LEADER 05424nam 2200649 450 001 9910141180703321 005 20170810190554.0 010 $a1-283-33206-X 010 $a9786613332066 010 $a1-118-03330-2 010 $a1-118-03140-7 035 $a(CKB)2670000000133546 035 $a(EBL)699963 035 $a(OCoLC)768230302 035 $a(SSID)ssj0000555273 035 $a(PQKBManifestationID)11939892 035 $a(PQKBTitleCode)TC0000555273 035 $a(PQKBWorkID)10518069 035 $a(PQKB)10834777 035 $a(MiAaPQ)EBC699963 035 $a(PPN)16972011X 035 $a(EXLCZ)992670000000133546 100 $a20160816h20062006 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aPartial differential equations of applied mathematics /$fErich Zauderer 205 $a3rd ed. 210 1$aHoboken, New Jersey :$cWiley Publishing, Inc.,$d2006. 210 4$dİ2006 215 $a1 online resource (964 p.) 225 1 $aPure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts 300 $aDescription based upon print version of record. 311 $a0-471-69073-2 320 $aIncludes bibliographical references and index. 327 $aPartial Differential Equations of Applied Mathematics; CONTENTS; Preface; 1 Random Walks and Partial Differential Equations; 1.1 The Diffusion Equation and Brownian Motion; Unrestricted Random Walks and their Limits; Brownian Motion; Restricted Random Walks and Their Limits; Fokker-Planck and Kolmogorov Equations; Properties of Partial Difference Equations and Related PDEs; Langevin Equation; Exercises 1.1; 1.2 The Telegrapher's Equation and Diffusion; Correlated Random Walks and Their Limits; Partial Difference Equations for Correlated Random Walks and Their Limits 327 $aTelegrapher's, Diffusion, and Wave EquationsPosition-Dependent Correlated Random Walks and Their Limits; Exercises 1.2; 1.3 Laplace's Equation and Green's Function; Time-Independent Random Walks and Their Limits; Green's Function; Mean First Passage Times and Poisson's Equation; Position-Dependent Random Walks and Their Limits; Properties of Partial Difference Equations and Related PDEs; Exercises 1.3; 1.4 Random Walks and First Order PDEs; Random Walks and Linear First Order PDEs: Constant Transition Probabilities; Random Walks and Linear First Order PDEs: Variable Transition Probabilities 327 $aRandom Walks and Nonlinear First Order PDEsExercises 1.4; 1.5 Simulation of Random Walks Using Maple; Unrestricted Random Walks; Restricted Random Walks; Correlated Random Walks; Time-Independent Random Walks; Random Walks with Variable Transition Probabilities; Exercises 1.5; 2 First Order Partial Differential Equations; 2.1 Introduction; Exercises 2.1; 2.2 Linear First Order Partial Differential Equations; Method of Characteristics; Examples; Generalized Solutions; Characteristic Initial Value Problems; Exercises 2.2; 2.3 Quasilinear First Order Partial Differential Equations 327 $aMethod of CharacteristicsWave Motion and Breaking; Unidirectional Nonlinear Wave Motion: An Example; Generalized Solutions and Shock Waves; Exercises 2.3; 2.4 Nonlinear First Order Partial Differential Equations; Method of Characteristics; Geometrical Optics: The Eiconal Equation; Exercises 2.4; 2.5 Maple Methods; Linear First Order Partial Differential Equations; Quasilinear First Order Partial Differential Equations; Nonlinear First Order Partial Differential Equations; Exercises 2.5; Appendix: Envelopes of Curves and Surfaces; 3 Classification of Equations and Characteristics 327 $a3.1 Linear Second Order Partial Differential EquationsCanonical Forms for Equations of Hyperbolic Type; Canonical Forms for Equations of Parabolic Type; Canonical Forms for Equations of Elliptic Type; Equations of Mixed Type; Exercises 3.1; 3.2 Characteristic Curves; First Order PDEs; Second Order PDEs; Exercises 3.2; 3.3 Classification of Equations in General; Classification of Second Order PDEs; Characteristic Surfaces for Second Order PDEs; First Order Systems of Linear PDEs: Classification and Characteristics; Systems of Hyperbolic Type; Higher-Order and Nonlinear PDEs 327 $aQuasilinear First Order Systems and Normal Forms 330 $aThis new edition features the latest tools for modeling, characterizing, and solving partial differential equationsThe Third Edition of this classic text offers a comprehensive guide to modeling, characterizing, and solving partial differential equations (PDEs). The author provides all the theory and tools necessary to solve problems via exact, approximate, and numerical methods. The Third Edition retains all the hallmarks of its previous editions, including an emphasis on practical applications, clear writing style and logical organization, and extensive use of real-world examples.