Youtor
Harmonic functions Harmonic conjugate Complex Analysis 3
>> YOUR LINK HERE: ___ http://youtube.com/watch?v=Vhm225csPsY
The definition of a Harmonic function, Harmonic conjugate function and how Analytic functions and Harmonic functions are related through some theorems. Examples for each concept are included. • LINK TO COMPLEX ANALYSIS PLAYLIST • • The Complete Guide to Complex Analysi... • LINK TO CANVAS • https://drive.google.com/file/d/0B0vT... • SUPPORT • Consider subscribing and liking if you enjoyed this video or if it helped you understand the subject. It really helps me a lot. • IMPORTANT LINKS • Recap about the Cauchy Riemann Equations: https://goo.gl/QVM8pG • Cauchy Riemann Equations in polar form and cartesian form: https://goo.gl/Qxp3SS • CONCEPTS FROM THE VIDEO • ► Harmonic Functions • Is a real-valued function u(x,y) with continuous second partial derivative which satisfies Laplace's equation. • ► Harmonic Conjugate Functions • The harmonic conjugate to a given function u(x,y) is a function v(x,y) such that f(x,y) = u(x,y) + iv(x,y) is differentiable. • ► Complex Differentiability • A function f(z) = u(x,y)+iv(x,y) is differentiable in a region R if and only if the following conditions are fulfilled in R: • 1) du/dx, dv/dy, du/dy, dv/dx are continous • 2) du/dx, dv/dy, du/dy, dv/dx satisfies the Cauchy Riemann Equations • The derivative is defined as f'(z) =du/dx + i*dv/dx=du/dy - i*dv/dy • ► Analytic Continuation • It provides a way of extending the domain over which a complex function is defined. Let f_1 and f_2 be analytic functions which are defined on the domains d_1 and d_2, if f_1 = f_2 is true in the intersection of the domains then f_2 is called an analytic continuation of f_1 to d_2 and vice versa. This analytic continuation is unique if it exists. • TIMESTAMPS • Definition: Harmonic functions: 00:00 - 00:23 • Theorem: Analytic function to Harmonic function: 00:23 - 00:48 • Theorem: Analytic function to Harmonic function: 00:48 - 01:13 • Definition: Harmonic functions: 01:13 - 01:35 • Example: 01:35 - 01:59 • SOCIAL • ► Follow me on Youtube: http://bit.ly/1NQhPJ9 • ► Follow me on Twitter: / the_mathcoach • HASHTAGS • #TheMathCoach #ComplexAnalysis
#############################
