📚 In this video, we solve a complex analysis problem step by step, covering:
✔ How to check if a given function u(x,y) is harmonic.
✔ Using the Cauchy-Riemann (CR) equations to find the harmonic conjugate v(x,y).
✔ Constructing the complex potential w(z) from u and v.
🔹 Problem Statement:
An electric potential near a conducting boundary is given by:
u(x,y) = x*y + x / (x² + y²)
We prove it's harmonic, find its conjugate, and derive the complex potential!
📖 Key Concepts Covered:
Laplace’s equation (Harmonic Functions)
Cauchy-Riemann conditions
Complex potential in electrostatics
💡 Useful for:
Math & Physics students
Engineering majors (EM theory, complex variables)
Exam prep & problem-solving practice
📌 Timestamps:
0:00 - Problem Introduction
00:43 - Checking if u(x,y) is Harmonic
05:43 - Finding Harmonic Conjugate v(x,y)
15:22 - Constructing Complex Potential w(z)
👍 If you found this helpful, like & subscribe for more problem-solving videos!
#ComplexAnalysis #MathProblems #EngineeringMath #CauchyRiemann #HarmonicFunctions
