Courses:

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Differential Equations (18.03 or 18.034). Complex Variables with Applications (18.04) or Functions of a Complex Variable (18.112) are useful, as well as previous acquaintance with the equations as they arise in scientific applications.

Either one of the following textbooks will do.

Guenther, R. B., and J. W. Lee. Partial Differential Equations of Mathematical Physics and Integral Equations. New York, NY: Dover Publications, 1996. ISBN: 0486688895.

Myint-U, Tyn, and Lokenath Debnath. Linear Partial Differential Equations for Scientists and Engineers. 4th ed. Boston, MA: Birkhauser, 2006. ISBN: 0817643931.

There will be 6 problem sets given throughout the term. There will be two in-class tests and a final exam.

I. The Heat Equation in One Space Variable

• Separation of Variables, Fourier Series, Sturm-Liouville Eigenvalue Problems

II. The Wave Equation in One Space Variable

• Method of Characteristics

III. Method of Characteristics Solution to Quasilinear PDEs

IV. The Heat and Wave Equations with Two or Three Space Variables

• Bessel Functions, Laplace's Equation

V. The Heat Equation and Laplace's Equation on Unbounded Spacial Domains

• Fourier Transform

VI. Green's Function Method for Solving ODEs, PDEs