Complex Variables with Applications

Lecture Notes

LEC #	TOPICS
1	Course Introduction (PDF) Topic 1: Complex Algebra and the Complex Plane (PDF) [Topic 1.1–1.6.2]
2	Topic 1: Complex Algebra and the Complex Plane (PDF) [Topic 1.6.3–1.14.2]
3–4	Topic 2: Analytic Functions (PDF) [Topic 2.1–2.5]
5–6	Topic 2: Analytic Functions (PDF) [Topic 2.6–2.9]
7	Review of 18.02 Multivariable Calculus (PDF)
8–9	Topic 3: Cauchy’s Theorem (PDF)
10–12	Topic 4: Cauchy Integral Formula (PDF)
13	Topic 5: Harmonic Functions (PDF) [Topic 5.1–5.4]
14	Review for Exam 1
15	Topic 5: Harmonic Functions (PDF) [Topic 5.5–5.6] Topic 6: Two-Dimensional Hydrodynamics and Complex Potentials (PDF) [Topic 6.1–6.4]
16	Topic 6: Two-Dimensional Hydrodynamics and Complex Potentials (PDF) [Topic 6.5–6.7]
17–19	Topic 7: Taylor and Laurent Series (PDF)
20–22	Topic 8: Residue Theorem (PDF)
23–25	Topic 9: Definite Integrals Using the Residue Theorem (PDF)
26	Topic 10: Conformal Transformations (PDF) [Topic 10.1–10.4]
27	Review for Exam 2
28	Topic 10: Conformal Transformations (PDF) [Topic 10.5–10.8]
29	Topic 10: Conformal Transformations (PDF) [Topic 10.8–10.11]
30–33	Topic 11: Argument Principle (PDF)
34–36	Topic 12: Laplace Transform (PDF)
37	Topic 13: Analytic Continuation and the Gamma Function (PDF)