Harmonic Function Courses and Certifications

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

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

Approaching Music Theory: Melodic Forms and Simple Harmony

158 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
• Free Online Course (Audit)

Musicianship: Tensions, Harmonic Function, and Modal Interchange

399 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
• 10 hours 21 minutes
• On-Demand
• Free Online Course (Audit)

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

Hausdorff Center for Mathematics

Henrik Shahgholian - Free Boundaries on Lattice, and Their Scaling Limits

Explore lattice-based potential theory, examining harmonic functions and free boundary problems. Discover intriguing numerical results and their implications for facet formation in scaling limits.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Joint Mathematics Meetings

Nonsmooth Boundary Value Problems

Explore nonsmooth boundary value problems in complex function theory, covering BMO functions, Hilbert transforms, and solvability in bounded domains. Insights into open problems and recent developments.

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

Fields Institute

Mini-course on Hardy Spaces - Part 3

Explore Hardy spaces with a focus on rotation, generalization, and approximate identities. Delve into uniform boundedness, Poisson PR constructions, and harmonic functions.

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

Fields Institute

Inverse Problems and the Anisotropic Calderón Conjecture

Explore geometric inverse problems, focusing on the Calderon Problem and its anisotropic variant. Learn about harmonic functions, complex geometric optics, and wave equation properties in this advanced mathematics lecture.

• YouTube
• 48 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

Fields Institute

Introduction to Random Walks on Groups - Lecture 3

Explore random walks on groups, their properties, and applications in mathematics and probability theory. Learn key concepts and techniques for analyzing group-based stochastic processes.

• YouTube
• 1 hour 49 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

HyperComplex Seminar

Monogenic Functions in Infinite-Dimensional Vector Spaces with Commutative Multiplication and Harmonic Vectors

Explore monogenic functions in infinite-dimensional vector spaces, their relation to spatial harmonic functions, and implications for complex analysis beyond traditional Cauchy integral formulas.

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