Modules  Area  Type  Hours  Teacher(s)  
MODELLI MATEMATICI IN BIOMEDICINA  MAT/05  LEZIONI  42 

Partial differential equations of mathematical physics and biomedicine, with the emphasis on model derivation from the underlying physical principles, distributional formulation, fundamental solutions in free space, Fourier techniques, separation of variables and special functions. Several examples of nonlinear equations and phenomena associated with nonlinearities will also be discussed.
week 1: PDEs of mathematical physics, conservation laws, equation types, model
derivations
week 2: First order equations and the method of characteristics, classification of
second order quasilinear PDEs
week 3: Distributions in R^N, convolutions, tempered distributions. Fourier transform
week 4: Fundamental solutions for linear differential operators
week 5: Distributional Cauchy problem for the wave equation, wave propagation,
Helmholtz operator
week 6: Distributional Cauchy problem for the heat equation, Newtonian potential
week 7: Elliptic boundary value problems, eigenvalue problems
week 8: SturmLiouville problem, Bessel functions, spherical functions
week 9: Initialboundary value problems
week 1011: Nonlinear equations and nonlinear phenomena: existence, regularity,
special solutions, blowup
There is no required textbook for this class. The following texts can be used as references:
 Equations of Mathematical Physics, by V. S. Vladimirov, 1985, ISBN 9780828528771
(available in Italian)
 Partial Differential Equations, by J. Kevorkian, 2010, ISBN 9781441931399
 Partial Differential Equations: An Introduction, by W. A. Strauss, 2008,
ISBN 9780470054567
final oral presentation