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Informationen zum Autor Dr. Walter A. Strauss is a professor of mathematics at Brown University. He has published numerous journal articles and papers. Not only is he is a member of the Division of Applied Mathematics and the Lefschetz Center for Dynamical Systems, but he is currently serving as the Editor in Chief of the SIAM Journal on Mathematical Analysis . Dr. Strauss' research interests include Partial Differential Equations, Mathematical Physics, Stability Theory, Solitary Waves, Kinetic Theory of Plasmas, Scattering Theory, Water Waves, Dispersive Waves. Klappentext Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations.In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs, the wave, heat and Lapace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics. Zusammenfassung Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. Inhaltsverzeichnis Chapter 1/Where PDEs Come From 1.1* What is a Partial Differential Equation? 1 1.2* First-Order Linear Equations 6 1.3* Flows, Vibrations, and Diffusions 10 1.4* Initial and Boundary Conditions 20 1.5 Well-Posed Problems 25 1.6 Types of Second-Order Equations 28 Chapter 2/Waves and Diffusions 2.1* The Wave Equation 33 2.2* Causality and Energy 39 2.3* The Diffusion Equation 42 2.4* Diffusion on the Whole Line 46 2.5* Comparison of Waves and Diffusions 54 Chapter 3/Reflections and Sources 3.1 Diffusion on the Half-Line 57 3.2 Reflections of Waves 61 3.3 Diffusion with a Source 67 3.4 Waves with a Source 71 3.5 Diffusion Revisited 80 Chapter 4/Boundary Problems 4.1* Separation of Variables, The Dirichlet Condition 84 4.2* The Neumann Condition 89 4.3* The Robin Condition 92 Chapter 5/Fourier Series 5.1* The Coefficients 104 5.2* Even, Odd, Periodic, and Complex Functions 113 5.3* Orthogonality and General Fourier Series 118 5.4* Completeness 124 5.5 Completeness and the Gibbs Phenomenon 136 5.6 Inhomogeneous Boundary Conditions 147 Chapter 6/Harmonic Functions 6.1* Laplace's Equation 152 6.2* Rectangles and Cubes 161 6.3* Poisson's Formula 165 6.4 Circles, Wedges, and Annuli 172 Chapter 7/Green's Identities and Green's Functions 7.1 Green's First Identity 178 7.2 Green's Second Identity 185 7.3 Green's Functions 188 7.4 Half-Space and Sphere 191 Chapter 8/Computation of Solutions 8.1 Opportunities and Dangers 199 8.2 Approximations of Diffusions 203 8.3 Approximations of Waves 211 8.4 Approximations of Laplace's Equation 218 8.5 Finite Element Method 222 Chapter 9/Waves in Space 9.1 Energy and Causality 228 9.2 The Wave Equation in Space-Time 234 9.3 Rays, Singular...
