MARC Record from Library of Congress

LEADER: 04822cam a22003377a 4500
001 2011288119
003 DLC
005 20121129081255.0
008 110803s2011 si a b 001 0 eng d
010 $a 2011288119
016 7 $a015781899$2Uk
020 $a9789814295512
020 $a9814295515
035 $a(OCoLC)ocn502034689
040 $aBTCTA$beng$cBTCTA$dYDXCP$dSINTU$dBWX$dNBU$dUAB$dUKMGB$dSINLB$dCDX$dDEBBG$dUPM$dZWZ$dDLC
042 $alccopycat
050 00 $aQA377$b.B685 2011
082 04 $a515.353$222
084 $aRB 10115$2rvk
100 1 $aBóna, Andrej.
245 10 $aWavefronts and rays as characteristics and asymptotics /$cAndrej Bóna, Michael A. Slawinski.
260 $aSingapore :$bWorld Scientific,$c2011.
300 $axvii, 276 p. :$bill. ;$c24 cm.
504 $aIncludes bibliographical references (p. 263-265) and index.
505 0 $aMachine generated contents note: 1.Characteristic equations of first-order linear partial differential equations -- Preliminary remarks -- 1.1.Motivational example -- 1.1.1.General and particular solutions -- 1.1.2.Characteristics -- 1.2.Directional derivatives -- 1.3.Nonlinear digression: Inviscid Burgers's equation -- 1.4.Taylor series of solutions -- 1.5.Incompatibility of side conditions -- 1.6.Semilinear equations -- 1.7.Systems of equations -- Closing remarks -- 1.8.Exercises -- 2.Characteristic equations of second-order linear partial differential equations -- Preliminary remarks -- 2.1.Motivational examples -- 2.1.1.Equation with directional derivative -- 2.1.2.Wave equation in one spatial dimension -- 2.1.3.Heat equation in one spatial dimension -- 2.1.4.Laplace equation in two spatial dimensions -- 2.2.Hyperbolic, parabolic and elliptic equations -- 2.3.Characteristics -- 2.3.1.Semilinear equations -- 2.3.2.Wave, heat and Laplace equations -- 2.3.3.Solution of wave equation -- 2.3.4.Systems of semilinear equations -- 2.3.5.Elastodynamic and Maxwell equations -- 2.3.6.Quasilinear equations -- Closing remarks -- 2.4.Exercises -- 3.Characteristic equations of first-order nonlinear partial differential equations -- Preliminary remarks -- 3.1.Motivational example -- 3.2.Characteristics -- 3.3.Side conditions -- 3.4.Physical applications -- 3.4.1.Elastodynamic equations -- 3.4.2.Maxwell equations -- Closing remarks -- 3.5.Exercises -- 4.Propagation of discontinuities for linear partial differential equations -- Preliminary remarks -- 4.1.Motivational example -- 4.2.Discontinuities and frequency content -- 4.3.Asymptotic series -- 4.3.1.General formulation -- 4.3.2.Choice of asymptotic sequence -- 4.4.Eikonal equation -- 4.4.1.Derivation -- 4.4.2.Solution -- 4.5.Transport equation -- 4.5.1.Derivation -- 4.5.2.Solution -- 4.6.Higher-order transport equations -- 4.7.Physical applications -- 4.7.1.Elastodynamic equations -- 4.7.2.Maxwell equations -- Closing remarks -- 4.8.Exercises -- 5.Caustics -- Preliminary remarks -- 5.1.Singularities of transport equations -- 5.2.Caustics as envelopes of characteristics -- 5.3.Phase change on caustics -- 5.3.1.Waves in isotropic homogeneous media -- 5.3.2.Method of stationary phase -- 5.3.3.Phase change -- Closing remarks -- 5.4.Exercises -- Appendix A Integral theorems -- Preliminary remarks -- A.1.Divergence Theorem -- A.1.1.Statement -- A.1.2.Plausibility argument -- A.2.Curl Theorem -- A.2.1.Statement -- A.2.2.Plausibility argument -- Closing remarks -- Appendix B Elastodynamic equations -- Preliminary remarks -- B.1.Cauchy's equations of motion -- B.2.Stress-strain equations -- B.3.Elastodynamic equations -- B.4.Scalar and vector potentials -- B.4.1.Isotropy and homogeneity -- B.4.2.Equations of motion -- B.4.3.Scalar and vector potentials -- B.4.4.Wave equations -- B.5.Equations of motion versus wave equations -- Closing remarks -- Appendix C Maxwell equations in vacuo -- Preliminary remarks -- C.1.Formulation -- C.1.1.Fundamental equations -- C.1.2.Coulomb's law -- C.1.3.No-monopole law -- C.1.4.Faraday's law -- C.1.5.Ampere's law -- C.1.6.Speed of light -- C.1.7.Maxwell equations -- C.2.Scalar and vector potentials -- Closing remarks -- Appendix D Fourier series and transforms -- Preliminary remarks -- D.1.Similarity of functions -- D.2.Fourier series -- D.3.Fourier transform -- Closing remarks -- Appendix E Distributions -- Preliminary remarks -- E.1.Definition of distributions -- E.2.Operations on distributions -- E.3.Symbol -- E.4.Principal symbol -- Closing remarks.
650 0 $aDifferential equations, Hyperbolic.
650 7 $aOndes$xPropagation$xModèles mathématiques.
650 7 $aPhysique mathématique.
650 07 $aWellenausbreitung.
700 1 $aSlawinski, M. A.$q(Michael A.),$d1961-
856 4 $uhttp://www.gbv.de/dms/tib-ub-hannover/659043149.pdf$mDE-601$nBibl.ISILDE-601$qpdf/application$yInhaltsverzeichnis$304