Professor Dave Explains

We already learned about the Laplace transform for solving partial differential equations, so now let's learn about the Fourier transform. We will also want to check out something called the Fourier series, which is kind of like a Maclaurin series, but instead of adding up powers of x, it adds up trigonometric functions. Let's take a look!

Script by Lorcan Nicholls

Watch the whole Differential Equations playlist: http://bit.ly/ProfDaveDiffeq
Watch the whole Mathematics playlist: http://bit.ly/ProfDaveMath

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What came next after addition and subtraction? Why, multiplication and division, of course! Multiplication is kind of like addition, really. In fact, it's just repeated addition. Take a look at this early innovation in arithmetic, and the properties associated with these operations.

Watch the whole Mathematics playlist: http://bit.ly/ProfDaveMath

Classical Physics Tutorials: http://bit.ly/ProfDavePhysics1
Modern Physics Tutorials: http://bit.ly/ProfDavePhysics2
General Chemistry Tutorials: http://bit.ly/ProfDaveGenChem
Organic Chemistry Tutorials: http://bit.ly/ProfDaveOrgChem
Biochemistry Tutorials: http://bit.ly/ProfDaveBiochem
Biology Tutorials: http://bit.ly/ProfDaveBio

EMAIL► [email protected]
PATREON► http://patreon.com/ProfessorDaveExplains

Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!
Amazon: https://amzn.to/2HtNpVH
Bookshop: https://bit.ly/39cKADM

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Use code professordave at https://incogni.com/professordave to get an exclusive 60% off an annual Incogni plan.

Recently, Piers Morgan hosted a panel regarding trans issues. This was specifically centered around the resignation of Jerry Coyne, Richard Dawkins, and Stephen Pinker from the board of the Freedom From Religion Foundation on the basis of their stance on trans issues. I was asked to be on the panel but regrettably could not participate due to a scheduling conflict, so I decided to make another one of these videos summarizing what I would have said if I were present. If you're one of those people who whines about "woke trans ideology" or other idiotic catchphrases conservative propaganda tries to implant in you, please watch this video and learn something.

My other Piers Morgan video: https://www.youtube.com/watch?v=3_2LqixG9Cw

Watch my other debunks/debates/discussions: http://bit.ly/ProfDaveDebunk

EMAIL► [email protected]
PATREON► http://patreon.com/ProfessorDaveExplains

Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!
Amazon: https://amzn.to/2HtNpVH
Bookshop: https://bit.ly/39cKADM
Barnes and Noble: https://bit.ly/3pUjmrn

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We know about the commutative property and the associative property, but there are more to learn! This next one, the distributive property, is very important in algebra, so let's introduce it now so that when we get there we already have this covered.

Watch the whole Mathematics playlist: http://bit.ly/ProfDaveMath

Classical Physics Tutorials: http://bit.ly/ProfDavePhysics1
Modern Physics Tutorials: http://bit.ly/ProfDavePhysics2
General Chemistry Tutorials: http://bit.ly/ProfDaveGenChem
Organic Chemistry Tutorials: http://bit.ly/ProfDaveOrgChem
Biochemistry Tutorials: http://bit.ly/ProfDaveBiochem
Biology Tutorials: http://bit.ly/ProfDaveBio

EMAIL► [email protected]
PATREON► http://patreon.com/ProfessorDaveExplains

Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!
Amazon: https://amzn.to/2HtNpVH
Bookshop: https://bit.ly/39cKADM

Barnes and Noble: https://bit.ly/3pUjmrn
Book Depository: http://bit.ly/3aOVDlT

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It seems like it's been forever since we've dunked on James Tour, the lying creationist fraud who rages against origin of life research because it hurts his feelings. But he's been mouthing off quite a bit lately, so it's time to dunk on him harder than ever before! Remember how I make fun of James all the time for never having the balls to try and publish his lies in a peer-reviewed journal? Well it looks like he's done exactly that! Or no, not exactly. But he's pretending it's what he did. So as usual, let's tear his bullshit to smithereens and humiliate him something awful, shall we?

Szostak paper: https://jsystchem.springeropen.com/articles/10.1186/1759-2208-3-2
Grabow & Andrews paper: https://www.sciencedirect.com/science/article/abs/pii/S0303264719303077?via%3Dihub
Attwater paper: https://www.nature.com/articles/s41557-025-01830-y

Watch all of my content humiliating James: http://bit.ly/ProfDaveTour
Watch my other debunks/debates/discussions: http://bit.ly/ProfDaveDebunk

EMAIL► [email protected]
PATREON► http://patreon.com/ProfessorDaveExplains

Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!
Amazon: https://amzn.to/2HtNpVH
Bookshop: https://bit.ly/39cKADM
Barnes and Noble: https://bit.ly/3pUjmrn

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We just learned about Fourier series and Fourier transforms, so now let's put them together and learn about some applications. What is spectral density? How can we use Fourier transforms to classify linear second-order partial differential equations as elliptic, parabolic, or hyperbolic? Where do these concepts show up in modern technology? Let's find out!

