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AuthorDautray, Robert. author
TitleMathematical Analysis and Numerical Methods for Science and Technology [electronic resource] : Volume 3 Spectral Theory and Applications / by Robert Dautray, Jacques-Louis Lions
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 2000
Connect tohttp://dx.doi.org/10.1007/978-3-642-61529-0
Descript X, 542 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

VIII. Spectral Theory -- Appendix. โ{128}{156}Krein-Rutman Theoremโ{128}{157}* -- IX. Examples in Electromagnetism and Quantum Physics* -- A. Examples in Electromagnetism -- B. Examples in Quantum Physics -- Appendix. Some Spectral Notions -- 2. โ{128}{156}Continuous Operational Calculusโ{128}{157} for a (Bounded) Normal Operator -- 3. โ{128}{156}Continuous Operational Calculusโ{128}{157} for an (Unbounded) Self-Adjoint Operator -- 4. Simultaneous Spectrum of a Commutative Family of (Bounded) Normal Operators -- 8. von Neumann Algebras -- 9. โ{128}{156}Bounded Operational Calculusโ{128}{157} -- 10. Maximal Commutative von Neumann Algebras -- 11. โ{128}{156}Maximalโ{128}{157} Spectral Decomposition. โ{128}{156}Complete Family of Observables which Commuteโ{128}{157} -- Table of Notations -- of Volumes 1, 2, 4โ{128}{147}6


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



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