Math Method course - aa 2011-2012

Program of the course and notes

• Linear first order Partial Differential Equations
  • Notes

• Quasi linear first order Partial Differential Equations
  • Notes
  • For a more detailed presentation also refer to:
    Chapter 3 in http://www.stanford.edu/class/math220a/lecturenotes.html
    3.1 Motivation
    3.2 Weak solutions

• Wave equation in R: Chapter 5 in http://www.stanford.edu/class/math220a/lecturenotes.html
  • 5.2: general solution for Wave Equation in R
  • 5.3: Initial value problem (d'Alambert's formula
  • 5.4: Energy methods
    5.4.1: Domain of dependence
    5.4.1: Energy and Domain of dependence
  • 5.5: Wave with a Source

• Wave Equation in Higher Dimensions: Chapter 7 in http://www.stanford.edu/class/math220a/lecturenotes.html

• Heat equation:
  • Derivation and the most common boundary conditions Chapter 2.1 in http://www.stanford.edu/class/math220b/lecturenotes.html
  • the Fundamental solution The presentatino made in class does not involve the Fourier transform
  • Inhomogeneous Heat Equation Chapter 2.7 in http://www.stanford.edu/class/math220b/lecturenotes.html
  • Maximum Principle and Uniqueness of Solutions Chapter 2.8 in http://www.stanford.edu/class/math220b/lecturenotes.html

Other Suggested texts

Suggested exercices

• exercices on first order PDE
• solved exercices on first order PDE:
  C. Constanda: Solution techniques for elementary PDE - chapter 12
  available at the library of Dept of Mathematics, Piazza di Porta S. Donato 5
• notion of weak solution
• classification of second order PDE
• Minima of functionals

Results of written test

• Written test of 4/2/2011
• Written test of 1/7/2011
• Results of oral: please check prof. Ferri web page