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- Gerald B. Folland,
*Introduction to partial differential equations*. Princeton 1995. - Jeffrey Rauch,
*Partial differential equations*. Springer 1991.

- Previous incarnations: 2012, 2013, 2014, 2019
- Lecture notes by Bruce Driver (UCSD)
- Teaching page of John Hunter (UC Davis)

- Cauchy-Kovalevskaya theorem
- Distributions, Fourier transform
- Constant coefficient linear systems
- Ellipticity, parabolicity, hyperbolicity
- Spectral theory
- Nonlinear evolution equations (if time permits)

**Instructor:** Dr. Gantumur Tsogtgerel

**Prerequisite:** MATH 580 (PDE1), MATH 355 (Honours Analysis 4) or equivalent

**Note:** If you plan to take this course without taking MATH 580, please consult with the
instructor.

**Calendar description:**
Systems of conservation laws and Riemann invariants.
Cauchy-Kowalevskaya theorem, powers series solutions.
Distributions and transforms.
Weak solutions; introduction to Sobolev spaces with applications.
Elliptic equations, Fredholm theory and spectra of elliptic operators.
Second order parabolic and hyperbolic equations.
Further advanced topics may be included.

**Grading:** Homework assignments 50% + Course project 50%.

**Homework:** Assigned and graded roughly every other week, through MyCourses.

**Course project:** The course project consists of the student reading a paper or monograph on an
advanced topic, typing up notes, and giving a lecture.