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Record Nr. |
UNINA9910830072903321 |
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Autore |
Zauderer Erich |
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Titolo |
Partial differential equations of applied mathematics / / Erich Zauderer |
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Pubbl/distr/stampa |
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Hoboken, New Jersey : , : Wiley Publishing, Inc., , 2006 |
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©2006 |
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ISBN |
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1-283-33206-X |
9786613332066 |
1-118-03330-2 |
1-118-03140-7 |
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Edizione |
[3rd ed.] |
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Descrizione fisica |
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1 online resource (964 p.) |
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Collana |
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Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts |
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Disciplina |
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Soggetti |
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Differential equations, Partial |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Partial 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 |
Telegrapher'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 |
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Random 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 |
Method 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 |
3.1 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 |
Quasilinear First Order Systems and Normal Forms |
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Sommario/riassunto |
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This 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.<br |
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