Invitation to Partial Differential Equations

Maxim Braverman, Northeastern University, Boston, MA.Robert McOwen, Northeastern University, Boston, MA.Peter Topalov, Northeastern University, Boston, MA.

“It is a great pleasure to see this book--written by a great master of the subject--finally in print. This treatment of a core part of mathematics and its applications offers the student both a solid foundation in basic calculations techniques in the subject, as well as a basic introduction to the more general machinery, e.g., distributions, Sobolev spaces, etc., which are such a key part of any modern treatment. As such this book is ideal for more advanced undergraduates as well as mathematically inclined students from engineering or the natural sciences. Shubin has a lovely intuitive writing style which provides a gentle introduction to this beautiful subject. Many good exercises (and solutions) are provided!” - Rafe Mazzeo, Stanford University“This text provides an excellent semester's introduction to classical and modern topics in linear PDE, suitable for students with a background in advanced calculus and Lebesgue integration. The author intersperses treatments of the Laplace, heat, and wave equations with developments of various functional analytic tools, particularly distribution theory and spectral theory, introducing key concepts while deftly avoiding heavy technicalities.” - Michael Taylor, University of North Carolina, Chapel Hill

• Linear differential operatorsOne-dimensional wave equationThe Sturm-Liouville problemDistributionsConvolution and Fourier transformHarmonic functionsThe heat equationSobolev spaces. A generalized solution of Dirichlet's problemThe eigenvalues and eigenfunctions of the Laplace operatorThe wave equationProperties of the potentials and their computationWave fronts and short-wave asymptotics for hyperbolic equationsAnswers and hints. SolutionsBibliographyIndex