LEADER 05425nam 2200673 450 001 9910819250603321 005 20200520144314.0 010 $a1-118-44146-X 035 $a(CKB)3710000000225197 035 $a(EBL)918621 035 $a(OCoLC)889674258 035 $a(SSID)ssj0001334795 035 $a(PQKBManifestationID)12495746 035 $a(PQKBTitleCode)TC0001334795 035 $a(PQKBWorkID)11272375 035 $a(PQKB)10258926 035 $a(MiAaPQ)EBC918621 035 $a(Au-PeEL)EBL918621 035 $a(CaPaEBR)ebr10915813 035 $a(CaONFJC)MIL639068 035 $a(MiAaPQ)EBC7147457 035 $a(Au-PeEL)EBL7147457 035 $a(EXLCZ)993710000000225197 100 $a20140901h20122012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aPartial differential equations $etheory and completely solved problems /$fThomas Hillen, I. Ed Leonard, Henry van Roessel 205 $a1st ed. 210 1$aHoboken, New Jersey :$cWiley,$d2012. 210 4$dİ2012 215 $a1 online resource (694 p.) 300 $aDescription based upon print version of record. 311 $a1-118-06330-9 311 $a1-322-07817-3 320 $aIncludes bibliographical references and index. 327 $aCover; Title Page ; Copyright; Contents ; Preface ; PART I: THEORY ; Chapter 1: Introduction ; 1.1 Partial Differential Equations ; 11.2 Classification of Second-order Linear Pdes ; 1.3 Side Conditions ; 1.3.1 Boundary Conditions on an Interval ; 1.4 Linear Pdes ; 1.4.1 Principle of Superposition ; 1.5 Steady-state and Equilibrium Solutions ; 1.6 First Example for Separation of Variables ; 1.7 Derivation of the Diffusion Equation ; 1.7.1 Boundary Conditions ; 1.8 Derivation of the Heat Equation ; 1.9 Derivation of the Wave Equation ; 1.10 Examples of Laplace''s Equation ; 1.11 Summary 327 $a1.11.1 Problems and Notes Chapter 2: Fourier Series ; 2.1 Piecewise Continuous Functions ; 2.2 Even, Odd, and Periodic Functions ; 2.3 Orthogonal Functions ; 2.4 Fourier Series ; 2.4.1 Fourier Sine and Cosine Series ; 2.5 Convergence of Fourier Series ; 2.5.1 Gibbs'' Phenomenon ; 2.6 Operations on Fourier Series ; 2.7 Mean Square Error ; 2.8 Complex Fourier Series ; 2.9 Summary ; 2.9.1 Problems and Notes ; Chapter 3: Separation of Variables ; 3.1 Homogeneous Equations ; 3.1.1 General Linear Homogeneous Equations ; 3.1.2 Limitations of the Method of Separation of Variables 327 $a3.2 Nonhomogeneous Equations 3.2.1 Method of Eigenfunction Expansions ; 3.3 Summary ; 3.3.1 Problems and Notes ; Chapter 4: Sturm Liouville Theory ; 4.1 Formulation ; 4.2 Properties of Sturm-liouville Problems ; 4.3 Eigenfunction Expansions ; 4.4 Rayleigh Quotient ; 4.5 Summary ; 4.5.1 Problems and Notes ; Chapter 5: Heat, Wave, and Laplace Equations ; 5.1 One-dimensional Heat Equation ; 5.2 Two-dimensional Heat Equation ; 5.3 One-dimensional Wave Equation ; 5.3.1 d'' Alembert''s Solution ; 5.4 Laplace''s Equation ; 5.4.1 Potential in a Rectangle ; 5.5 Maximum Principle 327 $a5.6 Two-dimensional Wave Equation 5.7 Eigenfunctions in Two Dimensions ; 5.8 Summary ; 5.8.1 Problems and Notes ; Chapter 6: Polar Coordinates ; 6.1 Interior Dirichlet Problem for a Disk ; 6.1.1 Poisson Integral Formula ; 6.2 Vibrating Circular Membrane ; 6.3 Bessel''s Equation ; 6.3.1 Series Solutions of Odes ; 6.4 Bessel Functions ; 6.4.1 Properties of Bessel Functions ; 6.4.2 Integral Representation of Bessel Functions ; 6.5 Fourier-bessel Series ; 6.6 Solution to the Vibrating Membrane Problem ; 6.7 Summary ; 6.7.1 Problems and Notes ; Chapter 7: Spherical Coordinates 327 $a7.1 Spherical Coordinates 7.1.1 Derivation of the Laplacian ; 7.2 Legendre''s Equation ; 7.3 Legendre Functions ; 7.3.1 Legendre Polynomials ; 7.3.2 Fourier-legendre Series ; 7.3.3 Legendre Functions of the Second Kind ; 7.3.4 Associated Legendre Functions ; 7.4 Spherical Bessel Functions ; 7.5 Interior Dirichlet Problem for a Sphere ; 7.6 Summary ; 7.6.1 Problems and Notes ; Chapter 8: Fourier Transforms ; 8.1 Fourier Integrals ; 8.1.1 Fourier Integral Representation ; 8.1.2 Examples ; 8.1.3 Fourier Sine and Cosine Integral Representations ; 8.1.4 Proof of Fourier''s Theorem 327 $a8.2 Fourier Transforms 330 $a Uniquely provides fully solved problems for linear partial differential equations and boundary value problems Partial Differential Equations: Theory and Completely Solved Problems utilizes real-world physical models alongside essential theoretical concepts. With extensive examples, the book guides readers through the use of Partial Differential Equations (PDEs) for successfully solving and modeling phenomena in engineering, biology, and the applied sciences. The book focuses exclusively on linear PDEs and how they can be solved using the separation of variables technique. The authors begin 606 $aDifferential equations, Partial 615 0$aDifferential equations, Partial. 676 $a515/.353 686 $aMAT007000$2bisacsh 700 $aHillen$b Thomas$f1966-$0520266 702 $aLeonard$b I. Ed.$f1938- 702 $aVan Roessel$b Henry$f1956- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910819250603321 996 $aPartial differential equations$93927447 997 $aUNINA