دانلود کتاب Mathematical Models of Physics Problems

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COVER
MATHEMATICAL MODELS OF PHYSICS PROBLEMS
MATHEMATICAL MODELS OF PHYSICS PROBLEMS
Library of Congress Cataloging-in-Publication Data
Contents
Preface
Chapter1ComplexAnalysis
1.1.ComplexAlgebra
1.2.FunctionsofaComplexVariable
1.3.Cauchy’sTheoremandItsApplications
1.4.IsolatedSingularitiesandResidues
Exercises
Chapter2ElementsofLinearAlgebra
2.1.LinearSpaces
2.2.CauchySequencesandCompleteSpaces
2.3.LinearOperatorsonEuclideanSpaces
Exercises
Chapter3OrdinaryDifferentialEquations
3.1.SettingtheStage
3.2.InitialValueProblem
3.2.1.ExistenceandUniquenessofSolutions
3.2.2.SystemofFirst-orderLinearDifferentialEquations
3.2.3.GreenMatrixasaGeneralizedFunction
3.3.BoundaryValueProblem
3.3.1.Self-adjointnessofSturm-LiouvilleOperator
3.3.2.GreenFunctionforSturm-LiouvilleOperator
3.3.3.SeriesSolutionstoHomogeneousLinearEquations
3.4.FourierAnalysis
3.4.1.FourierSeries
3.4.2.FourierTransform
Exercises
Chapter4PartialDifferentialEquations
4.1.Taxonomy
4.2.WaveEquation
4.2.1.VibratingString
4.2.2.d’AlembertSolution
4.2.3.LinearAlgebraofSpacetime
4.2.4.CausalGreenFunction
4.3.DiffusionEquation
4.3.1.HeatFlow
4.3.2.DiffusioninanInfinitelyLongMetalBar
4.3.3.DiffusioninaFiniteMetalBbar
(((iii)))HomogeneousEquation
(((iiiiii)))InhomogeneousEquation
4.4.LaplaceEquation
4.4.1.HarmonicFunctions
4.4.2.SphericalHarmonics
4.4.3.GreenFunctionforLaplaceOperator
4.5.ApplicationstoQuantumMechanics
4.5.1.Schr¨odingerandKlein-GordonEquations
4.5.2.FeynmanPropagator
Exercises
AppendixAConformalTransformations
AppendixBGammaFunction
AppendixCGibbsPhenomenon
AppendixDLaplaceTransform
AppendixEAusstrahlungsbedingung
AnswersandCommentsontheExercises
Chapter1
Chapter2
Chapter3
Chapter4
References
Index