Harmonic Function Courses and Certifications

Schmid College, Chapman University

Shift Operators on Harmonic Hilbert Function Spaces on Real Unit Ball

Explore shift operators on harmonic function spaces, their properties, and applications in reproducing kernel Hilbert spaces. Discover new identities and inequalities in harmonic analysis.

• YouTube
• 50 minutes
• On-Demand
• Free Video

Musicianship: Tensions, Harmonic Function, and Modal Interchange

403 ratings at Coursera

Explore advanced musicianship concepts including harmonic function, modal interchange, and chord tensions. Develop ear training skills and learn to compose using popular chord progressions.

• Coursera
• 9 hours 25 minutes
• On-Demand
• Paid Course

Hausdorff Center for Mathematics

Boundary Unique Continuation and the Estimate of the Singular Set

Explore boundary unique continuation for harmonic functions and its application in estimating singular sets of elliptic PDEs. Gain insights into local growth rates and their global implications in mathematical analysis.

• YouTube
• 49 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Bounds on the Hausdorff Measure of Zero Sets of Steklov Eigenfunctions

Explore upper bounds on Hausdorff measure of Steklov eigenfunction zero sets, comparing with Laplace eigenfunctions and discussing recent breakthroughs in this mathematical domain.

• YouTube
• 31 minutes
• On-Demand
• Free Video

Gautam Varde

Harmonic Function Problems - Numerical and Analytic Functions in Complex Variables

Explore harmonic functions in complex variables through numerical problems and analytical approaches, essential for engineering mathematics and competitive exams.

• YouTube
• 11 minutes
• On-Demand
• Free Video

One Man And His Songs

Harmonic Function and Cadence in Music Theory

Explore fundamental concepts of harmonic function and cadence in music theory, understanding how chords work together to create musical resolution and progression.

• YouTube
• 17 minutes
• On-Demand
• Free Video

Approaching Music Theory: Melodic Forms and Simple Harmony

170 ratings at Coursera

Explore melodic structures, harmony, and music theory through diverse styles. Develop a theoretical vocabulary to enhance appreciation and analysis of musical compositions.

• Coursera
• 22 hours 20 minutes
• On-Demand
• Paid Course

Michael Penn

A Series Involving Harmonic Numbers - Featuring the Dilogarithm Function

Explore generating functions to calculate sums of series with harmonic numbers, featuring the dilogarithm function in advanced mathematical analysis.

• YouTube
• 21 minutes
• On-Demand
• Free Video

Fields Institute

Shift Operators on Harmonic Hilbert Function Spaces - Von Neumann Inequality - Harmonic Polynomials

Exploring shift operators, von Neumann inequality, and harmonic polynomials in function spaces, with focus on spherical harmonics and their applications in analysis.

• YouTube
• 34 minutes
• On-Demand
• Free Video

Let's Code Physics

Wave Function Evolver for 2D Harmonic Oscillator - Episode 7

Explore a working wave function evolver for a Gaussian wave in a 2-D harmonic oscillator potential, with debugging and tweaks demonstrated in VPython.

• YouTube
• 18 minutes
• On-Demand
• Free Video

Gautam Varde

Analytic Function Construction in Complex Variables - Harmonic Conjugate

Discover how to construct analytic functions in complex variables using harmonic conjugates, essential for engineering mathematics and competitive exams.

• YouTube
• 19 minutes
• On-Demand
• Free Video

GDC

Math for Game Programmers - Harmonic Functions and Mean-Value

Explore harmonic functions and mean-value parameterizations for procedural geometry in game development, with applications in mesh manipulation and UV generation.

• YouTube
• 30 minutes
• On-Demand
• Conference Talk

Steve Brunton

Complex Analysis - Analytic Functions Solve Laplace's Equation

Explore how analytic complex functions' real and imaginary parts solve Laplace's equation, introducing harmonic functions in this in-depth mathematical analysis.

• YouTube
• 41 minutes
• On-Demand
• Free Video

Fields Institute

Connections Between Geometry and Partial Differential Equations

Explore the fascinating interplay between geometric structures and partial differential equations, uncovering deep mathematical insights and applications.

• YouTube
• 43 minutes
• On-Demand
• Free Video

NPTEL-NOC IITM

The Laplace Equation: Dirichlet and Neumann Boundary Conditions - Lecture 67

Explore Dirichlet and Neumann boundary conditions for the Laplace Equation, enhancing understanding of partial differential equations and their applications.

• YouTube
• 29 minutes
• On-Demand
• Free Video