Script by Lorcan Nicholls

Watch the whole Differential Equations playlist: http://bit.ly/ProfDaveDiffeq
Watch the whole Mathematics playlist: http://bit.ly/ProfDaveMath

Classical Physics Tutorials: http://bit.ly/ProfDavePhysics1
Modern Physics Tutorials: http://bit.ly/ProfDavePhysics2
General Chemistry Tutorials: http://bit.ly/ProfDaveGenChem
Organic Chemistry Tutorials: http://bit.ly/ProfDaveOrgChem
Biochemistry Tutorials: http://bit.ly/ProfDaveBiochem
Biology Tutorials: http://bit.ly/ProfDaveBio

EMAIL► [email protected]
PATREON► http://patreon.com/ProfessorDaveExplains

Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!
Amazon: https://amzn.to/2HtNpVH
Bookshop: https://bit.ly/39cKADM

Barnes and Noble: https://bit.ly/3pUjmrn

Learn more about your ad choices. Visit megaphone.fm/adchoices

We know how to add and subtract small numbers, but what about big numbers? Is it complicated? No, not really, but there is a bit of an algorithm to learn. Check this out!

Watch the whole Mathematics playlist: http://bit.ly/ProfDaveMath

Classical Physics Tutorials: http://bit.ly/ProfDavePhysics1
Modern Physics Tutorials: http://bit.ly/ProfDavePhysics2
General Chemistry Tutorials: http://bit.ly/ProfDaveGenChem
Organic Chemistry Tutorials: http://bit.ly/ProfDaveOrgChem
Biochemistry Tutorials: http://bit.ly/ProfDaveBiochem
Biology Tutorials: http://bit.ly/ProfDaveBio

EMAIL► [email protected]
PATREON► http://patreon.com/ProfessorDaveExplains

Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!
Amazon: https://amzn.to/2HtNpVH
Bookshop: https://bit.ly/39cKADM

Barnes and Noble: https://bit.ly/3pUjmrn
Book Depository: http://bit.ly/3aOVDlT

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Check out https://www.strawberry.me/professordave to get started with your career coach today!

So I went on Piers Morgan recently to explain to Piers how RFK Jr. is a massive fraud who should be yanked from office immediately. I was supposed to debate Bret Weinstein about this, but the little wiener declined. Why do you suppose that might be? Oh right, because he knows he's a lying douchebag, and that I would humiliate him. But he can't stop me from making a video demolishing all the dumb things he said in his part of the segment. So let's do that!

Check out the full Piers segment: https://www.youtube.com/watch?v=v3NOPzEyonU
(My section begins around 39 minutes)

My big RFK debunk: https://www.youtube.com/watch?v=HqI_z1OcenQ
My first Piers commentary video: https://www.youtube.com/watch?v=3_2LqixG9Cw
My second Piers commentary video: https://www.youtube.com/watch?v=A_VPCJfYh4U

Watch all of my content exposing the Weinstein brothers: http://bit.ly/ProfDaveWeinsteins
Watch all my debunks: http://bit.ly/ProfDaveDebunk

EMAIL► [email protected]
PATREON► http://patreon.com/ProfessorDaveExplains

Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!
Amazon: https://amzn.to/2HtNpVH
Bookshop: https://bit.ly/39cKADM

Barnes and Noble: https://bit.ly/3pUjmrn

Learn more about your ad choices. Visit megaphone.fm/adchoices

You may have this scary looking upper case sigma before. But don't worry, it just means to add some things up! Once we understand how series work, we can do all kinds of other things. Also, have you ever seen numbers with exclamation points after them? No it, doesn't mean that you shout the number. Those are factorials! We will learn about those in here as well. Lots of good stuff in here!

Watch the whole Mathematics playlist: http://bit.ly/ProfDaveMath

Classical Physics Tutorials: http://bit.ly/ProfDavePhysics1
Modern Physics Tutorials: http://bit.ly/ProfDavePhysics2
General Chemistry Tutorials: http://bit.ly/ProfDaveGenChem
Organic Chemistry Tutorials: http://bit.ly/ProfDaveOrgChem
Biochemistry Tutorials: http://bit.ly/ProfDaveBiochem
Biology Tutorials: http://bit.ly/ProfDaveBio

EMAIL► [email protected]
PATREON► http://patreon.com/ProfessorDaveExplains

Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!
Amazon: https://amzn.to/2HtNpVH
Bookshop: https://bit.ly/39cKADM

Barnes and Noble: https://bit.ly/3pUjmrn
Book Depository: http://bit.ly/3aOVDlT

Learn more about your ad choices. Visit megaphone.fm/adchoices

Alright, so we've decided to learn all of the maths, but where shall we start? Well, let's start at the beginning. The first kind of math we developed was simple arithmetic. We needed this at the dawn of civilization to communicate very simple ideas. Most of us can add small numbers together easily, but is there any more we can say about these operations? Let's find out!

Watch the whole Mathematics playlist: http://bit.ly/ProfDaveMath

Classical Physics Tutorials: http://bit.ly/ProfDavePhysics1
Modern Physics Tutorials: http://bit.ly/ProfDavePhysics2
General Chemistry Tutorials: http://bit.ly/ProfDaveGenChem
Organic Chemistry Tutorials: http://bit.ly/ProfDaveOrgChem
Biochemistry Tutorials: http://bit.ly/ProfDaveBiochem
Biology Tutorials: http://bit.ly/ProfDaveBio

EMAIL► [email protected]
PATREON► http://patreon.com/ProfessorDaveExplains

Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!
Amazon: https://amzn.to/2HtNpVH
Bookshop: https://bit.ly/39cKADM

Barnes and Noble: https://bit.ly/3pUjmrn
Book Depository: http://bit.ly/3aOVDlT

Learn more about your ad choices. Visit megaphone.fm/adchoices