Free ebook http://tinyurl.com/EngMathYT How to integrate over 2 curves. This example discusses the additivity property of line integrals (sometimes called path integrals).
From playlist Engineering Mathematics
Integration 11 Lengths of Plane Curves Part 1
Using Integration to determine the length of a curve.
From playlist Integration
In this talk, we will define elliptic curves and, more importantly, we will try to motivate why they are central to modern number theory. Elliptic curves are ubiquitous not only in number theory, but also in algebraic geometry, complex analysis, cryptography, physics, and beyond. They were
From playlist An Introduction to the Arithmetic of Elliptic Curves
#Cycloid: A curve traced by a point on a circle rolling in a straight line. (A preview of this Sunday's video.)
From playlist Miscellaneous
Elliptic curves: point at infinity in the projective plane
This video depicts point addition and doubling on elliptic curve in simple Weierstrass form in the projective plane depicted using stereographic projection where the point at infinity can actually be seen. Explanation is in the accompanying article https://trustica.cz/2018/04/05/elliptic-
From playlist Elliptic Curves - Number Theory and Applications
Curves from Antiquity | Algebraic Calculus One | Wild Egg
We begin a discussion of curves, which are central objects in calculus. There are different kinds of curves, coming from geometric constructions as well as physical or mechanical motions. In this video we look at classical curves that go back to antiquity, such as prominently the conic sec
From playlist Algebraic Calculus One from Wild Egg
The geometric series.
From playlist Advanced Calculus / Multivariable Calculus
Areas Between Curves: Definite Integral Illustrator
Link: https://www.geogebra.org/m/YCt3bvBE
From playlist Calculus: Dynamic Interactives!
3D Trigonometry Example (1 of 2: Setting up the triangles)
More resources available at www.misterwootube.com
From playlist Trigonometry and Measure of Angles
Curves in Modern Times | Algebraic Calculus One | Wild Egg
This video introduces some key objects, and also challenges, when we move beyond the Greek tradition to the more modern view of "curves". This rests crucially on the development of analytic geometry, or Cartesian coordinates, by Fermat and Descartes in the 17th century. They, along with Jo
From playlist Algebraic Calculus One from Wild Egg
De Casteljau Bezier Curves | Algebraic Calculus One | Wild Egg
Paul de Casteljau and Pierre Bezier were French car engineers working for competing companies who around 1960 initiated the most important development in the theory of curves of the modern era. The curves they studied we call de Casteljau Bezier curves, or dCB curves for short, are specifi
From playlist Algebraic Calculus One from Wild Egg
Areas of Slices and Caps, and Archimedes' Formula | Algebraic Calculus One | Wild Egg
We introduce the signed areas of slices of curve segments, obtained from chords, and areas of caps, obtained from tangents to curve segments. For the case of quadratic polynomially parametrized curves, or de Casteljau Bezier curves, we derive important formulas for these areas, and exten
From playlist Old Algebraic Calculus Videos
Archimedes Parabolic Area Formula for Cubics! | Algebraic Calculus One | Wild Egg
The very first and arguably most important calculation in Calculus was Archimedes' determination of the slice area of a parabola in terms of the area of a suitably inscribed triangle, involving the ratio 4/3. Remarkably, Archimedes' formula extends to the cubic case once we identify the ri
From playlist Old Algebraic Calculus Videos
Linearly Parametrized Curves | Algebraic Calculus One | Wild Egg
Parametrized curves figure prominently in the Algebraic Calculus, and they coincide with de Casteljau Bezier curves. The simplest case are the linearly parametrized curves given by a pair of linear polynomials of polynumbers. This gives us an alternate view of oriented polygonal splines.
From playlist Algebraic Calculus One
Integration by Parts and Areas under Curves | Algebraic Calculus One | Wild Egg
We start with a purely algebraic Integration by Parts formula, which is a consequence of the Product Rule for Faulhaber Derivatives. Then we apply this to the Fundamental Theorem to get two asymmetric versions of it. Looking at the geometrical significance following a favourite picture o
From playlist Algebraic Calculus One
Signed Area for Polynomially Parametrized Curves | Algebraic Calculus One | Wild Egg
We make the very big shift from considering signed areas of linearly parametrized curves to polynomially parametrized curves. Pleasantly these are exactly the de Casteljau Bezier curves. Our approach is to concentrate on the properties of the signed area that are valid in the linear case:
From playlist Algebraic Calculus One
Bi Polynumbers and Tangents to Algebraic Curves | Algebraic Calculus One | Wild Egg
We introduce the important technology of defining, and computing the tangent line to an algebraic curve at a point lying on it. We start with a discussion on bi polynumbers, which are two dimensional arrays that are equivalent to polynomials in two variables, but without us having to fret
From playlist Algebraic Calculus One from Wild Egg
Approximating Conics with Polynomial Curves | Algebraic Calculus One | Wild Egg
We introduce two important families of polynumbers: the cosine and sine polynumbers associated to the unit circle with equation x^2+y^2=1, and the cosh and sinh polynumbers associated to the relativistic hyperbola with equation x^2-y^2=1. These work together to give us circular polynumber
From playlist Algebraic Calculus One
Math 139 Fourier Analysis Lecture 12: Fourier series and the isoperimetric inequality
Fourier Series and the Isoperimetrric Inequality. Basic knowledge about curves: parametrized curve; length of a curve; arclength parametrization. Area enclosed by simple closed curve is maximized if the curve is a circle.
From playlist Course 8: Fourier Analysis
Álvaro Lozano-Robledo: Recent progress in the classification of torsion subgroups of...
Abstract: This talk will be a survey of recent results and methods used in the classification of torsion subgroups of elliptic curves over finite and infinite extensions of the rationals, and over function fields. Recording during the meeting "Diophantine Geometry" the May 22, 2018 at th
From playlist Math Talks