{"product_id":"partial-differential-equations-9780470054567","title":"Partial Differential Equations","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eOur understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of \u003ci\u003ePartial Differential Equations\u003c\/i\u003e 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.  \u003cp\u003eIn this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace 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.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eChapter 1\/Where PDEs Come From\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1* What is a Partial Differential Equation? 1\u003c\/p\u003e \u003cp\u003e1.2* First-Order Linear Equations 6\u003c\/p\u003e \u003cp\u003e1.3* Flows, Vibrations, and Diffusions 10\u003c\/p\u003e \u003cp\u003e1.4* Initial and Boundary Conditions 20\u003c\/p\u003e \u003cp\u003e1.5 Well-Posed Problems 25\u003c\/p\u003e \u003cp\u003e1.6 Types of Second-Order Equations 28\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 2\/Waves and Diffusions\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1* The Wave Equation 33\u003c\/p\u003e \u003cp\u003e2.2* Causality and Energy 39\u003c\/p\u003e \u003cp\u003e2.3* The Diffusion Equation 42\u003c\/p\u003e \u003cp\u003e2.4* Diffusion on the Whole Line 46\u003c\/p\u003e \u003cp\u003e2.5* Comparison of Waves and Diffusions 54\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 3\/Reflections and Sources\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Diffusion on the Half-Line 57\u003c\/p\u003e \u003cp\u003e3.2 Reflections of Waves 61\u003c\/p\u003e \u003cp\u003e3.3 Diffusion with a Source 67\u003c\/p\u003e \u003cp\u003e3.4 Waves with a Source 71\u003c\/p\u003e \u003cp\u003e3.5 Diffusion Revisited 80\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 4\/Boundary Problems\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1* Separation of Variables, The Dirichlet Condition 84\u003c\/p\u003e \u003cp\u003e4.2* The Neumann Condition 89\u003c\/p\u003e \u003cp\u003e4.3* The Robin Condition 92\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 5\/Fourier Series\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1* The Coefficients 104\u003c\/p\u003e \u003cp\u003e5.2* Even, Odd, Periodic, and Complex Functions 113\u003c\/p\u003e \u003cp\u003e5.3* Orthogonality and General Fourier Series 118\u003c\/p\u003e \u003cp\u003e5.4* Completeness 124\u003c\/p\u003e \u003cp\u003e5.5 Completeness and the Gibbs Phenomenon 136\u003c\/p\u003e \u003cp\u003e5.6 Inhomogeneous Boundary Conditions 147\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 6\/Harmonic Functions\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1* Laplace’s Equation 152\u003c\/p\u003e \u003cp\u003e6.2* Rectangles and Cubes 161\u003c\/p\u003e \u003cp\u003e6.3* Poisson’s Formula 165\u003c\/p\u003e \u003cp\u003e6.4 Circles, Wedges, and Annuli 172\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 7\/Green’s Identities and Green’s Functions\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Green’s First Identity 178\u003c\/p\u003e \u003cp\u003e7.2 Green’s Second Identity 185\u003c\/p\u003e \u003cp\u003e7.3 Green’s Functions 188\u003c\/p\u003e \u003cp\u003e7.4 Half-Space and Sphere 191\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 8\/Computation of Solutions\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Opportunities and Dangers 199\u003c\/p\u003e \u003cp\u003e8.2 Approximations of Diffusions 203\u003c\/p\u003e \u003cp\u003e8.3 Approximations of Waves 211\u003c\/p\u003e \u003cp\u003e8.4 Approximations of Laplace’s Equation 218\u003c\/p\u003e \u003cp\u003e8.5 Finite Element Method 222\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 9\/Waves in Space\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Energy and Causality 228\u003c\/p\u003e \u003cp\u003e9.2 The Wave Equation in Space-Time 234\u003c\/p\u003e \u003cp\u003e9.3 Rays, Singularities, and Sources 242\u003c\/p\u003e \u003cp\u003e9.4 The Diffusion and Schrodinger Equations 248 ¨\u003c\/p\u003e \u003cp\u003e9.5 The Hydrogen Atom 254\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 10\/Boundaries in the Plane and in Space\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Fourier’s Method, Revisited 258\u003c\/p\u003e \u003cp\u003e10.2 Vibrations of a Drumhead 264\u003c\/p\u003e \u003cp\u003e10.3 Solid Vibrations in a Ball 270\u003c\/p\u003e \u003cp\u003e10.4 Nodes 278\u003c\/p\u003e \u003cp\u003e10.5 Bessel Functions 282\u003c\/p\u003e \u003cp\u003e10.6 Legendre Functions 289\u003c\/p\u003e \u003cp\u003e10.7 Angular Momentum in Quantum Mechanics 294\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 11\/General Eigenvalue Problems\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 The Eigenvalues Are Minima of the Potential Energy 299\u003c\/p\u003e \u003cp\u003e11.2 Computation of Eigenvalues 304\u003c\/p\u003e \u003cp\u003e11.3 Completeness 310\u003c\/p\u003e \u003cp\u003e11.4 Symmetric Differential Operators 314\u003c\/p\u003e \u003cp\u003e11.5 Completeness and Separation of Variables 318\u003c\/p\u003e \u003cp\u003e11.6 Asymptotics of the Eigenvalues 322\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 12\/Distributions and Transforms\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Distributions 331\u003c\/p\u003e \u003cp\u003e12.2 Green’s Functions, Revisited 338\u003c\/p\u003e \u003cp\u003e12.3 Fourier Transforms 343\u003c\/p\u003e \u003cp\u003e12.4 Source Functions 349\u003c\/p\u003e \u003cp\u003e12.5 Laplace Transform Techniques 353\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 13\/PDE Problems from Physics\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Electromagnetism 358\u003c\/p\u003e \u003cp\u003e13.2 Fluids and Acoustics 361\u003c\/p\u003e \u003cp\u003e13.3 Scattering 366\u003c\/p\u003e \u003cp\u003e13.4 Continuous Spectrum 370\u003c\/p\u003e \u003cp\u003e13.5 Equations of Elementary Particles 373\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 14\/Nonlinear PDEs\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Shock Waves 380\u003c\/p\u003e \u003cp\u003e14.2 Solitons 390\u003c\/p\u003e \u003cp\u003e14.3 Calculus of Variations 397\u003c\/p\u003e \u003cp\u003e14.4 Bifurcation Theory 401\u003c\/p\u003e \u003cp\u003e14.5 Water Waves 406\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA.1 Continuous and Differentiable Functions 414\u003c\/p\u003e \u003cp\u003eA.2 Infinite Series of Functions 418\u003c\/p\u003e \u003cp\u003eA.3 Differentiation and Integration 420\u003c\/p\u003e \u003cp\u003eA.4 Differential Equations 423\u003c\/p\u003e \u003cp\u003eA.5 The Gamma Function 425\u003c\/p\u003e \u003cp\u003eReferences 427\u003c\/p\u003e \u003cp\u003eAnswers and Hints to Selected Exercises 431\u003c\/p\u003e \u003cp\u003eIndex 446\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402273562967,"sku":"9780470054567","price":195.71,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470054567.jpg?v=1730479910","url":"https:\/\/bookcurl.com\/products\/partial-differential-equations-9780470054567","provider":"Book Curl","version":"1.0","type":"link"}