \n\u003cbr\u003eAppendix F. Completion \n\u003cbr\u003eAppendix G. Sturm-Liouville systems \n\u003cbr\u003eAppendix H. Fourier's theorem \n\u003cbr\u003eAppendix I. Proofs of 9.24 and 9.25 \n\u003cbr\u003e Notes on the Problems; Supplementary Problems; Symbol index; References and name index; Subject index\u003cbr\u003e\u003cbr\u003e\n\u003cstrong\u003ePublisher Marketing\u003c\/strong\u003e:\u003cbr\u003e\n\t\t\t\t\t\t\t\tA stimulating introductory text, this volume examines many important applications of functional analysis to mechanics, fluid mechanics, diffusive growth, and approximation. Detailed enough to impart a thorough understanding, the text is also sufficiently straightforward for those unfamiliar with abstract analysis. Its four-part treatment begins with distribution theory and discussions of Green's functions. Essentially independent of the preceding material, the second and third parts deal with Banach spaces, Hilbert space, spectral theory, and variational techniques. The final part outlines the ideas behind Frechet calculus, stability and bifurcation theory, and Sobolev spaces. 25 Figures. 9 Appendices. Supplementary Problems. Indexes.\u003cbr\u003e\u003cbr\u003e\n\u003c\/p\u003e\n\u003cbr\u003e\n\u003cbr\u003e\n\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\n","brand":"Dover Publications","offers":[{"title":"Default Title","offer_id":46581104771203,"sku":"SPTM-9780486422589","price":24.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0564\/6830\/8099\/files\/9780486422589_spiral_13bf2b40-dca5-46b5-85c3-de10c6b78612.png?v=1776829016","url":"https:\/\/sebink.com\/products\/applied-functional-analysis-dover-books-on-mathematics","provider":"Sebink","version":"1.0","type":"link"}