Instructor: Andrew Hanlon

Course on canvas.dartmouth.edu.⇗

Syllabus

Date Topic References
M 3/25 Why complex analysis? Complex algebra §1.1, Notes Download Notes
W 3/27 Visualizing the complex plane §1.2, 1.3, Notes Download Notes
F 3/29 Complex exponential and powers §1.4, 1.5, Notes Download Notes, a fun article Links to an external site.
M 4/1 Domains §1.6, Notes Download Notes
W 4/3 Functions and continuity §2.1, 2.2, Notes Download Notes
F 4/5 Complex derivative, CR equations §2.3, 2.4, Notes Download Notes
M 4/8 Harmonic functions, Julia and Mandelbrot sets §2.5, 2.7, Notes Download Notes, a fun article Links to an external site. and pictures Links to an external site.
W 4/10 Complex polynomials §3.1, Notes Download Notes
F 4/12 Rational functions §3.1, 1.7, Notes Download Notes
M 4/15 Trig functions and complex logarithm §3.2-3.5, Notes Download Notes
W 4/17 More on log §3.3-3.5, Notes Download Notes
F 4/19 Contour integrals and path-independence §4.1-4.3, Notes Download Notes
M 4/22 Cauchy's integral formula §4.4b, 4.5, Notes Download Notes
W 4/24 Continuity of f'(z) and infinite differentiability §4.5, Notes Download Notes
F 4/26 Liouville's theorem and maximum principle §4.6, 4.7, Notes Download Notes
M 4/29 Power series §5.1-5.4, Notes Download Notes
W 5/1 More on power series §5.1-5.4, Notes Download Notes
F 5/3 Zeroes and Laurent series §5.5, 5.6, Notes Download Notes
M 5/6 Laurent series expansion on annulus §5.5, Notes Download Notes
W 5/8 Singularity types, meromorphic functions §5.6, Notes Download Notes
F 5/10 Infinity, analytic continuation §5.7, 5.8, Notes Download Notes
M 5/13 Fourier series §8.1, Notes Download Notes and a fun article Links to an external site.
W 5/15 Residue theorem and applications §6.1-6.4, Notes Download Notes
F 5/17 Keyhole integration §6.5, 6.6
M 5/20 Rouche's theorem and open mapping principle §6.7
W 5/22 Conformal maps and Mobius transformations §7.1-7.4
F 5/24 Riemann surfaces
W 5/29 Review