LEC #	TOPICS	KEY DATES
I. Complex Algebra and Functions
1	Algebra of Complex Numbers Complex Plane Polar Form
2	cis(y) = exp(iy) Powers Geometric Series
3	Functions of Complex Variable Analyticity
4	Cauchy-Riemann Conditions Harmonic Functions
5	Simple Mappings: az+b, z2, √z Idea of Conformality
6	Complex Exponential
7	Complex Trigonometric and Hyperbolic Functions
8	Complex Logarithm	Problem set 1 due
9	Complex Powers Inverse Trig. Functions
10	Broad Review ... Probably focusing on sin-1z
II. Complex Integration
11	Contour Integrals
12	Path Independence
		Exam 1
13	Cauchy's Integral Theorem
14	Cauchy's Integral Formula Higher Derivatives
15	Bounds Liouville's Theorem Maximum Modulus Principle
16	Mean-value Theorems Fundamental Theorem of Algebra
17	Radius of Convergence of Taylor Series	Problem set 2 due
III. Residue Calculus
18	Laurent Series
19	Poles Essential Singularities Point at Infinity
20	Residue Theorem Integrals around Unit Circle
21	Real Integrals From -∞ to +∞ Conversion to cx Contours
22	Ditto ... including Trig. Functions Jordan's Lemma
		Exam 2
23	Singularity on Path of Integration Principal Values
24	Integrals involving Multivalued Functions
IV. Conformal Mapping
25	Invariance of Laplace's Equation
26	Conformality again Inversion Mappings
27	Bilinear/Mobius Transformations	Problem set 3 due
28	Applications I
29	Applications II
V. Fourier Series and Transforms
30	Complex Fourier Series
31	Oscillating Systems Periodic Functions
32	Questions of Convergence Scanning Function Gibbs Phenomenon
33	Toward Fourier Transforms
34	Applications of FTs
		Exam 3
35	Special Topic: The Magic of FFTs I
36	Special Topic: The Magic of FFTs II
	Final Exam