LEADER 05824nam 2200709 450 001 9910791029003321 005 20200520144314.0 010 $a1-118-83210-8 035 $a(CKB)2550000001317608 035 $a(EBL)1687538 035 $a(SSID)ssj0001226121 035 $a(PQKBManifestationID)11742601 035 $a(PQKBTitleCode)TC0001226121 035 $a(PQKBWorkID)11269888 035 $a(PQKB)10701027 035 $a(MiAaPQ)EBC1687538 035 $a(DLC) 2013035005 035 $a(JP-MeL)3000065409 035 $a(Au-PeEL)EBL1687538 035 $a(CaPaEBR)ebr10882755 035 $a(CaONFJC)MIL618883 035 $a(OCoLC)857234464 035 $a(MiAaPQ)EBC7103899 035 $a(PPN)195533631 035 $a(EXLCZ)992550000001317608 100 $a20140625h20142014 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aBeginning partial differential equations /$fPeter V. O'Neil 205 $aThird edition. 210 1$aHoboken, New Jersey :$cWiley,$d2014. 210 4$d2014 215 $a1 online resource (453 p.) 225 0 $aPure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts 300 $aIncludes index. 311 $a1-118-62994-9 311 $a1-306-87632-X 320 $aIncludes bibliographical references and index. 327 $aBeginning Partial Differential Equations; Copyright; Contents; Preface; 1 First Ideas; 1.1 Two Partial Differential Equations; 1.1.1 The Heat, or Diffusion, Equati; 1.1.2 The Wave Equation; 1.2 Fourier Series; 1.2.1 The Fourier Series of a Function; 1.2.2 Fourier Sine and Cosine Series; 1.3 Two Eigenvalue Problems; 1.4 A Proof of the Fourier Convergence Theorem; 1.4.1 The Role of Periodicity; 1.4.2 Dirichlet's Formula; 1.4.3 The Riemann-Lebesgue Lemma; 1.4.4 Proof of the Convergence Theorem; 2 Solutions of the Heat Equation; 2.1 Solutions on an Interval [0, L] 327 $a2.1.1 Ends Kept at Temperature Zero2.1.2 Insulated Ends; 2.1.3 Ends at Different Temperatures; 2.1.4 A Diffusion Equation with Additional Terms; 2.1.5 One Radiating End; 2.2 A Nonhomogeneous Problem; 2.3 The Heat Equation in Two Space Variables; 2.4 The Weak Maximum Principle; 3 Solutions of the Wave Equation; 3.1 Solutions on Bounded Intervals; 3.1.1 Fixed Ends; 3.1.2 Fixed Ends with a Forcing Term; 3.1.3 Damped Wave Motion; 3.2 The Cauchy Problem; 3.2.1 d'Alembert's Solution; 3.2.1.1 Forward and Backward Waves; 3.2.2 The Cauchy Problem on a Half Line 327 $a3.2.3 Characteristic Triangles and Quadrilaterals3.2.4 A Cauchy Problem with a Forcing Term; 3.2.5 String with Moving Ends; 3.3 The Wave Equation in Higher Dimensions; 3.3.1 Vibrations in a Membrane with Fixed Frame; 3.3.2 The Poisson Integral Solution; 3.3.3 Hadamard's Method of Descent; 4 Dirichlet and Neumann Problems; 4.1 Laplace's Equation and Harmonic Functions; 4.1.1 Laplace's Equation in Polar Coordinates; 4.1.2 Laplace's Equation in Three Dimensions; 4.2 The Dirichlet Problem for a Rectangle; 4.3 The Dirichlet Problem for a Disk; 4.3.1 Poisson's Integral Solution 327 $a4.4 Properties of Harmonic Functions4.4.1 Topology of Rn; 4.4.2 Representation Theorems; 4.4.2.1 A Representation Theorem in R3; 4.4.2.2 A Representation Theorem in the Plane; 4.4.3 The Mean Value Property and the Maximum Principle; 4.5 The Neumann Problem; 4.5.1 Existence and Uniqueness; 4.5.2 Neumann Problem for a Rectangle; 4.5.3 Neumann Problem for a Disk; 4.6 Poisson's Equation; 4. 7 Existence Theorem for a Dirichlet Problem; 5 Fourier Integral Methods of Solution; 5.1 The Fourier Integral of a Function; 5.1.1 Fourier Cosine and Sine Integrals; 5.2 The Heat Equation on the Real Line 327 $a5.2.1 A Reformulation of the Integral Solution5.2.2 The Heat Equation on a Half Line; 5.3 The Debate over the Age of the Earth; 5.4 Burger's Equation; 5.4.1 Traveling Wave Solutions of Burger's Equation; 5.5 The Cauchy Problem for the Wave Equation; 5.6 Laplace's Equation on Unbounded Domains; 5.6.1 Dirichlet Problem for the Upper Half Plane; 5.6.2 Dirichlet Problem for the Right Quarter Plane; 5.6.3 A Neumann Problem for the Upper Half Plane; 6 Solutions Using Eigenfunction Expansions; 