Winter 2001

e-mail:

Phone: (530) 752-3189

Office: 654 Kerr Hall

Office hours: M F 1:00–2:00 p.m., W 3:00–4:00 p.m.

Lectures: MWF 2:10–3:00 p.m., Wellman 208

L. C. Evans, * Partial Differential Equations *, Graduate Studies in
Mathematics, Volume 19, AMS.

Some other references are the following.

An introduction to elliptic and parabolic PDEs is in:

N. V. Krylov, * Lectures on Elliptic and Parabolic Partial Differential Equations in
Holder Spaces *, Graduate Studies in Mathematics 12, AMS Providence RI, 1996.

A standard reference on elliptic PDEs is:

D. Gilbarg, and N. S. Trudinger, * Elliptic Partial Differential Equations of Second
Order *, Springer-Verlag, New York, 1983.

For a readable account of maximum principles, see:

M. H. Protter, and H. F. Weinberger, * Maximum Principles in Differential Equations
*, Prentice-Hall, Englewood Cliffs, 1967.

Spherical means are discussed in:

F. John, * Plane Waves and Spherical Means Applied to Partial Differential Equations
*, Springer-Verlag, New York, 1981.

For the Tychonoff solution of the heat equation, and Lewy's example of a PDE without solutions, see:

F. John, * Partial Differential Equations
*, 4th ed., Springer-Verlag, New York, 1982.

The Cauchy-Kowalewski theorem is proved in:

P. Garabedian, * Partial Differential Equations *, John Wiley & Sons, New York,
1964.

Characteristic surfaces of hyperbolic PDEs are described in:

R. Courant, and D. Hilbert, * Methods of Mathematical Physics *, Vol. 2,
Interscience, New York, 1961.

For a thorough account of distribution theory and the Fourier transform, see:

L. Hormander, * The Analysis of Linear Partial Differential Operators *,
Vol. 1, Springer-Verlag, Berlin, 1983.

For the solution of linear initial value problems by the Fourier transform, and the Hadamard-Petrowsky dichotomy, see:

J. Rauch, * Partial Differential Equations *, Springer-Verlag, New York, 1991.

For an introduction to the physical aspects of Burger's equations, see:

G. Whitham, * Linear and Nonlinear Waves *, Wiley-Interscience, New York,
1973.

An account of the mathematical theory of conservation laws is in

J. Smoller, * Shock Waves and Reaction-Diffusion Equations *,
Springer-Verlag, New York, 1983.

For the numerical solution of conservation laws, see

R. J. LeVeque, * Numerical Methods for Conservation Laws *,
Birkhauser, Basel, 1992.

Set 1:

latex file

postscript file

Set 2:

latex file

postscript file

Set 3:

latex file

postscript file

Set 4:

latex file

postscript file

Set 5:

latex file

postscript file

Set 6:

latex file

postscript file