In mathematics, Faulhaber's formula, named after the early 17th century mathematician Johann Faulhaber, expresses the sum of the p-th powers of the first n positive integers as a (p + 1)th-degree polynomial function of n, the coefficients involving Bernoulli numbers Bj, in the form submitted by Jacob Bernoulli and published in 1713: where is a falling factorial. (Wikipedia).
Faulhaber's polynomials via Excel | Algebraic Calculus One | Anna Tomskova
Dr Anna Tomskova shows how Excel is a powerful tool for generating important mathematical sequences and objects -- in this case the Faulhaber polynomials that capture the sums of powers of natural numbers, and that contain the Bernoulli numbers as coefficients. Excel is not just oriented
From playlist Algebraic Calculus One
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
The discriminant and finding the solutions using quadratic formula
👉 Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | x^2+bx+c
The Derivative, the Integral, and the formula Faulhaber missed | Algebraic Calculus One | Wild Egg
In this video we present a new simplified inductive procedure to determine Faulhaber polynomials for sums of powers of natural numbers, and the closely associated Bernoulli numbers that what essentially discovered by Jacobi in 1834, and which John Conway also described in his lecture at ht
From playlist Algebraic Calculus One from Wild Egg
Solve a Bernoulli Differential Equation Initial Value Problem
This video provides an example of how to solve an Bernoulli Differential Equations Initial Value Problem. The solution is verified graphically. Library: http://mathispower4u.com
From playlist Bernoulli Differential Equations
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
Celsius to Fahrenheit to Kelvin Formula Conversions - Temperature Units C to F to K
This chemistry and physics video tutorial explains how to convert from celsius to fahrenheit to kelvin using a two formulas / equations. This video contains plenty of examples and practice problems. My E-Book: https://amzn.to/3B9c08z Video Playlists: https://www.video-tutor.net Homewor
From playlist New Physics Video Playlist
Describe and solve for the zeros using quadratic formula
👉 Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | x^2+bx+c
Signed Areas of Curves via Limits | Algebraic Calculus One | Wild Egg
The Fundamental Formula of the Algebraic Calculus gives us a completely algebraic way of introducing integrals for polynomially parametrized curves. But does it agree with the more usual limit based derivations found in traditional courses? Here we show that at least in some important cas
From playlist Algebraic Calculus One
Faulhaber's Formula and Bernoulli Numbers | Algebraic Calculus One | Wild Egg
This is a lecture in the Algebraic Calculus One course, which will present an exciting new approach to calculus, sticking with rational numbers and high school algebra, and avoiding all "infinite processes", "real numbers" and other modern fantasies. The course will be carefully framed on
From playlist Algebraic Calculus One from Wild Egg
Understanding the discriminant as a part of the quadratic formula
👉 Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | x^2+bx+c
26C3: UNBILD Pictures and Non-Pictures 2/7
Clip 2/7 Speaker: Christoph Faulhaber Reterritorialisierung und Globalisierung Mit seinen Projekten arbeitet Christoph Faulhaber an einer Fortschreibung von Konzeptkunst, Performance und Sozialer Skulptur. In "Ich wie es wirklich war" berichtet Faulhaber über die Folgen des Projektes
From playlist 26C3: Here be dragons day 1
26C3: UNBILD Pictures and Non-Pictures 5/7
Clip 5/7 Speaker: Christoph Faulhaber Reterritorialisierung und Globalisierung Mit seinen Projekten arbeitet Christoph Faulhaber an einer Fortschreibung von Konzeptkunst, Performance und Sozialer Skulptur. In "Ich wie es wirklich war" berichtet Faulhaber über die Folgen des Projektes
From playlist 26C3: Here be dragons day 1
26C3: UNBILD Pictures and Non-Pictures 7/7
Clip 7/7 Speaker: Christoph Faulhaber Reterritorialisierung und Globalisierung Mit seinen Projekten arbeitet Christoph Faulhaber an einer Fortschreibung von Konzeptkunst, Performance und Sozialer Skulptur. In "Ich wie es wirklich war" berichtet Faulhaber über die Folgen des Projektes
From playlist 26C3: Here be dragons day 1
26C3: UNBILD Pictures and Non-Pictures 3/7
Clip 3/7 Speaker: Christoph Faulhaber Reterritorialisierung und Globalisierung Mit seinen Projekten arbeitet Christoph Faulhaber an einer Fortschreibung von Konzeptkunst, Performance und Sozialer Skulptur. In "Ich wie es wirklich war" berichtet Faulhaber über die Folgen des Projektes
From playlist 26C3: Here be dragons day 1
26C3: UNBILD Pictures and Non-Pictures 1/7
Clip 1/7 Speaker: Christoph Faulhaber Reterritorialisierung und Globalisierung Mit seinen Projekten arbeitet Christoph Faulhaber an einer Fortschreibung von Konzeptkunst, Performance und Sozialer Skulptur. In "Ich wie es wirklich war" berichtet Faulhaber über die Folgen des Projektes
From playlist 26C3: Here be dragons day 1
26C3: UNBILD Pictures and Non-Pictures 6/7
Clip 6/7 Speaker: Christoph Faulhaber Reterritorialisierung und Globalisierung Mit seinen Projekten arbeitet Christoph Faulhaber an einer Fortschreibung von Konzeptkunst, Performance und Sozialer Skulptur. In "Ich wie es wirklich war" berichtet Faulhaber über die Folgen des Projektes
From playlist 26C3: Here be dragons day 1
Ex: Solve a Bernoulli Differential Equation Using Separation of Variables
This video explains how to solve a Bernoulli differential equation. http://mathispower4u.com
From playlist Bernoulli Differential Equations
How to solve a quadratic using the quadratic formula
👉 Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | ax^2+bx+c
Polynomials, Matrices and Pascal Arrays | Algebraic Calculus One | Wild Egg
We introduce some basic orientation towards polynomials and matrices in the context of the Pascal-type arrays that figured in our analysis of the Faulhaber polynomials and Bernoulli numbers in the previous video. The key is to observe some beautiful factorizations that occur involving diag
From playlist Algebraic Calculus One from Wild Egg