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Complex Variables with Applications >> Content Detail



Calendar / Schedule



Calendar

Week #Lec #TopicsKey Dates
111.1 Complex Algebra. Complex Plane. Motivation and History
21.2 Polar Form. Complex Exponential. DeMoivre's Theorem
31.3 Newton's Method. Fractals
2-342.1 Complex Functions. Analyticity
52.2 Cauchy-Riemann Eqns. Harmonic Functions
62.3 Exponential and Trig. Functions. Logarithmic Function
72.4 Branch Cuts. Applications
82.5 Complex Powers and Inverse Trig. Functions
4-593.1 Contour Integrals
103.2 Path Independence
113.3 Cauchy's Theorem
123.4 Cauchy's Integral Formula
133.5 Liuville's Theorem. Mean Value and Max. Modulus
143.6 Dirichlet Problem
15EXAM #1: covering 1, 2 and about 1/2 of 3.
6164.1 Taylor Series. Radius of Convergence
174.2 Laurent Series
184.3 Zeros. Singularities. Point at Infinity
7-8195.1 Residue Theorem. Integrals over the Unit Circle
205.2 Real Integrals. Conversion to Complex Contours
215.3 Trig. Integrals. Jordan's Lemma
225.4 Indented Contours. Principal Value
235.5 Integrals Involving Multi-valued Functions
245.6 Argument Principle and Rouche's Theorem
25EXAM #2: covering second half of 3, 4 and 5.
9-10266.1 Complex Fourier Series
276.2 Oscillating Systems. Periodic Functions
286.3 Applications of Fourier Series
296.4 Fourier Transform and Applications
306.5 Laplace Transform and Inversion Formula
11-12317.1 Invariance of Laplace's Eqn. Conformality
327.2 Inversion Mapping. Bilinear Mappings
337.3 Examples and Applications
347.4 More Examples (if time permits)
35EXAM #3: covering 6 and 7.

 








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