1MA216 Homepage
Vladimir Tkachev's lecture notes
A collection of links to various PDE lecture notes
Practice problems
Timetable


Textbooks:
Text I: Fritz John. Partial Differential Equations, SpringerVerlag, New York, 1995.
Text II: Robert C. McOwen, Partial Differential Equations, Methods and Applications, Prentice Hall/Pearson Education, Inc., 2003 (Second Edition)
Occasionally: Lawrence C. Evans. Partial Differential Equations, AMS, Providence, RI.
Series: Graduate Studies in Mathematics, Vol. 19, 1998.
Here is an explanation of the method of reflection for the halfplane, section 4.2. .
Here is a sample final and solutions .
You can find the first day handout here .
Updated course contents, with sections from R. McOwen. some sections from F. John included (and more will be added).
Some extra useful reading: Notes on CauchyKovalevskaya theorem and characteristic surfaces.
Notes on volumes, areas and masses
and an EnsglishSwedishFrenchGerman list of math terms by Christer Kiselman.
Things to know and remember for the
final .
 Definitions and concepts: spaces, L^p, Sobolev, Banach,
Hilbert, etc;
norms,
L^p, L^infinity, Sobolev, etc, norms on Hilbert spaces; what is: a fundumental
solution; Green's function; bilinear form for a
second order differential operator; functional; linear
operator; adjoint of a differential operator; weak derivative;
convalution; Dirichlet problem and Neumann problem;
harmonic/subharmonic function; spherical mean and mean value
property; weak/strong maximum principle; Cauchy sequence and completeness; method of
images (refelction) for Green's function; Riesz representation theorem.
 Inequalities: CauchySchwarzBunyakovsky, triangle, Minkovsky,
Holder, Poincare, Sobolev, mean value property for subharmonic functions;
 Formulas: second Green's identity, domain and single layer
potential, fundamental solution for Laplacian, Poisson integral formula/Poisson kernel;
 Embeddings: which L^p spaces are contained in which, Sobolev
embedding theorems.