6.1 A Theory of Eigenfunction Expansions; 6.1.1 A Closer Look at Expansion Coefficients 327 $a6.2 Bessel Functions 330 $a"Featuring a challenging, yet accessible, introduction to partial differential equations, Beginning Partial Differential Equations provides a solid introduction to partial differential equations, particularly methods of solution based on characteristics, separation of variables, as well as Fourier series, integrals, and transforms. Thoroughly updated with novel applications, such as Poe's pendulum and Kepler's problem in astronomy, this third edition is updated to include the latest version of Maples, which is integrated throughout the text. New topical coverage includes novel applications, such as Poe's pendulum and Kepler's problem in astronomy"--$cProvided by publisher. 330 $a"This Third Edition provides a solid introduction to partial differential equations, particularly methods of solution based on characteristics, separation of variables, as well as Fourier series, integrals, and transforms"--$cProvided by publisher. 410 0$aPure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts 606 $aDifferential equations, Partial 615 0$aDifferential equations, Partial. 676 $a515/.353 686 $aMAT007000$2bisacsh 700 $aO'Neil$b Peter V.$0511885 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910791029003321 996 $aBeginning partial differential equations$91974468 997 $aUNINA LEADER 03073nas 2200865-a 450 001 9910218146503321 005 20240413013109.0 035 $a(CKB)1000000000223126 035 $a(CONSER)---96655931- 035 $a(EXLCZ)991000000000223126 100 $a19961230a19939999 -a- - 101 0 $aspa 200 00$aEconomía, trabajo y sociedad $ememoria sobre la situación socioeconómica y laboral 210 $aMadrid $cConsejo Económico y Social$d1994- 215 $a1 online resource 225 1 $aColección Memorias 300 $aAt head of title: España. 311 $aPrint version: Economía, trabajo y sociedad : (DLC) 96655931 (OCoLC)36141931 1136-9221 410 0$aColección Memorias (Consejo Económico y Social (Spain)) 517 1 $aMemoria sobre la situación socioeconómica y laboral de España en ... 517 1 $aMemoria sobre la situación socioeconómica y laboral España ... 531 1 $aEcon. trab. soc. 606 $aLabor$zSpain$vPeriodicals 606 $aeconomic situation$2eurovocen 606 $asocial situation$2eurovocen 606 $asocioeconomic conditions$2eurovocen 606 $alabour market$2eurovocen 606 $areport$2eurovocen 606 $aeconomic policy$2eurovocen 606 $aSpain$2eurovocen 606 $ayearbook$2eurovocen 606 $asituation économique$2eurovocfr 606 $asituation sociale$2eurovocfr 606 $acondition socio-économique$2eurovocfr 606 $amarché du travail$2eurovocfr 606 $arapport$2eurovocfr 606 $apolitique économique$2eurovocfr 606 $aEspagne$2eurovocfr 606 $aannuaire$2eurovocfr 606 $aEconomic history$2fast$3(OCoLC)fst00901974 606 $aLabor$2fast$3(OCoLC)fst00989798 606 $aSocial conditions$2fast$3(OCoLC)fst01919811 607 $aSpain$xSocial conditions$y1975-$vPeriodicals 607 $aSpain$xEconomic conditions$y1975-2008$vPeriodicals 607 $aSpain$2fast$1https://id.oclc.org/worldcat/entity/E39PBJqFTrvj6Mhw6JfTGmqJDq 608 $aPeriodicals.$2fast 610 $aEspaña$aCondiciones económicas$aAnuarios 610 $aEspaña$aCondiciones sociales$aAnuarios 615 0$aLabor 615 7$aeconomic situation. 615 7$asocial situation. 615 7$asocioeconomic conditions. 615 7$alabour market. 615 7$areport. 615 7$aeconomic policy. 615 7$aSpain. 615 7$ayearbook. 615 7$asituation économique. 615 7$asituation sociale. 615 7$acondition socio-économique. 615 7$amarché du travail. 615 7$arapport. 615 7$apolitique économique. 615 7$aEspagne. 615 7$aannuaire. 615 7$aEconomic history. 615 7$aLabor. 615 7$aSocial conditions. 676 $a306/.0946/05 712 02$aConsejo Econo?mico y Social (Spain) 906 $aJOURNAL 912 $a9910218146503321 920 $aexl_impl conversion 996 $aEconomi?a, trabajo y sociedad$92121374 997 $aUNINA