In applied mathematics, the Joukowsky transform, named after Nikolai Zhukovsky (who published it in 1910), is a conformal map historically used to understand some principles of airfoil design. The transform is where is a complex variable in the new space and is a complex variable in the original space.This transform is also called the Joukowsky transformation, the Joukowski transform, the Zhukovsky transform and other variations. In aerodynamics, the transform is used to solve for the two-dimensional potential flow around a class of airfoils known as Joukowsky airfoils. A Joukowsky airfoil is generated in the complex plane (-plane) by applying the Joukowsky transform to a circle in the -plane. The coordinates of the centre of the circle are variables, and varying them modifies the shape of the resulting airfoil. The circle encloses the point (where the derivative is zero) and intersects the point This can be achieved for any allowable centre position by varying the radius of the circle. Joukowsky airfoils have a cusp at their trailing edge. A closely related conformal mapping, the Kármán–Trefftz transform, generates the broader class of Kármán–Trefftz airfoils by controlling the trailing edge angle. When a trailing edge angle of zero is specified, the Kármán–Trefftz transform reduces to the Joukowsky transform. (Wikipedia).
Animated Mandelbrot transform - linear interpolation
http://code.google.com/p/mandelstir/
From playlist mandelstir
The 5 ways to visualize complex functions | Essence of complex analysis #3
Complex functions are 4-dimensional: its input and output are complex numbers, and so represented in 2 dimensions each, so how do we visualize complex functions if we are living in a 3D world? There are actually 5 different ways to visualize a complex function, and this video is going to e
From playlist Essence of complex analysis
Lec 24 | MIT 18.085 Computational Science and Engineering I, Fall 2008
Lecture 24: Laplace's equation (part 2) License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 18.085 Computational Science & Engineering I, Fall 2008
This object is transformable hyperboloid,you can transform from cylinder to various hyperboloids.See video. Buy at http://www.shapeways.com/shops/GeometricToy Copyright (c) 2014,AkiraNishihara
From playlist 3D printed toys
England's World Cup Win | British Pathé
THE BEAUTIFUL GAME - FOOTBALL MONTH ON BRITISH PATHÉ (JUNE 2016): Newsreels of the Week: England's World Cup Win. Take a look back at England's World Cup win in 1966, as well as clips of the footballs being made for the tournament, the winning teams arrival back in England and Pickles -
From playlist The World Cup Throughout History | British Pathé
Messing with Mona: Introduction to Geometric Transformations
Link: https://www.geogebra.org/m/KFtdRvyv
From playlist Geometry: Dynamic Interactives!
This turned out a little math-ier than I expected, but I hope that's alright! Let me know if you have any questions in the comment section! I would like to apologize again for my absence for the past few months. Work was rough, and so was creating the new library. I'll Hopefully be back t
From playlist Simuleios
Understanding Aerodynamic Lift
Get access to the extended version of this video (ad-free!) on Nebula - https://nebula.tv/videos/the-efficient-engineer-understanding-aerodynamic-lift-extended-version. Humanity has long been obsessed with heavier-than-air flight, and to this day it remains a topic that is shrouded in a b
From playlist Fluid Mechanics
Solving a Cubic Equation Using a Triangle
There is this surprising fact about cubic equations with 3 real solutions where an equilateral triangle centered on the inflection point can always be scaled/rotated by some amount such that its vertices will line up with the roots of the equation. But is there any way that this can be us
From playlist Summer of Math Exposition Youtube Videos
Animated Mandelbrot Transform - linear interpolation, applied to an image of the Set itself
http://code.google.com/p/mandelstir/
From playlist mandelstir
Live CEOing Ep 282: Visualization Features for WL 12.1
Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Visualization Features for WL 12.1.
From playlist Behind the Scenes in Real-Life Software Design
From the d’Alembert Paradox to the 1984 Kato Criteria via the 1941 1/3.... by Claude Bardos
Program Turbulence: Problems at the Interface of Mathematics and Physics (ONLINE) ORGANIZERS: Uriel Frisch (Observatoire de la Côte d'Azur and CNRS, France), Konstantin Khanin (University of Toronto, Canada) and Rahul Pandit (Indian Institute of Science, Bengaluru) DATE: 07 December 202
From playlist Turbulence: Problems at The Interface of Mathematics and Physics (Online)
To Understand the Fourier Transform, Start From Quantum Mechanics
Develop a deep understanding of the Fourier transform by appreciating the critical role it plays in quantum mechanics! Get the notes for free here: https://courses.physicswithelliot.com/notes-sign-up Sign up for my newsletter for additional physics lessons: https://www.physicswithelliot.c
From playlist Physics Mini Lessons
Wavelets: a mathematical microscope
Wavelet transform is an invaluable tool in signal processing, which has applications in a variety of fields - from hydrodynamics to neuroscience. This revolutionary method allows us to uncover structures, which are present in the signal but are hidden behind the noise. The key feature of w
From playlist Fourier
Electrical Engineering: Ch 19: Fourier Transform (2 of 45) What is a Fourier Transform? Math Def
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the mathematical definition and equation of a Fourier transform. Next video in this series can be seen at: https://youtu.be/yl6RtWp7y4k
From playlist ELECTRICAL ENGINEERING 18: THE FOURIER TRANSFORM
z-Transform Analysis of LTI Systems
http://AllSignalProcessing.com for more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. Introduction to analysis of systems described by linear constant coefficient difference equations using the z-transform. Definition of the system fu
From playlist The z-Transform
Compositional Structure of Classical Integral Transforms
The recently implemented fractional order integro-differentiation operator, FractionalD, is a particular case of more general integral transforms. The majority of classical integral transforms are representable as compositions of only two transforms: the modified direct and inverse Laplace
From playlist Wolfram Technology Conference 2022
Lecture 22, The z-Transform | MIT RES.6.007 Signals and Systems, Spring 2011
Lecture 22, The z-Transform Instructor: Alan V. Oppenheim View the complete course: http://ocw.mit.edu/RES-6.007S11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT RES.6.007 Signals and Systems, 1987
Lecture 7 | The Fourier Transforms and its Applications
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood reintroduces the Fourier Transform and its inverse, then he goes into specific properties and transforms. The Fourier transform is a tool for s
From playlist Lecture Collection | The Fourier Transforms and Its Applications
An introduction to the wavelet transform (and how to draw with them!)
The wavelet transform allows to change our point of view on a signal. The important information is condensed in a smaller space, allowing to easily compress or filter the signal. A lot of approximations are made in this video, like a lot of missing √2 factors. This choice was made to keep
From playlist Summer of Math Exposition Youtube Videos