Complex analysis
Undergraduate · Math
Syllabus focus
Theoretical / proof-based
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$1,162 · Complex analysis · 18 tutoring hrs
Study guides, worksheets, reviews, practice tests, and answer keys for 1 class. 18 tutoring hours (1 hr / week · semester). Bundle discount applied vs buying separately. Pay in full via Zelle or Venmo.
Topics typically covered
Theoretical / proof-based
Complex numbers and analytic functions
- Complex numbers, polar form, and Euler's formula
- Limits, continuity, and differentiability in the complex sense
- Cauchy–Riemann equations and harmonic functions
- Elementary analytic functions: exp, log, powers, and trig functions
- Branch cuts and multivalued functions
Integration and series
- Contour integrals and parametrization
- Cauchy's integral theorem and integral formula
- Liouville's theorem and the maximum modulus principle
- Taylor and Laurent series; classification of singularities
- Residue theorem and evaluation of real integrals
Conformal mapping and advanced topics
- Conformal maps and the Riemann mapping theorem (statement)
- Möbius transformations and the extended complex plane
- Argument principle and Rouché's theorem (introduction)
- Schwarz lemma and normal families (optional capstone)
Notes
Topics reflect common upper-division complex analysis syllabi for mathematics majors at US universities. A strong background in real analysis and multivariable calculus is expected.