Complex Analysis

Complex analysis is a study of functions of a complex variable. This is a one quarter course in complex analysis at the undergraduate level.

Articles

• Algebra II
• Dummy variable
• Materials Science and Engineering/Equations/Quantum Mechanics

Slides for Lectures

Chapter 1 - Intoduction

• Complex Numbers - (Wiki2Reveal slides)
  • Heine-Borel Theorem
• Riemann sphere - (Wiki2Reveal slides)
• Exponentiation and roots - (Wiki2Reveal slides)

Chapter 2 - Topological Foundations

• Sequences and series - (Wiki2Reveal slides)
• Power series
• Topological algebra - (Wiki2Reveal slides)
• Topological space - Definition: Topology
• Norms, metrics, topology - (Wiki2Reveal slides)

Chapter 3 - Complex Derivative

• Holomorphic function - (Wiki2Reveal slides)
• Partial Derivative - (Wiki2Reveal slides)
• Cauchy-Riemann Equations (CRE) - (Wiki2Reveal slides)
• Application of Cauchy-Riemann Equations - (Wiki2Reveal slides)

Chapter 4 - Curves and Line Integrals

• Line integral in $\mathbb {R} ^{n}$ - (Wiki2Reveal slides)

• Curves
  • Wikipedia: Holomorphic function
  • Wikipedia: Integral
• Line Integral

Lectures

• Cauchy-Riemann equations
• Cauchy Theorem for a triangle
• Complex analytic function
• Complex Numbers
• Divergent series
• Estimation lemma
• Fourier series
• Fourier transform
• Fourier transforms
• Laplace transform
• Riemann hypothesis
• The Real and Complex Number System
• Warping functions

Sample exams

Sample Midterm Exam 1 Sample Midterm Exam 2

See also

• Boundary Value Problems
• Introduction to Elasticity
• The Prime Sequence Problem
• Wikipedia: Complex analysis
• Complex number