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Columbian College of Arts and Sciences
Mathematics (MATH)
MATH
3343
Partial Differential Equations
Partial Differential Equations
Fall 2017
3
Course Type
Lecture

No
No
MATH 3342
Corequisites

30

Frequency of Offering

Term(s) Offered

Are there Course Equivalents?
No

No
Fee Type

No

A first course in partial differential equations. Fourier series and separation of variables, vibrations of a string, Sturm–Liouville problems, series solutions, Bessel’s equation, linear partial differential equations, wave and heat equations.
The student will have studied the significant categories of linear partial differ- ential equations through their prototypical examples: (i) parabolic (heat equa- tion); (ii) hyperbolic (wave equation); (3) elliptic (Laplace’s equation). The student will have learned solution strategies on bounded domains such as in- tervals, rectangles, and disks, and unbounded domains, such as the real line and half-plane. For bounded domains, the student will have learned how to use separation of variables to construct special solutions satisfying the differential equation and boundary conditions, and will understand how to employ the prin- ciple of superposition to construct infinite series solutions. The special solutions depend on the geometry of the domain. Fourier series, and more generally the orthogonal solutions of Sturm-Liouville problems, play an important role. For unbounded domains, the student will have learned the Fourier transform and its properties, and how it can be used to solve the heat equation in the infinite rod and Laplace’s equation on the half-plane. The student will also have studied Bessel functions, the Poisson integral representation, and other useful topics as time permits.