Math 656     Spring 2008

Partial Differential Equations II

Instructor

Catalog Description

Math 655, Partial Differential Equations. (3-0) Cr. 3. Prereq: Math 515 or 519. First order equations and systems, conservation laws, general theory of linear partial differential eqautions of elliptic, parabolic and hyperbolic types, maximum principles, fundamental solutions, Sobolev spaces, variational and Hilbert space methods.

Math 656, Partial Differential Equations. (3-0) Cr. 3. Prereq: Math 655. Continuation of Math 655

Textbook

TEXTBOOK: Partial Differential Equations , by Lawrence C. Evans .

List of References

Classic Texts on The General Theory of PDE's

1. Methods of Mathematical Physics, Vol 2, by R. Courant and D. Hilbert, Wiley Interscience, 1962.


2. Partial Differential Equations, by P. Garabedian, Wiley, 1964.
3. A First Course in Partial Differential Equations, by H. Weinberger, Blaisdell, 1965.
4. Maximum Principles in Differential Equations, by M. Protter and H. Weinberger, Prentice-Hall, 1967.
5. Partial Differential Equations, by F. John, Springer-Verlag, 1971.
6. Basic Linear Partial Differential Equations, by F. Treves, Academic Press, 1975.
7. Introduction to Partial Differential Equations, by G. Folland, Princeton University Press, 1976.

Classic Texts on Particular Classes of PDE's

1. Partial Differential Equations of Parabolic Type, by A. Friedman, Prentice-Hall, 1964.
2. Linear and Quasilinear Equations of Parabolic Type, by O. Ladyzenskaja, V. Solonnikov, N. Uralceva, American Mathematical Society, 1968. (Translated from Russian Edition)
3. Elliptic Partial Differential Equations of Second Order, by D. Gilbarg and N. Trudinger, Springer-Verlag, 1983.
4. Shock Waves and Reaction-Diffusion Equations, by J. Smoller, Springer-Verlag, 1983.

Texts on Semigroups and Abstract DE's

1. Functional analysis and semi-groups, E. Hille and R.S. Phillips, Amer. Math. Soc. Colloq. Publ. Vol. 31, Providence, RI, 1957.
2. Geometric theory of semilinear parabolic equations, D. Henry, Lecture notes in Math. 840, Springer-Verlag, New York, NY, 1981.
3. Semigroups of linear Operators and Applications to Partial Differential Equations, A. Pazy, Springer-Verlag, New York, NY, 1983.
4. Semigroups of Linear Operators and Applications, G. Goldstein, Oxford Press.
5. Infinite-dimensional dynamical systems in Mathematics and Physics, R. Temam, Springer-Verlag, New York, NY, 1988.

More Recent Noteworthy Texts on The General Theory of PDE's

1. Parital Differential Equations, J. Rauch, Springer-Verlag, 1992.
2. A First Graduate Course in Partial Differential Equations, by M. Renardy and R. Rogers, Springer-Verlag, 1993.
3. Partial Differential Equations, by E. DiBenedetto, Birkhauser, 1995.

Advanced Calculus Books

1. Advanced Calculus of Several Variables, by C.H. Edwards, Academic Press, 1973.
2. Principles of Mathematical Analysis, 2d ed., by W. Rudin, McGraw-Hill, 1964.
3. Introduction to Analysis, by M. Rosenlicht, Scott-Roresman, 1968.

Grading Policy

Course grades will be determined from student performance on homework assignments. There will be four to six homework assignments.

Disability Resources

Iowa State University complies with the American with Disabilities Act and Section 504 of the Rehabilitation Act. If you have a disability and require accommodations, please contact the instructor early in the semester so that your learning needs may be appropriately met. You should contact the Disability Resources office for information on appropriate policies and procedures. The Disability Resources office is located on the main floor of the Student Services Building, Room 1076; their phone is 515-294-6624.

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