## Past Courses

- 2018
- Winter:
**Real Analysis**(Math 105A - UCSC). - Winter:
**Analysis II**(graduate) (Math 205 - UCSC).

- Winter:
- 2017
- Fall:
**Calculus with Apps**(Math 11A - UCSC).

Topics: the first quarter of the calculus sequence. - Spring:
**Complex Analysis**(graduate) (Math 207A - UCSC)

- Winter:
**Real Analysis**(Math 105A - UCSC).

Topics: Chapters 1 through 6 of Strichartz' "The way of Analysis". - Winter:
**Partial Differential Equations I**(graduate) (Math 213A - UCSC).

Topics: Laplace, heat and wave equations, studied using various techniques: classical solutions, potential theory, distributions and Fourier analysis, stationary phase, weak formulations, L2 Sobolev spaces and other Hilbert space methods.

- Fall:
- 2016
- Winter:
**Introductory Differential Equations**(Math 216, two sections, U. Michigan) - (Course website). Additional material specific to the sections I taught available here.

- Winter:
- 2015
- Winter:
**Complex Analysis II**(Math 428 A, U. Washington) - Course website.

Draft of lecture notes here. (topics similar to Winter '14) - Winter:
**Introductory Real Analysis I**(Math 327 B, U. Washington) - Course website.

(topics similar to Autumn '13)

- Winter:
- 2014
- Summer:
**Introductory Real Analysis II**(Math 328 B, U. Washington) - Course website

Topics: power series, continuity, uniform continuity, theory of integration, improper integrals, the Gamma function, Stirling's formula. Emphasis on proofs. - Summer:
**Seminar in Analysis**(Math 530 C, U. Washington)

Preparatory problem-solving sessions for graduate students toward taking the "Linear Analysis" Preliminary Exam. Topics: distributions, linear algebra, spectral theory, Fourier analysis, numerical methods for ODEs. - Summer:
**Special Lecture on math and origami**, taught at SIMUW 2014 and at the 2014 discovery seminar on "Left brain, right brain: creative thinking in the sciences and in the arts.". Slides (Warning: 47MB file). - Winter:
**Complex Analysis II**(Math 428 A, U. Washington) - Course website

Topics: Some applications of residues, Rouché's theorem, conformal mappings, linear fractional transformations, Riemann mapping theorem, complex dynamics of rational maps.

- Summer:
- 2013
- Autumn:
**Introductory Real Analysis I**(Math 327 A, U. Washington) - Course website

Topics: sequences of real numbers, limits, point set theory, uniform continuity. - Autumn:
**Complex Analysis I**(Math 427 A, U. Washington) - Course website

Topics: making our way from the algebra of complex numbers to residue theory, omitting no proof. - Summer:
**Computer Labs at MSRI Summer School on "The mathematics of seismic imaging"**. - Summer:
**Computer Labs at UW RTG IPDE Summer School**- Detail of sessions

Topics: Implementation and inversion of the thermoacoustic tomography problem. Illustration of the principle of propagation of singularities for the wave equation. Generalized X-ray transforms.

- Autumn:
- 2012
- Autumn:
**Linear Analysis**(Math 309 B&C, U. Washington) - Course website

Topics: systems of ODE's, solutions to PDE's using Fourier series and separation of variables. Emphasis on problem-solving.

- Autumn:
- 2011
- Summer '11:
**Computer Labs at UW RTG IPDE Summer School**- Detail of sessions

Topics: The fast fourier transform. Implementation of the Radon tranform and attenuated Radon transform, and their inversion. Partial data problems. Generalization to other families of integration curves.

- Summer '11: