Rosetta stone
Jump to:
Vladimir Tkachev's Homepage
Matematisa institutionen, UU
FMB
Schemasökning, UU
Back


Calendar
Textbooks:
[Evans] Lawrence C. Evans. Partial Differential Equations, AMS, Providence, RI.
Series: Graduate Studies in Mathematics, Vol. 19, 1998.
[McOwen] Robert C. McOwen, Partial Differential Equations, Methods and Applications,
Prentice Hall/Pearson Education, Inc., 2003 (Second Edition)
Dates/Topics
 20080901
 Introduction, course information
 Review of ordinary differential equations (existence, uniqueness and nonuniqueness)
 Example of derivation of PDE
 1st order PDE, I: characteristic curves for a linear equation
 Formulation of the Cauchy problem for a first order equation
 20080902
 1st order PDE, II: examples of quasilinear equations
 The inviscid Burger equation as a model for breaking surface waves
 Method characteristics for Burger's equation, shocks and entropy condition
 20080903
 1st order PDE, III: general nonlinear partial differential equations
 The method of characteristic strips and the method of envelopes
 The eikonal equation of geometric optics
 20080904 Exercise session: Problem set 1
 20080905 (McOwen 4954)
 Second order equations
 Linear equations of the second order: canonical forms
 The Laplace and Poisson equations; the wave equation; the heat equation
 20080908
 The wave equation, I: onedimensional case
 Initial value problem
 Weak solutions
 20080909
 The wave equation, II: higher dimensions
 Solution of the wave equation in three space variables using radial functions
 20080910
 The Laplace and Poisson equation, I: introduction
 20080917
 The Dirichlet and Neumann problems for the Laplace equation
 Fundamental solution to the Laplacian
 20080918
 The Laplace and Poisson equation, II
 Harmonic functions
 20080919 Exercise session: Problem set 2
 20080922, 10:15 12:00
 20080922, 15:15 17:00
 Functional spaces. Banach and Hilbert spaces.
 Hölder spaces
 20080923
 Weak derivative. Distributions.
 20080924 Exercise session: Problem set 3
 20080925,
 Sobolev spaces, I: introduction.
 20080930, 10:15  12:00
 Sobolev spaces, II: Sobolev inequalities and embeddings (subcritical case)
 20080930, 15:15  17:00,
 Sobolev spaces, III: Sobolev inequalities and embeddings (supercritical case)
 20081006, 13:15  15:00
 Elementary elliptic equations, weak problems
 20081006, 15:15  17:00
 General elliptic equations. LaxMilgram theorem
 20081007 Exercise session
 20081009
 Maximum principles for elliptic equations
 20081010
 The heat equation, II. Presentations
