Complex Variables with Applications

Calendar

Week #	Lec #	Topics	Key Dates
1	1	1.1 Complex Algebra. Complex Plane. Motivation and History
	2	1.2 Polar Form. Complex Exponential. DeMoivre’s Theorem
	3	1.3 Newton’s Method. Fractals
2-3	4	2.1 Complex Functions. Analyticity
	5	2.2 Cauchy-Riemann Eqns. Harmonic Functions
	6	2.3 Exponential and Trig. Functions. Logarithmic Function
	7	2.4 Branch Cuts. Applications
	8	2.5 Complex Powers and Inverse Trig. Functions
4-5	9	3.1 Contour Integrals
	10	3.2 Path Independence
	11	3.3 Cauchy’s Theorem
	12	3.4 Cauchy’s Integral Formula
	13	3.5 Liuville’s Theorem. Mean Value and Max. Modulus
	14	3.6 Dirichlet Problem
	15		EXAM #1: covering 1, 2 and about 1/2 of 3.
6	16	4.1 Taylor Series. Radius of Convergence
	17	4.2 Laurent Series
	18	4.3 Zeros. Singularities. Point at Infinity
7-8	19	5.1 Residue Theorem. Integrals over the Unit Circle
	20	5.2 Real Integrals. Conversion to Complex Contours
	21	5.3 Trig. Integrals. Jordan’s Lemma
	22	5.4 Indented Contours. Principal Value
	23	5.5 Integrals Involving Multi-valued Functions
	24	5.6 Argument Principle and Rouche’s Theorem
	25		EXAM #2: covering second half of 3, 4 and 5.
9-10	26	6.1 Complex Fourier Series
	27	6.2 Oscillating Systems. Periodic Functions
	28	6.3 Applications of Fourier Series
	29	6.4 Fourier Transform and Applications
	30	6.5 Laplace Transform and Inversion Formula
11-12	31	7.1 Invariance of Laplace’s Eqn. Conformality
	32	7.2 Inversion Mapping. Bilinear Mappings
	33	7.3 Examples and Applications
	34	7.4 More Examples (if time permits)
	35		EXAM #3: covering 6 and 7.