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181   $ctxt
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183   $acr
200 10$aFoundations and applications of variational and perturbation methods /$fS. Raj Vatsya
205   $a1st ed.
210   $aHauppauge, NY $cNova Science Publishers$dc2009
215   $a1 online resource (349 p.)
300   $aDescription based upon print version of record.
311 08$a1-60692-591-1 
320   $aIncludes bibliographical references (p. [327]-330) and index.
327   $aIntro -- FOUNDATIONS AND APPLICATIONS OFVARIATIONAL AND PERTURBATIONMETHODS -- FOUNDATIONS AND APPLICATIONS OFVARIATIONAL AND PERTURBATIONMETHODS -- CONTENTS -- PREFACE -- ACKNOWLEDGEMENTS -- I. FOUNDATIONS -- 1. INTEGRATION AND VECTOR SPACES -- 1. I. PRELIMINARIES -- 1. II. INTEGRATION -- 1.II.1. Basic Concepts -- 1.II.2. Integration over Trajectories -- 1. III. VECTOR SPACES -- 2. OPERATORS IN VECTOR SPACES -- 2.I. OPERATORS IN BANACH SPACES -- 2.II. Operators in Hilbert Spaces -- 2.III. Forms in Hilbert Spaces -- 2.IV. Integral Transforms -- 2.V. Differential Operators -- 3. VARIATIONAL METHODS -- 3.I. FORMULATION -- 3.II. CONVERGENCE -- 3.II.1. Basic Results -- 3.II.2. Compact Operators -- 3.II.3. Bounded Operators -- 3.II.4. Semi-Bounded Operators -- 3.III. PADÉ APPROXIMANTS -- 3.III.1. Formulation -- 3.III.2. Representations -- 3.III.3. Convergence And Applications -- 3.IV. MONOTONIC CONVERGENCE -- 3.IV.1. Diagonal Forms -- 3.IV.2. Eigenvalues -- 4. PERTURBATION METHODS -- 4.I. PERTURBED OPERATOR -- 4.II. SPECTRAL PERTURBATION -- 4.II.1. Resolvent and Point Spectrum -- 4.II.2. Continuous Spectrum -- 4.III. SPECTRAL DIFFERENTIATION -- 4.IV. ITERATION -- II. APPLICATIONS -- 5. MATRICES -- 5.I. TRIDIAGONAL MATRICES -- 5.II. STRUCTURED MATRICES -- 6. ATOMIC SYSTEMS -- 6.I. PRELIMINARIES -- 6.II. EIGENVALUES AND CRITICAL POINTS -- 6.II.1. Helium Atom -- 6.II.2. Short Range Potentials -- 6.III. SCATTERING -- 6.III.1. Formulation -- 6.III.2. Born Series -- 6.III.3. Schwinger's Method -- 6.III.4. Hulthén -Kohn Methods -- 6.III.5. Rotated Hamiltonians -- 7. SUPPLEMENTARY EXAMPLES -- 7.I. RAY TOMOGRAPHY -- 7.II. MAXWELL'S EQUATIONS -- 7.III. POSITIVITY LEMMA FOR THE ELLIPTIC OPERATORS -- 7.III.1. Basic Results -- 7.III.2. Applications -- 7.IV. TRANSPORT AND PROPAGATION -- 7.IV.1. Reaction-Diffusion -- 7.IV.2. Heat Transfer.
327   $a7.IV.3. Radiative Transfer -- 7.IV.4. Turbulent Diffusion -- 7.IV.5. Optical Beam Propagation -- 7.V. QUANTUM THEORY -- REFERENCES -- INDEX.
330   $aContents: Preface; Integration and vector spaces; Operators in vector spaces; Variational methods; Perturbation methods; Matrices; Atomic systems; Supplementary examples; References; Index.
606   $aPerturbation (Mathematics)
606   $aPerturbation (Quantum dynamics)
606   $aVariational principles
615  0$aPerturbation (Mathematics)
615  0$aPerturbation (Quantum dynamics)
615  0$aVariational principles.
676   $a515/.392
700   $aVatsya$b S. Raj$01869352
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910969394303321
996   $aFoundations and applications of variational and perturbation methods$94477503
997   $aUNINA