OF PARTIAL DIFFERENTIAL EQUATIONS"
|Please, consult the Undergraduate
Module Catalogue to have a description of the course Math 3414.
This lecture aims to give a general feel of analytical solutions of
So, why should we study PDEs and, in particular, analytic methods of
PDEs? We study PDEs because most of mathematical physics is described
in terms of PDEs (fluid mechanics, and more generally continuous media
mechanics, electromagnetism, quantum
mechanics, etc.). It is the case that typically, a given PDE will only
be accessible to numerical solution. However, it is crucial that
we know the general theory in order to conduct a sensible numerical
approach. For example, certain types of equations need certain types
of boundary conditions; without a knowledge of the general theory it is
possible that a problem may be ill-posed or that the method of
solution is erroneous.
If you need more
information on the course, please contact Evy Kersalé.
|I shall try to put
my lecture notes on-line; hopefully I shall manage to converge
toward a sensible document. The following chapters should be included:
Outlines & Course Summary
Please, feel free to report any
errors, typos or frenglish grammatical structures!
2-First Order PDEs
2.1-Linear & Semilinear
2.4-System of Linear
3-Second Order Linear and Semilinear PDEs in Two
3.1-Classification and Standard
3.2-Extensions of the Theory
Laplace's and Poison's Equations
Equation Using Green's Functions
of the Theory
Solution of the Heat Equation
Principles and Comparison Theorems
Many thanks to Dr. R. Sturman, Prof. D. W. Hughes
& Prof. J. H. Merkin for providing me with their lecture notes; it