Finite differences

Faulhaber's formula

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 formula
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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

Related pages

Jacob Bernoulli | Richard K. Guy | Triangular number | Vector space | Q-analog | John Horton Conway | Polynomial | Bernoulli number | Umbral calculus | Generating function | Polynomial function | Stirling numbers of the second kind | Binomial theorem | Bernoulli polynomials | Indefinite sum | Mathematics | Identity (mathematics) | Pascal's triangle | Squared triangular number | Square pyramidal number | Polynomials calculating sums of powers of arithmetic progressions | Telescoping series | Riemann zeta function | Invertible matrix