Methods of Applied Mathematics I.
MATH 383C (Unique #55275), CAM 385C (Unique #61120); Fall 2001

Office Hours:

By appointment

Meeting:

TTh 11:00-12:30, RLM 10.176,

Course Description:

This is the first semester of a course on methods of applied mathematics. It is open to mathematics, science, engineering, and finance students. It is suitable to prepare graduate students for the Applied Mathematics Preliminary Exam in mathematics and the Area A Preliminary Exam in CAM.

Bibliography:

  • Lecturer-prepared notes by Todd Arbogast and Jerry Bona.
    1. R. A. Adams, Sobolev Spaces, Academic Press, 1975.
    2. J.-P. Aubin, Applied Functional Analysis, Wiley, 1979.
    3. C. Caratheodory, Calculus of Variations and Partial Differential Equations of the First Order, 1982.
    4. L. Debnath and P. Mikusinski, Introduction to Hilbert Spaces with Applications, Academic Press, 1990.
    5. G.B. Folland, Introduction to Partial Differential Equations, Princeton, 1976.
    6. I.M. Gelfand and S.V. Fomin, Calculus of Variations, Prentice-Hall, 1963.
    7. J. Jost and X. Li-Jost, Calculus of Variations, Cambridge, 1998,
    8. E. Kreyszig, Introductory Functional Analysis with Applications, Wiley, 1978.
    9. E.H. Lieb and M. Loss, Analysis, AMS, 1997.
    10. J.T. Oden & L.F. Demkowicz, Applied Functional Analysis, CRC Press, 1996.
    11. F.W.J. Olver, Asymptotics and Special Functions, Academic Press, 1974.
    12. M. Reed & B. Simon, Methods of Modern Physics, Vol. 1, Functional analysis.
    13. W. Rudin, Functional Analysis, McGraw Hill, 1991.
    14. W. Rudin, Real and Complex Analysis, 3rd Ed., McGraw Hill, 1987.
    15. H. Sagan, Introduction to the Calculus of Variations, Dover, 1969.
    16. R.E. Showalter, Hilbert Space Methods for Partial Differential Equations.
    17. E. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton, 1971.
    18. K. Yosida, Functional Analysis, Springer-Verlag, 1980.
    19. See also: E.W. Cheney and H.A. Koch, Notes on Applied Mathematics, Department of Mathematics, University of Texas at Austin.

    Homework, Exams, and Grades:

    Homework will be assigned regularly. Students are encouraged to work in groups; however, each student must write up his or her own work. One mid-term exam will be given. The final exam will be given during finals week The final grade will be based on the homework and the two exams.

    Semester I.

    1. Preliminaries
    2. Banach Spaces
    3. Hilbert Spaces
    4. Distributions