Harmonic series (mathematics)

3_3 The Harmonic Series

An example of a harmonic series.

From playlist Advanced Calculus / Multivariable Calculus

The Harmonic Series

This video introduces the harmonic series, explains why it is divergent and also examples infinite series that resemble the harmonic series. Site: http://mathispower4u.com

From playlist Infinite Series

The Harmonic Series

Just a short video where we discuss the Harmonic Series sum(1/n, n = 1, ...). We talk about whether it converges or diverges and discuss the p-test. I hope this helps someone who is learning calculus and studying infinite series. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording G

From playlist Infinite Series

Fourier Series Coefficients (where did they come from?)

Learn how to derive the Fourier series coefficients formulas. Remember, a Fourier series is a series representation of a function with sin(nx) and cos(nx) as its building blocks. Meanwhile, a Taylor series is a series representation of a function with x^n as its building blocks. These are

From playlist Fourier Series

Lecture 9.2 Fourier Series (part 1)

We introduce the theory of Fourier series, which allows us to analyse a periodic function in terms an infinite series of simple sines and cosines. In this lecture, we show how to calculate the coefficients of the series using integrals over the period of the function.

From playlist MATH2018 Engineering Mathematics 2D

How to compute a Fourier series: an example

Free ebook http://tinyurl.com/EngMathYT This video is a demonstration on how to compute a Fourier series of a simple given function. I discuss how to calculate the Fourier coefficients through integration and the simplifications involved. Fourier series are an important area of applied

From playlist Engineering Mathematics

What is the formula to find the sum of an arithmetic sequence

👉 Learn all about series. A series is the sum of the terms of a sequence. Just like in sequences, there are many types of series, among which are: arithmetic and geometric series. An arithmetic series is the sum of the terms of an arithmetic sequence. A geometric series is the sum of the t

From playlist Series

Fourier series revision

Free ebook http://tinyurl.com/EngMathYT A review question involving Fourier series, including their calculation and related concepts.

From playlist Engineering Mathematics

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

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

Data Science - Part XVI - Fourier Analysis

For downloadable versions of these lectures, please go to the following link: http://www.slideshare.net/DerekKane/presentations https://github.com/DerekKane/YouTube-Tutorials This lecture provides an overview of the Fourier Analysis and the Fourier Transform as applied in Machine Learnin

From playlist Data Science

Proof: The Harmonic Series is Divergent!

More resources available at www.misterwootube.com

From playlist Mathematical Exploration

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

Edward Frenkel: Langlands Program and Unification

Abstract: Sophia Kovalevskaya wrote, "It is not possible to be a mathematician without being a poet at heart. A poet should see what others can’t see, see deeper than others. And that’s the job of a mathematician as well.” The work of Robert Langlands sets a great example for this maxim, a

From playlist Abel Lectures

Eugenia Malinnikova : Uncertainty principles for discrete Schrödinger evolutions

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist Analysis and its Applications

The Biggest Project in Modern Mathematics

In a 1967 letter to the number theorist André Weil, a 30-year-old mathematician named Robert Langlands outlined striking conjectures that predicted a correspondence between two objects from completely different fields of math. The Langlands program was born. Today, it's one of the most amb

From playlist Explainers

What is the Riemann Hypothesis?

This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation

From playlist Mathematics

Musimathics: Fractals & Self-Similarity (Part 10)

Welcome to the Musimathics series! Musimathics gives an overview of some of the most interesting topics in the field of mathematical music theory! You are watching the tenth video in the series. In this video, Chloe goes over the basics of fractals and self-similarity, as well as their ap

From playlist Musimathics: Music & Math

Scott Kim - Musical Illusions - CoM Oct 2020

Ever heard a sound that keeps going up in pitch, but comes back to where it started? It’s called a Shepard tone, and it was invented by psychologist Roger Shepard in the 1960s. Filmmaker Christopher Nolan recently used this effect for the soundtrack of his movie Dunkirk, to create an endle

From playlist Celebration of Mind

What are Fourier series?

Free ebook http://tinyurl.com/EngMathYT A tutorial on Fourier series and how to calculate them. Plenty of examples are discussed to illustrate the ideas.

From playlist Engineering Mathematics