LEADER 07679nam 2201885 a 450 001 9910778218403321 005 20200520144314.0 010 $a1-282-15878-3 010 $a9786612158780 010 $a1-4008-2816-3 024 7 $a10.1515/9781400828166 035 $a(CKB)1000000000788557 035 $a(EBL)457890 035 $a(OCoLC)436086359 035 $a(SSID)ssj0000269429 035 $a(PQKBManifestationID)11240978 035 $a(PQKBTitleCode)TC0000269429 035 $a(PQKBWorkID)10247246 035 $a(PQKB)10096694 035 $a(DE-B1597)446876 035 $a(OCoLC)979835070 035 $a(DE-B1597)9781400828166 035 $a(Au-PeEL)EBL457890 035 $a(CaPaEBR)ebr10312574 035 $a(CaONFJC)MIL215878 035 $a(MiAaPQ)EBC457890 035 $a(PPN)170253678 035 $a(EXLCZ)991000000000788557 100 $a20061204d2007 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aWave scattering by time dependent perturbations$b[electronic resource] $ean introduction /$fG.F. Roach 205 $aCourse Book 210 $aPrinceton, N.J. $cPrinceton University Press$d2007 215 $a1 online resource (300 p.) 225 1 $aPrinceton series in applied mathematics 300 $aDescription based upon print version of record. 311 $a0-691-11340-8 320 $aIncludes bibliographical references (p. [275]-283) and index. 327 $t Frontmatter -- $tContents -- $tPreface -- $tChapter One. Introduction and Outline of Contents -- $tChapter Two. Some Aspects of Waves on Strings -- $tChapter Three. Mathematical Preliminaries -- $tChapter Four. Spectral Theory and Spectral Decompositions -- $tChapter Five. On Nonautonomous Problems -- $tChapter Six. On Scattering Theory Strategies -- $tChapter Seven. Echo Analysis -- $tChapter Eight. Wave Scattering from Time-Periodic Perturbations -- $tChapter Nine Concerning Inverse Problems -- $tChapter Ten. Some Remarks on Scattering in Other Wave Systems -- $tChapter Eleven. Commentaries and Appendices -- $tBibliography -- $tIndex 330 $aThis book offers the first comprehensive introduction to wave scattering in nonstationary materials. G. F. Roach's aim is to provide an accessible, self-contained resource for newcomers to this important field of research that has applications across a broad range of areas, including radar, sonar, diagnostics in engineering and manufacturing, geophysical prospecting, and ultrasonic medicine such as sonograms. New methods in recent years have been developed to assess the structure and properties of materials and surfaces. When light, sound, or some other wave energy is directed at the material in question, "imperfections" in the resulting echo can reveal a tremendous amount of valuable diagnostic information. The mathematics behind such analysis is sophisticated and complex. However, while problems involving stationary materials are quite well understood, there is still much to learn about those in which the material is moving or changes over time. These so-called non-autonomous problems are the subject of this fascinating book. Roach develops practical strategies, techniques, and solutions for mathematicians and applied scientists working in or seeking entry into the field of modern scattering theory and its applications. Wave Scattering by Time-Dependent Perturbations is destined to become a classic in this rapidly evolving area of inquiry. 410 0$aPrinceton series in applied mathematics. 606 $aWaves$xMathematics 606 $aScattering (Physics)$xMathematics 606 $aPerturbation (Mathematics) 610 $aAcoustic wave equation. 610 $aAcoustic wave. 610 $aAffine space. 610 $aAngular frequency. 610 $aApproximation. 610 $aAsymptotic analysis. 610 $aAsymptotic expansion. 610 $aBanach space. 610 $aBasis (linear algebra). 610 $aBessel's inequality. 610 $aBoundary value problem. 610 $aBounded operator. 610 $aC0-semigroup. 610 $aCalculation. 610 $aCharacteristic function (probability theory). 610 $aClassical physics. 610 $aCodimension. 610 $aCoefficient. 610 $aContinuous function (set theory). 610 $aContinuous function. 610 $aContinuous spectrum. 610 $aConvolution. 610 $aDifferentiable function. 610 $aDifferential equation. 610 $aDimension (vector space). 610 $aDimension. 610 $aDimensional analysis. 610 $aDirac delta function. 610 $aDirichlet problem. 610 $aDistribution (mathematics). 610 $aDuhamel's principle. 610 $aEigenfunction. 610 $aEigenvalues and eigenvectors. 610 $aElectromagnetism. 610 $aEquation. 610 $aExistential quantification. 610 $aExponential function. 610 $aFloquet theory. 610 $aFourier inversion theorem. 610 $aFourier series. 610 $aFourier transform. 610 $aFredholm integral equation. 610 $aFrequency domain. 610 $aHelmholtz equation. 610 $aHilbert space. 610 $aInitial value problem. 610 $aIntegral equation. 610 $aIntegral transform. 610 $aIntegration by parts. 610 $aInverse problem. 610 $aInverse scattering problem. 610 $aLebesgue measure. 610 $aLinear differential equation. 610 $aLinear map. 610 $aLinear space (geometry). 610 $aLocally integrable function. 610 $aLongitudinal wave. 610 $aMathematical analysis. 610 $aMathematical physics. 610 $aMetric space. 610 $aOperator theory. 610 $aOrdinary differential equation. 610 $aOrthonormal basis. 610 $aOrthonormality. 610 $aParseval's theorem. 610 $aPartial derivative. 610 $aPartial differential equation. 610 $aPhase velocity. 610 $aPlane wave. 610 $aProjection (linear algebra). 610 $aPropagator. 610 $aQuantity. 610 $aQuantum mechanics. 610 $aReflection coefficient. 610 $aRequirement. 610 $aRiesz representation theorem. 610 $aScalar (physics). 610 $aScattering theory. 610 $aScattering. 610 $aScientific notation. 610 $aSelf-adjoint operator. 610 $aSelf-adjoint. 610 $aSeries expansion. 610 $aSine wave. 610 $aSpectral method. 610 $aSpectral theorem. 610 $aSpectral theory. 610 $aSquare-integrable function. 610 $aSubset. 610 $aTheorem. 610 $aTheory. 610 $aTime domain. 610 $aTime evolution. 610 $aUnbounded operator. 610 $aUnitarity (physics). 610 $aVector space. 610 $aVolterra integral equation. 610 $aWave function. 610 $aWave packet. 610 $aWave propagation. 615 0$aWaves$xMathematics. 615 0$aScattering (Physics)$xMathematics. 615 0$aPerturbation (Mathematics) 676 $a531/.1133 700 $aRoach$b G. F$g(Gary Francis)$013774 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910778218403321 996 $aWave scattering by time dependent perturbations$93861442 997 $aUNINA