Introduction to Partial Differential Equations (eBook)

Second Edition

Gerald B. Folland (Autor)

eBook Download: PDF

2020 | 2. Auflage
Princeton University Press (Verlag)
978-0-691-21303-3 (ISBN)

Infos

The second edition of Introduction to Partial Differential Equations, which originally appeared in the Princeton series Mathematical Notes, serves as a text for mathematics students at the intermediate graduate level. The goal is to acquaint readers with the fundamental classical results of partial differential equations and to guide them into some aspects of the modern theory to the point where they will be equipped to read advanced treatises and research papers. This book includes many more exercises than the first edition, offers a new chapter on pseudodifferential operators, and contains additional material throughout. The first five chapters of the book deal with classical theory: first-order equations, local existence theorems, and an extensive discussion of the fundamental differential equations of mathematical physics. The techniques of modern analysis, such as distributions and Hilbert spaces, are used wherever appropriate to illuminate these long-studied topics. The last three chapters introduce the modern theory: Sobolev spaces, elliptic boundary value problems, and pseudodifferential operators.

Produkt-Details

• Erscheint lt. Verlag: 26.5.2020
• Reihe/Serie: Mathematical Notes
• Reihe/Serie: Mathematical Notes
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Schlagworte: Adjoint • algebraic equation • Amplitude • analytic function • Applied mathematics • A priori estimate • asymptotic expansion • Bernhard Riemann • Bessel function • Boundary value problem • Bounded set (topological vector space) • Calculation • Cancellation property • Cauchy data • Cauchy–Kowalevski theorem • Cauchy problem • Cauchy–Riemann equations • Cauchy's theorem (geometry) • central limit theorem • Change of variables • Characteristic function (probability theory) • Characterization (mathematics) • coefficient • continuous function • corollary • cotangent space • Derivative • Difference quotient • differential equation • differential form • Differential operator • diffusion process • Dirichlet boundary condition • Dirichlet Integral • Dirichlet problem • Dirichlet's principle • Divergence Theorem • Eigenvalues and Eigenvectors • elliptic operator • Equation • existential quantification • Feynman propagator • First-order partial differential equation • fourier analysis • Fourier inversion theorem • Fourier transform • Fredholm Theory • Functional Analysis • fundamental solution • Gaussian kernel • Green's Function • Hadamard example • heat equation • Heat operator • hilbert space • Hilbert transform • holomorphic function • Hyperbolic function • hyperbolic partial differential equation • hypoelliptic operator • implicit function theorem • Initial Value Problem • integral equation • integral transform • Integration by parts • interpolation theorem • Intersection (set theory) • Kelvin transform • Laplace Operator • Laplace's equation • Laplacian • Lebesgue integration • Lewy equation • Limit of a sequence • linear differential equation • Linear map • Liouville's theorem (Hamiltonian) • Locally integrable function • Mathematical Physics • Maximum principle • Maxwell's equations • mean value theorem • Neumann problem • Newtonian Potential • normal derivative • Norm (mathematics) • Operator (physics) • ordinary differential equation • oriented hypersurface • Orthonormal basis • parametric equation • Parametrix • partial differential equation • Poisson Bracket • Poisson kernel • polynomial • Potential Theory • power series • Projection (linear algebra) • Projection (mathematics) • pseudo-differential operator • radial function • Regularity theorem • Rellich's theorem • Restriction (mathematics) • second law of thermodynamics • Sesquilinear form • Simultaneous Equations • Singular integral • Sobolev norm • Sobolev Space • Special case • subharmonic function • Support (mathematics) • Taylor's theorem • Theorem • uniqueness theorem • Variable (mathematics) • wave equation • wave operator • weak solution
• ISBN-10: 0-691-21303-8 / 0691213038
• ISBN-13: 978-0-691-21303-3 / 9780691213033