Math 218: Partial Differential Equations
Winter 2001


John Hunter
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

Texts for Math 218

The recommended text for Math 218 is:

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.

Homework Assignments

Latex and postscript files for the problem sets can be found here.

Set 1:
latex file
postscript file

Set 2:
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postscript file

Set 3:
latex file
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Set 4:
latex file
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Set 5:
latex file
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Set 6:
latex file
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