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AuthorDautray, Robert. author
TitleMathematical Analysis and Numerical Methods for Science and Technology [electronic resource] : Volume 4 Integral Equations and Numerical Methods / by Robert Dautray, Jacques-Louis Lions
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 2000
Connect tohttp://dx.doi.org/10.1007/978-3-642-61531-3
Descript X, 493 p. online resource

SUMMARY

The advent of high-speed computers has made it possible for the first time to calculate values from models accurately and rapidly. Researchers and engineers thus have a crucial means of using numerical results to modify and adapt arguments and experiments along the way. Every facet of technical and industrial activity has been affected by these developments. The objective of the present work is to compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. Since the publication in 1924 of the "Methoden der mathematischen Physik" by Courant and Hilbert, there has been no other comprehensive and up-to-date publication presenting the mathematical tools needed in applications of mathematics in directly implementable form


CONTENT

X. Mixed Problems and the Tricomi Equation -- ยง 1. Description and Formulation of the Problem -- ยง 2. Methods for Solving Problems of Mixed Type -- Bibliographic Commentary -- XI. Integral Equations -- ยง 1. The Wiener-Hopf Method -- ยง 2. Sectionally Analytic Functions -- ยง 3. The Hilbert Problem -- ยง 4. Application to Some Problems in Physics -- ยง 1. Study of Certain Weighted Sobolev Spaces -- ยง 2. Integral Equations Associated with the Boundary Value Problems of Electrostatics -- ยง 3. Integral Equations Associated with the Helmholtz Equation -- ยง 4. Integral Equations Associated with Problems of Linear Elasticity -- ยง 5. Integral Equations Associated with the Stokes System -- XII. Numerical Methods for Stationary Problems -- ยง 1. Principal Aspects of the Finite Element Method Applied to the Problem of Linear Elasticity -- ยง 2. Treatment of Domains with Curved Boundaries -- ยง 3. A Non Conforming Method of Finite Elements -- ยง 4. Applications to the Problems of Plates and Shells -- ยง 5 Approximation of Eigenvalues and Eigenvectors -- ยง 6. An Example of the Approximate Calculation for a Problem of the Eigenvalues of a Non Self-Adjoint Operator -- Review of Chapter XII -- XIII. Approximation of Integral Equations by Finite Elements. Error Analysis -- ยง 1. The Case of a Polyhedral Surface -- ยง 2. The Case of a Regular Closed Surface -- Appendix. โ{128}{156}Singular Integralsโ{128}{157} -- ยง 1. Operator, Convolution Operator, Integral Operator -- ยง 2. The Hilbert Transformation -- ยง 3. Generalities on Singular Integral Operators -- ยง 5. The Calderon-Zygmund Theorem -- ยง 6. Marcinkiewicz Spaces -- 1. Definitions -- 2. Application to the Homogeneous Convolution Kernel -- 4. Operators of Weak Type. The Marcinkiewicz Theorem -- 5. The Maximal Hardy-Littlewood Operator. -- Proof of Lemma 1 in ยง 2 -- Table of Notations -- of Volumes1โ{128}{147}3, 5, 6


Mathematics Chemometrics Partial differential equations Numerical analysis Computational intelligence Mathematics Numerical Analysis Partial Differential Equations Math. Applications in Chemistry Computational Intelligence



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