Day 171: The Cauchy-Riemann Equations — Bridge to Harmonic Analysis

Learning Objectives

• •Derive the Cauchy-Riemann equations from the definition of complex differentiability
• •Apply Cauchy-Riemann to verify analyticity of complex functions
• •Convert Cauchy-Riemann to polar form
• •Prove that real and imaginary parts of analytic functions are harmonic
• •Understand the physical interpretation in terms of flows and potentials
• •Connect to the Schrödinger equation and quantum wave functions

Today's Schedule (7 hours)