Euler's Formula for the Quaternions
In this video, we will derive Euler's formula using a quaternion power, instead of a complex power, which will allow us to calculate quaternion exponentials such as e^(i+j+k). If you like quaternions, this is a pretty neat formula and a simple generalization of Euler's formula for complex
From playlist Math
Determining the sine of the sum of two angles
👉 Learn how to evaluate the sine of an angle in radians using the sum/difference formulas. To do this, we first express the given angle as a sum or a difference of two (easy to evaluate) angles, then we use the unit circle and the Pythagoras theorem to identify the angles and obtain all th
From playlist Sum and Difference Formulas
Pre-Calculus - Using the difference of angles for cosine to evaluate for an angle cos(225-30)
👉 Learn how to evaluate the cosine of an angle in radians using the sum/difference formulas. To do this, we first express the given angle as a sum or a difference of two (easy to evaluate) angles, then we use the unit circle and the Pythagoras theorem to identify the angles and obtain all
From playlist Sum and Difference Formulas
Using sum and difference formula to find the exact value with cosine
👉 Learn how to evaluate the cosine of an angle in radians using the sum/difference formulas. To do this, we first express the given angle as a sum or a difference of two (easy to evaluate) angles, then we use the unit circle and the Pythagoras theorem to identify the angles and obtain all
From playlist Sum and Difference Formulas
Trigonometry Identity Proofs Sum
E to the i theta, Euler's Equation, is a stunning connection between trigonometry and complex numbers and exponentiation. Euler's Equation can also prove the trigonometric identities neatly and quickly, making it immeasurably handy to know. In this video, Euler's Equation is used to prove
From playlist Trigonometry
When Does Exponentiation Commute ? (Part 2)
In this video, we continue the discussion of finding (x,y) pairs that will commute under exponentiation: x^y = y^x. This time, we will find another way of writing Euler's number and solve the equation x^y = y^x for y with the help of the Lambert W function. Ideas were adapted from the fol
From playlist Math
Sum formula for tangent of an angle trigonometry
👉 Learn how to evaluate the tangent of an angle in degrees using the sum/difference formulas. To do this, we first express the given angle as a sum or a difference of two (easy to evaluate) angles, then we use the unit circle and the Pythagoras theorem to identify the angles and obtain all
From playlist Sum and Difference Formulas
Tim Ferriss: Ask Absurd Questions and Stop Fetishizing Failure | Big Think
Tim Ferriss: Ask Absurd Questions and Stop Fetishizing Failure Watch the newest video from Big Think: https://bigth.ink/NewVideo Join Big Think Edge for exclusive videos: https://bigth.ink/Edge ---------------------------------------------------------------------------------- Silicon Val
From playlist How to learn from failure | Big Think
Euler's formulas, Rodrigues' formula
In this video I proof various generalizations of Euler's formula, including Rodrigues' formula and explain their 3 dimensional readings. Here's the text used in this video: https://gist.github.com/Nikolaj-K/eaaa80861d902a0bbdd7827036c48af5
From playlist Algebra
Peter Thiel Returns to Stanford to Share Business Tips from "Zero to One"
Venture capitalist Peter Thiel, JD '92, founded PayPal and was the first major investor in Facebook, shared business tips from his new book, Zero to One: Notes on Startups, or How to Build the Future, with students and alumni at Stanford on Sept. 29, 2014. He also recalled his days at Stan
From playlist Stanford
Xavier Warin: Branching for PDEs
Abstract: Branching methods have recently been developed to solve some PDEs. Starting from Mckean formulation, we give the initial branching method to solve the KPP equation. We then give a formulation to solve non linear equation with a non linearity polynomial in the value function u. Th
From playlist Probability and Statistics
Applications of twisted technology - Christoph Thiele
Analysis Math-Physics Seminar Topic: Applications of twisted technology Speaker: Christoph Thiele Affiliation: University of California, Los Angeles Date: March 29, 2017 For more video, visit http://video.ias.edu
From playlist Mathematics
The Vandermonde Matrix and Polynomial Interpolation
The Vandermonde matrix is a used in the calculation of interpolating polynomials but is more often encountered in the proof that such polynomial interpolates exist. It is also often encountered in the study of determinants since it has a really nice determinant formula. Chapters 0:00 - In
From playlist Interpolation
Geometric Algebra - Linear and Spherical Interpolation (LERP, SLERP, NLERP)
In this video, I'll derive the formulas for doing linear and spherical interpolations between two vectors. In deriving the latter formula, we will use rotors, an object used in geometric algebra. We will also discuss normalized linear interpolation and contrast it with spherical interpolat
From playlist Geometric Algebra
Maryna Viazovska (EPFL): Fourier interpolation
This lecture is about Fourier uniqueness and Fourier interpolation pairs. Suppose that we have two subsets X and Y of the Euclidean space. Can we reconstruct a function f from its restriction to the set X and the restriction of its Fourier transform to the set Y? We are interested in the p
From playlist Seminar Series "Arithmetic Applications of Fourier Analysis"
Lecture 17 | 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 begins his lecture on sampling and interpolation and discusses the associated properties. The Fourier transform is a tool for solving physical
From playlist Lecture Collection | The Fourier Transforms and Its Applications
How to evaluate sum of two angles using the sum formula for sine
👉 Learn how to evaluate the sine of an angle in radians using the sum/difference formulas. To do this, we first express the given angle as a sum or a difference of two (easy to evaluate) angles, then we use the unit circle and the Pythagoras theorem to identify the angles and obtain all th
From playlist Sum and Difference Formulas
Mod-01 Lec-05 Error in the Interpolating polynomial
Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics