MIT OpenCourseWare | Mathematics | 18.04 Complex Variables with Applications, Fall 1999

WEEK	LEC #	TOPIC	READINGS	IMPORTANT DATES
1	1	1.1 Complex Algebra. Complex Plane. Motivation and History	READ sections 1.1 & 1.2
	2	1.2 Polar Form. Complex Exponential. DeMoivre's Theorem	READ sections 1.3 - 1.5.
	3	1.3 Newton's Method. Fractals	READ handout
2 & 3	4	2.1 Complex Functions. Analyticity	READ sections 2.1 - 2.3.
	5	2.2 Cauchy-Riemann Eqns. Harmonic Functions	READ sections 2.4 - 2.6.
	6	2.3 Exponential and Trig. Functions. Logarithmic Function	READ sections 3.1 & 3.2.
	7	2.4 Branch Cuts. Applications	READ handout.
	8	2.5 Complex Powers and Inverse Trig. Functions.	READ section 3.3.
4 & 5	9	3.1 Contour Integrals.	READ sections 4.1 & 4.2.
	10	3.2 Path Independence	READ sections 4.3 & 4.4a.
	11	3.3 Cauchy's Theorem	READ section 4.4b.
	12	3.4 Cauchy's Integral Formula	READ section 4.5.
	13	3.5 Liuville's Theorem. Mean Value and Max. Modulus	READ section 4.6
	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	READ sections 5.1, 5.2 and handout.
	17	4.2 Laurent Series	READ section 5.5.
	18	4.3 Zeros. Singularities. Point at Infinity	READ sections 5.6 & 5.7.
7 & 8	19	5.1 Residue Theorem. Integrals over the Unit Circle	READ sections 6.1, 6.2 and handout.
	20	5.2 Real Integrals. Conversion to Complex Contours	READ section 6.3.
	21	5.3 Trig. Integrals. Jordan's Lemma	READ section 6.4.
	22	5.4 Indented Contours. Principal Value	READ section 6.5 and handout.
	23	5.5 Integrals Involving Multi-valued Functions	READ section 6.6 and handout.
	24	5.6 Argument Principle and Rouche's Theorem	READ section 6.7 and handout
	25			EXAM #2 \| covering second half of 3, 4 and 5.
9 & 10	26	6.1 Complex Fourier Series	READ section 8.1 - up to page 374.
	27	6.2 Oscillating Systems. Periodic Functions	READ section 3.4.
	28	6.3 Applications of Fourier Series	READ handout.
	29	6.4 Fourier Transform and Applications	READ section 8.2.
	30	6.5 Laplace Transform and Inversion Formula	READ section 8.3.
11 & 12	31	7.1 Invariance of Laplace's Eqn. Conformality.	READ sections 7.1, 7.2 and handout.
	32	7.2 Inversion Mapping. Bilinear Mappings.	READ section 7.3 and handout.
	33	7.3 Examples and Applications	READ section 7.6
	34	7.4 More Examples (if time permits).	READ section 7.7 and handout.
	35			EXAM #3 covering 6 and 7.