Calculus - The Fundamental Theorem, Part 1
The Fundamental Theorem of Calculus. First video in a short series on the topic. The theorem is stated and two simple examples are worked.
From playlist Calculus - The Fundamental Theorem of Calculus
Some identities involving the Riemann-Zeta function.
After introducing the Riemann-Zeta function we derive a generating function for its values at positive even integers. This generating function is used to prove two sum identities. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist The Riemann Zeta Function
More identities involving the Riemann-Zeta function!
By applying some combinatorial tricks to an identity from https://youtu.be/2W2Ghi9idxM we are able to derive two identities involving the Riemann-Zeta function. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist The Riemann Zeta Function
Proof: Supremum and Infimum are Unique | Real Analysis
If a subset of the real numbers has a supremum or infimum, then they are unique! Uniqueness is a tremendously important property, so although it is almost complete trivial as far as difficulty goes in this case, we would be ill-advised to not prove these properties! In this lesson we'll be
From playlist Real Analysis
What is the Fundamental theorem of Algebra, really? | Abstract Algebra Math Foundations 217
Here we give restatements of the Fundamental theorems of Algebra (I) and (II) that we critiqued in our last video, so that they are now at least meaningful and correct statements, at least to the best of our knowledge. The key is to abstain from any prior assumptions about our understandin
From playlist Math Foundations
Philosophy & Our Mental Life - Hilary Putnam (1973)
The question which troubles laymen, and which has long troubled philosophers, even if it is somewhat disguised by today's analytic style of writing philosophy, is this: Are we made of matter or soul-stuff? To put it as bluntly as possible, are we just material beings, or are we "something
From playlist Philosophy of Mind
Lies & Truth in the History of Science - A. Martínez - 2/27/2020
Galileo wrote that Pythagoras believed that the planets orbit the Sun. Newton credited Pythagoras for having discovered the inverse square law of gravity. Nowadays, science textbooks credit Pythagoras with the theory that Earth moves, and some expert historians claim that Pythagoras proved
From playlist Talks and Seminars
4. Introduction to Plato's Phaedo; Arguments for the existence of the soul, Part II
Death (PHIL 176) After a brief introduction to Plato's Phaedo, more arguments are offered in this lecture in defense of the existence of an immaterial soul. The emphasis here is on the fact that we need to believe in the existence of a soul in order to explain the claim that we possess fr
From playlist Death with Shelly Kagan
Learn to evaluate the integral with functions as bounds
👉 Learn about the fundamental theorem of calculus. The fundamental theorem of calculus is a theorem that connects the concept of differentiation with the concept of integration. The theorem is basically saying that the differentiation of the integral of a function yields the original funct
From playlist Evaluate Using The Second Fundamental Theorem of Calculus
Wigner–Eckart Theorem | Clebsch-Gordan & Spherical Tensor Operators
In this video, we will explain the Wigner-Eckart theorem in theory and then explicitly show how to use it to solve a problem. This theorem is closely related to Clebsch-Gordan coefficients and spherical tensor operators. 𝗥𝗲𝗳𝗲𝗿𝗲𝗻𝗰𝗲𝘀: [1] Particle Data Group, "The Review of Particle Phy
From playlist Mathematical Physics
Renato Bettiol - Scalar curvature rigidity and extremality in dimension 4
In this talk, I will discuss the Finsler--Thorpe trick for curvature operators in dimension 4, and how it can be combined with twisted spinor methods to show that large classes of compact 4-manifolds, with or without boundary, with nonnegative sectional curvature are area-extremal for scal
From playlist Not Only Scalar Curvature Seminar
A. Song - What is the (essential) minimal volume? 2
I will discuss the notion of minimal volume and some of its variants. The minimal volume of a manifold is defined as the infimum of the volume over all metrics with sectional curvature between -1 and 1. Such an invariant is closely related to "collapsing theory", a far reaching set of resu
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Calculus: The Fundamental Theorem of Calculus
This is the second of two videos discussing Section 5.3 from Briggs/Cochran Calculus. In this section, I discuss both parts of the Fundamental Theorem of Calculus. I briefly discuss why the theorem is true, and work through several examples applying the theorem.
From playlist Calculus
Bayes theorem, the geometry of changing beliefs
Perhaps the most important formula in probability. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/bayes-thanks Home page: https://www.3blue1brown.c
From playlist Prob and Stats
Karsten GROVE - Positive curvature and beyond: A status report and future peek
We will provide an overview of some of the main results around manifolds with positive and non-negative sectional curvature and discuss established and evolving approaches to the area.
From playlist Riemannian Geometry Past, Present and Future: an homage to Marcel Berger
History of Science and Technology Q&A (March 8, 2023)
Stephen Wolfram hosts a live and unscripted Ask Me Anything about the history of science and technology for all ages. Find the playlist of Q&A's here: https://wolfr.am/youtube-sw-qa Originally livestreamed at: https://twitch.tv/stephen_wolfram If you missed the original livestream of thi
From playlist Stephen Wolfram Ask Me Anything About Science & Technology
Here's a re-enactment of the famous paradox known as the "infinite monkey theorem."
From playlist Cosmic Journeys
Evaluate the integral with e as the lower bound
👉 Learn about the fundamental theorem of calculus. The fundamental theorem of calculus is a theorem that connects the concept of differentiation with the concept of integration. The theorem is basically saying that the differentiation of the integral of a function yields the original funct
From playlist Evaluate Using The Second Fundamental Theorem of Calculus
Presocratics Part 1: Early Greek Philosophy
When people think of philosophy, they often transport themselves to Ancient Greece. This era was a hotbed of intellectual activity, and it produced some of the most influential minds in human history. But before we get to the most famous ones, Socrates and his lineage, we have to discuss t
From playlist Philosophy/Logic