Continued fractions | Theorems in number theory
In number theory, Lochs's theorem concerns the rate of convergence of the continued fraction expansion of a typical real number. A proof of the theorem was published in 1964 by . The theorem states that for almost all real numbers in the interval (0,1), the number of terms m of the number's continued fraction expansion that are required to determine the first n places of the number's decimal expansion behaves asymptotically as follows: (sequence in the OEIS). As this limit is only slightly smaller than 1, this can be interpreted as saying that each additional term in the continued fraction representation of a "typical" real number increases the accuracy of the representation by approximately one decimal place. The decimal system is the last positional system for which each digit carries less information than one continued fraction quotient; going to base-11 (changing to in the equation) makes the above value exceed 1. The reciprocal of this limit, (sequence in the OEIS), is twice the base-10 logarithm of Lévy's constant. A prominent example of a number not exhibiting this behavior is the golden ratio—sometimes known as the "most irrational" number—whose continued fraction terms are all ones, the smallest possible in canonical form. On average it requires approximately 2.39 continued fraction terms per decimal digit. (Wikipedia).
C73 Introducing the theorem of Frobenius
The theorem of Frobenius allows us to calculate a solution around a regular singular point.
From playlist Differential Equations
Calculus 5.3 The Fundamental Theorem of Calculus
My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart
From playlist Calculus
The Fundamental Theorem of Calculus | Algebraic Calculus One | Wild Egg
In this video we lay out the Fundamental Theorem of Calculus --from the point of view of the Algebraic Calculus. This key result, presented here for the very first time (!), shows how to generalize the Fundamental Formula of the Calculus which we presented a few videos ago, incorporating t
From playlist Algebraic Calculus One
Differential Equations | Abel's Theorem
We present Abel's Theorem with a proof. http://www.michael-penn.net
From playlist Differential Equations
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
Proof of the Fundamental Theorem of Calculus (Part 2)
This video proves the Fundamental Theorem of Calculus (Part 2). http://mathispower4u.com
From playlist Definite Integrals and The Fundamental Theorem of Calculus
Prob & Stats - Bayes Theorem (1 of 24) What is Bayes Theorem?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is and define the symbols of Bayes Theorem. Bayes Theorem calculates the probability of an event or the predictive value of an outcome of a test based on prior knowledge of condition rela
From playlist PROB & STATS 4 BAYES THEOREM
Cryptid Profile - Loch Ness Monster Part 1
Today we tackle the monster, the myth, the legend: The Loch Ness Monster of Scotland, one of the most famous cryptids and most famous lake monster. This video is one of three planning to discuss whether this cryptid water beast is real or nothing more than outright fantasy. Part 1 focuses
From playlist Cryptozoology
Cryptid Profile - Loch Ness Monster Part 2
The long overdue part 2 to my Loch Ness Monster Cryptid Profile is here! In this episode I examine most of the Loch Ness Monster video and photographic evidence and try to determine their validity to prove the beast’s existence. I hope you enjoy and please request any new video ideas! Als
From playlist Cryptozoology
Differential Equations | Application of Abel's Theorem Example 2
We give an example of applying Abel's Theorem to construct a second solution to a differential equation given one solution. www.michael-penn.net
From playlist Differential Equations
COMPELLING EVIDENCE of Loch Ness Monster | The UnXplained (Season 4)
An eyewitness captures evidence of the Loch Ness monster on camera. See more in this clip from Season 4, "Real Life Monsters." Watch all new episodes of The UnXplained, streaming now, on The HISTORY Channel website at http://history.com/schedule. #TheUnXplained Subscribe for more from T
From playlist The UnXplained: Official Series Playlist | History
The Real Story Behind the Loch Ness Monster | History
Loch Ness expert Adrian Shine discusses his involvement with the Loch Ness Project and recaps his decades spent working to uncover the truth behind the Loch Ness monster. Subscribe for more HISTORY shows: http://histv.co/SubscribeHistoryYT Newsletter: https://www.history.com/newsletter
From playlist Haunted History
Loch Ness Monster Conspiracy EXPOSED | History's Greatest Mysteries (Season 4)
Is the Loch Ness Monster really out there? Or is it all a big hoax? Learn more in this clip from Season 4, Episode 1, "The Loch Ness Monster." Watch all new episodes of History's Greatest Mysteries, returning Monday, January 30 at 9/8c, and stay up to date on all of your favorite The HIST
From playlist History's Greatest Mysteries | Official Series Playlist | History
Video3-4: Existence and Uniqueness Them; Definition of Wronskian. Elementary Differential Equations
Elementary Differential Equations Video3-4: Existence and Uniqueness Theorem; the Definition and applications of Wronskian on linear dependence Course playlist: https://www.youtube.com/playlist?list=PLbxFfU5GKZz0GbSSFMjZQyZtCq-0ol_jD
From playlist Elementary Differential Equations
Stuff They Don't Want You To Know - Loch Ness Monster
Scientists from around the world have scoured Scotland's Loch Ness in an attempt to discover the infamous Loch Ness monster (affectionately known as 'Nessie'). Tune in to learn more about the search for Nessie in this episode. http://howstuffworks.com http://facebook.com/ConspiracyStuff h
From playlist Stuff They Don't Want You To Know
New Evidence of the Loch Ness Monster | In Search Of (Season 2) | History
The search continues with new episodes of In Search Of Fridays at 10/9c! In 2007, an eyewitness captured new footage of the fabled Loch Ness Monster that has reinvigorated the search for Scotland's elusive beast in this clip from Season 2, "Loch Ness Monster Part 1". #InSearchOf Subscribe
From playlist In Search Of: Official Series Playlist | History
Unissued / Unused material. Newspaper inserts from Scrapbook 1933. CU "Loch Ness Monster Hunt". CU "Is the Monster a Dolphin". CU. "What M.C.C. will do about body bowling". CU "We saw the Monster!". CU "£750,000 for Distressed Areas". CU "Seen in Loch Ness today". CU "Wiley Post wi
From playlist 8 Mysteries
Could the Loch Ness Monster be a Plesiosaur?
Today we finally finish up Loch Ness by speculating what the monster could be if I am completely wrong about it's apparent non-existence. I talk largely about plesiosaurs and leeches... so I hope you enjoy ;) All copyrighted footage and images in this video are protected under FAIR USE fo
From playlist Did dinosaurs and humans live together?
Moving on from Lagrange's equation, I show you how to derive Hamilton's equation.
From playlist Physics ONE
Science Stories: Loch Ness eDNA results, Poop Knives, and Skeleton Lovers
In this video I highlight/feature three recent scientific discoveries that I found interesting. I will discuss the results of a study that sought to find the Loch Ness Monster through DNA evidence, a study about blades and weapons made of human poop, and a story about two male roman skelet
From playlist Anthropology Profile