Math 382 - Complex Analysis
Additional Notes: Frank Jones' Notes, Notes 1, Notes 2, Notes 3.

Jan 11 Complex numbers, exp(z), and Euler's formula
Jan 13 properties of exp(z)
Jan 15 Roots of unity
Jan 18 Holiday
Jan 20 Mobius Transformation
Jan 22 Planner sets
Jan 25 Limit and Continuity
(Examples for real valued functions)
Jan 27 Derivatives, Cauchy-Riemann equations, Analytic functions, Entire functions
Jan 29 Harmonic functions, Singularities
Feb 01 Sequence and Series
Feb 03 Power series, radius of convergence
Feb 05 Uniform convergence, Weierstrass-M test, Taylor's Theorem
Feb 08 Line and contour integrals
Feb 10 Review for Midterm I
Feb 12 Green's Thorem, Cauchy's Theorem
Feb 15 Fundamental Theorem of Calculus
Feb 17 Cauchy's Integral Formula
Feb 19 General Cauchy's Integral Formula, Taylor's Theorem
Feb 22 Singularities and Laurent Series.
(Examples of Laurent Series)
Feb 24 Residues
Feb 26 Residues and Examples
Feb 29-Mar 4 Spring Breaks
Mar 7 Meromorphic function and Residue theorem
Mar 9 Applications to Residue theorem and Cauchy principle value
Mar 11 Applications to Residue theorem and Impropre integral
Feb 14 Applications to Residue theorem and Partial fraction expansions
Feb 16 Applications to Residue theorem, Partial fraction expansions, and Trigonometric integrals
Mar 18 More applications
Mar 21 More applications and Jordan's lemma
Mar 23 Applications to Residue therem, Maximum modulus principle
Feb 25 Maximum modulus principle, Liouville's theorem
Mar 28 Review and Midterm II
(Practice Problems)