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1MA053 Partiella differentialekvationer, intorduktionskurs (5.0 hp)
Contents:
Firstorder equations (the methof of characteristics,
Cauchy problem for quasilinear and fully nonlinear equations,
weak solutions).
General techniques and principles for secondorder equations
The wave equation (d'Alembert's formula, weak solutions, reflections, Duhamel's principle,
twodimensional and threedimensional wave equation, conservation of energy).
The Laplace equation (Mean Value Theorem and Maximum Principle,
the fundamental solution, Green's function, Poisson kernel).
The heat equation (Weak maximum principle, properties of the heat kernel,
properties of the solution to the pure initial value problem).
Textbooks:
Robert C. McOwen, Partial Differential Equations, Methods and Applications,
Prentice Hall/Pearson Education, Inc., 2003 (Second Edition)
* Lawrence C. Evans. Partial Differential Equations, AMS, Providence, RI.
Series: Graduate Studies in Mathematics, Vol. 19, 1998.
Instruction:
Lectures and problem solving sessions.
Examination:
Written examination at the end of the course.
