Harmonic analysis | Mathematical terminology
In mathematics, a number of concepts employ the word harmonic. The similarity of this terminology to that of music is not accidental: the equations of motion of vibrating strings, drums and columns of air are given by formulas involving Laplacians; the solutions to which are given by eigenvalues corresponding to their modes of vibration. Thus, the term "harmonic" is applied when one is considering functions with sinusoidal variations, or solutions of Laplace's equation and related concepts. (Wikipedia).
An example of a harmonic series.
From playlist Advanced Calculus / Multivariable Calculus
If the Laplacian of a function is zero everywhere, it is called Harmonic. Harmonic functions arise all the time in physics, capturing a certain notion of "stability", whenever one point in space is influenced by its neighbors.
From playlist Fourier
C67 The physics of simple harmonic motion
See how the graphs of simple harmonic motion changes with changes in mass, the spring constant and the values correlating to the initial conditions (amplitude)
From playlist Differential Equations
Lecture 1: Roal and Harmonic Analysis by Prof. Thiele
Lecture Series
From playlist Lecture Recordings
B04 Example problem of simple harmonic oscillation
Solving an example problem of simple harmonic oscillation, which requires calculating the solution to a second order ordinary differential equation.
From playlist Physics ONE
B03 Simple harmonic oscillation
Explaining simple (idealised) harmonic oscillation, through a second-order ordinary differential equation.
From playlist Physics ONE
Simple Harmonic Motion Example Question (1 of 3: Determining period of motion)
More resources available at www.misterwootube.com
From playlist Applications of Calculus to Mechanics
Can you hear the shape of a drum?
Bach, the Universe & Everything - Can you hear the shape of a drum? In Bach the Universe & Everything, mathematics and music share the stage. A partnership between Orchestra of the Age of Enlightenment and Oxford Mathematics, these secular services aim to reflect the community atmosphere
From playlist Music and Mathematics
Mathematics and Music: Vibrating Strings and Overtones
Friends Lunch with a Member: March 3, 2017 "Mathematics and Music: Vibrating Strings and Overtones" Ian Jauslin More videos on http://video.ias.edu
From playlist Friends of the Institute
Learn an effective strategy for solving standing wave problems in your physics class. After a quick review of the standing wave diagrams, the relationships, and the formulas, Mr. H introduces the strategy and models its use in six example problems. The Standing Waves and Harmonics video
From playlist Vibrations and Waves
Apollonius and harmonic conjugates | Universal Hyperbolic Geometry 2 | NJ Wildberger
Apollonius introduced the important idea of harmonic conjugates, concerning four points on a line. He showed that the pole polar duality associated with a circle produces a family of such harmonic ranges, one for every line through the pole of a line. Harmonic ranges also occur in the cont
From playlist Universal Hyperbolic Geometry
WSU Master Class: Mathematics, The Language of Nature with Edward Frenkel Course
Join mathematician Edward Frenkel as he discusses how the elegant mathematical formulation of symmetry has been used throughout math and physics and could, through the Langlands program, give rise to a grand unified theory of mathematics. This lecture was recorded on May 31, 2014, at the
From playlist WSU Master Classes
WSU Master Class: Mathematics, The Language of Nature with Edward Frenkel Course
Join mathematician Edward Frenkel as he discusses how the elegant mathematical formulation of symmetry has been used throughout math and physics and could, through the Langlands program, give rise to a grand unified theory of mathematics. This lecture was recorded on May 31, 2014, at the
From playlist WSU Master Class
The Abel lectures: Hillel Furstenberg and Gregory Margulis
0:30 Welcome by Hans Petter Graver, President of the Norwegian Academy of Science Letters 01:37 Introduction by Hans Munthe-Kaas, Chair of the Abel Prize Committee 04:16 Hillel Furstenberg: Random walks in non-euclidean space and the Poisson boundary of a group 58:40 Questions and answers
From playlist Gregory Margulis
Squares and Tilings - Numberphile
With 2006 Fields Medallist Andrei Okounkov More links & stuff in full description below ↓↓↓ Professor Okounkov website: http://www.math.columbia.edu/~okounkov/ Numberphile Field Medallist Playlist: https://bit.ly/Fields_Playlist Roger Penrose on the Numberphile Podcast: https://youtu.be
From playlist Fields Medallists on Numberphile
700 years of secrets of the Sum of Sums (paradoxical harmonic series)
Today's video is about the harmonic series 1+1/2+1/3+... . Apart from all the usual bits (done right and animated :) I've included a lot of the amazing properties of this prototypical infinite series that hardly anybody knows about. Enjoy, and if you are teaching this stuff, I hope you'l
From playlist Recent videos
Lecture 2 | New Revolutions in Particle Physics: Basic Concepts
(October 12, 2009) Leonard Susskind gives the second lecture of a three-quarter sequence of courses that will explore the new revolutions in particle physics. In this lecture he explores quantum field theory. Leonard Susskind, Felix Bloch Professor of Physics, received a PhD from Cornel
From playlist Lecture Collection | Particle Physics: Basic Concepts