LEADER 05709nam 22007813u 450 001 9911006803503321 005 20230802010948.0 010 $a9780486134734 010 $a0486134733 010 $a9781621985846 010 $a1621985849 035 $a(CKB)2550000001186531 035 $a(EBL)1894793 035 $a(SSID)ssj0001002763 035 $a(PQKBManifestationID)12389502 035 $a(PQKBTitleCode)TC0001002763 035 $a(PQKBWorkID)11015422 035 $a(PQKB)11506021 035 $a(MiAaPQ)EBC1894793 035 $a(Au-PeEL)EBL1894793 035 $a(CaONFJC)MIL565902 035 $a(OCoLC)868269904 035 $a(Perlego)110839 035 $a(EXLCZ)992550000001186531 100 $a20141222d2012|||| u|| | 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aPartial Differential Equations for Scientists and Engineers 205 $a1st ed. 210 $aNewburyport $cDover Publications$d2012 215 $a1 online resource (663 p.) 225 1 $aDover Books on Mathematics 300 $aDescription based upon print version of record. 311 08$a9780486676203 311 08$a048667620X 311 08$a9781306346511 311 08$a1306346517 327 $aTitle Page; Copyright Page; Preface; Table of Contents; PART 1 - Introduction; LESSON 1 - Introduction to Partial Differential Equations; What Are PDEs?; Why Are PDEs Useful?; How Do You Solve a Partial Differential Equation?; Kinds of PDEs; PART 2 - Diffusion-Type Problems; LESSON 2 - Diffusion-Type Problems (Parabolic Equations); A Simple Heat-Flow Experiment; The Mathematical Model of the Heat-Flow Experiment; More Diffusion-Type Equations; LESSON 3 - Boundary Conditions for Diffusion-Type Problems; Type 1 BC (Temperature specified on the boundary) 327 $aType 2 BC (Temperature of the surrounding medium specified)Type 3 BC (Flux specified-including the special case of insulated boundaries); Typical BCs for One-Dimensional Heat Flow; LESSON 4 - Derivation of the Heat Equation; Derivation of the Heat Equation; LESSON 5 - Separation of Variables; Overview of Separation of Variables; Separation of Variables; LESSON 6 - Transforming Nonhomogeneous BCs into Homogeneous Ones; Transforming Nonhomogeneous BCs to Homogeneous Ones; Transforming Time Varying BCs to Zero BCs; LESSON 7 - Solving More Complicated Problems by Separation of Variables 327 $aHeat-Flow Problem with Derivative BCLESSON 8 - Transforming Hard Equations into Easier Ones; Transforming a Heat-Flow Problem with Lateral Heat Loss into an Insulated Problem; LESSON 9 - Solving Nonhomogeneous PDEs (Eigenfunction Expansions); Solution by the Eigenfunction Expansion Method; Solution of a Problem by the Eigenfunction-Expansion Method; LESSON 10 - Integral Transforms (Sine and Cosine Transforms); The Spectrum of a Function; Solution of an Infinite-Diffusion Problem via the Sine Transform; Interpretation of the Solution; LESSON 11 - The Fourier Series and Transform 327 $aDiscrete Frequency Spectrum of a Periodic FunctionThe Fourier Transform; LESSON 12 - The Fourier Transform and Its Application to PDEs; Useful Properties of the Fourier Transform; Example of a Convolution of Two Functions; Solution of an Initial-Value Problem; LESSON 13 - The Laplace Transform; Properties of the Laplace Transform; Sufficient Conditions to Insure the Existence of a Laplace Transform; Definition of the Finite Convolution; Heat Conduction in a Semi Infinite Medium; LESSON 14 - Duhamel's Principle; Heat Flow within a Rod with Temperature Fixed on the Boundaries 327 $aThe Importance of Duhamel's PrincipleLESSON 15 - The Convection Term ux in the Diffusion Problems; Laplace Transform Solution to the Convection Problem; PART 3 - Hyperbolic-Type Problems; LESSON 16 - The One-Dimensional Wave Equation (Hyperbolic Equations); Vibrating-String Problem; Intuitive Interpretation of the Wave Equation; LESSON 17 - The D'Alembert Solution of the Wave Equation; D'Alembert's Solution to the One-Dimensional Wave Equation; Examples of the D'Alembert Solution; LESSON 18 - More on the D'Alembert Solution; The Space-Time Interpretation of D'Alembert's Solution 327 $aSolution of the Semi-infinite String via the D'Alembert Formula 330 $aMost physical phenomena, whether in the domain of fluid dynamics, electricity, magnetism, mechanics, optics, or heat flow, can be described in general by partial differential equations. Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations.This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing th 410 0$aDover Books on Mathematics 606 $aDifferential equations, Partial 606 $aDifferential equations, Partial 606 $aMathematics$2HILCC 606 $aPhysical Sciences & Mathematics$2HILCC 606 $aCalculus$2HILCC 615 4$aDifferential equations, Partial. 615 0$aDifferential equations, Partial. 615 7$aMathematics 615 7$aPhysical Sciences & Mathematics 615 7$aCalculus 676 $a515.3/53 676 $a515.353 700 $aFarlow$b Stanley J$042263 801 0$bAU-PeEL 801 1$bAU-PeEL 801 2$bAU-PeEL 906 $aBOOK 912 $a9911006803503321 996 $aPartial differential equations for scientists and engineers$982412 997 $aUNINA