Math 185A Classroom Lecture Notes

  • 0-Introduction to Complex Variables

  • I-The Complex Fundamental Theorem of Calculus

  • II-Proof of Cauchy Riemann Theorem

  • III-The Complex Exponential and Logarithm

  • IV-Complex Exponents

  • V-Topology of the Complex Plane and the Theory of Line Integrals

  • VI-The Cauchy-Goursat Theorem

  • VII-Applications of the Cauchy Integral Formula

  • VIII-Residue Theorem

  • IX-Calculating Residues

  • X-Integration around a branch cut