In geometry, an intrinsic equation of a curve is an equation that defines the curve using a relation between the curve's intrinsic properties, that is, properties that do not depend on the location and possibly the orientation of the curve. Therefore an intrinsic equation defines the shape of the curve without specifying its position relative to an arbitrarily defined coordinate system. The intrinsic quantities used most often are arc length , tangential angle , curvature or radius of curvature, and, for 3-dimensional curves, torsion . Specifically: * The is the curve given by its curvature and torsion. * The Whewell equation is obtained as a relation between arc length and tangential angle. * The CesΓ ro equation is obtained as a relation between arc length and curvature. The equation of a circle (including a line) for example is given by the equation where is the arc length, the curvature and the radius of the circle. These coordinates greatly simplify some physical problem. For elastic rods for example, the potential energy is given by where is the bending modulus . Moreover, as , elasticity of rods can be given a simple variational form. (Wikipedia).
Using one to one property when exponents do not have the same base, 25^(x+3) = 5
π Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo
From playlist Solve Exponential Equations without a Calculator
How to determine if an equation is a linear relation
π Learn how to determine if an equation is a linear equation. A linear equation is an equation whose highest exponent on its variable(s) is 1. The variables do not have negative or fractional, or exponents other than one. Variables must not be in the denominator of any rational term and c
From playlist Write Linear Equations
Learn how to use the equality property of exponents to solve with negative exponents
π Learn how to solve exponential equations involving fractions. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we make the base of both sides of the equation to be equal so that we can then equate the exponents. When the
From playlist Solve Exponential Equations with Fractions
Solving an equation by converting exponents to the same base
π Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo
From playlist Solve Exponential Equations without a Calculator
Solving an equation using the one to one property of exponents 5^(x+1) = 125^x
π Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo
From playlist Solve Exponential Equations without a Calculator
Solving a simple equations with exponents
π Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo
From playlist Solve Exponential Equations without a Calculator
Stability of the spacetime positive mass theorem in spherical symmetry - Marcus Khuri
More videos on http://video.ias.edu
From playlist Mathematics
Using the equality of exponents to get the same base and solve
π Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo
From playlist Solve Exponential Equations without a Calculator
What We've Learned from NKS Chapter 7: Mechanisms in Programs and Nature
In this episode of "What We've Learned from NKS", Stephen Wolfram is counting down to the 20th anniversary of A New Kind of Science with [another] chapter retrospective. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or th
From playlist Science and Research Livestreams
Using the property of equality of powers to solve an equation with exponents
π Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo
From playlist Solve Exponential Equations without a Calculator
How to use the same base to solve an equation with exponents
π Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo
From playlist Solve Exponential Equations without a Calculator
Intrinsic Curvature and Singularities
Positively, negatively, and infinitely curved space explained. Covers Ricci scalar (scalar curvature) and Gaussian curvature. Useful for Einstein's General Theory of Relativity. My Patreon page is at https://www.patreon.com/EugeneK
From playlist Physics
https://www.patreon.com/edmundsj If you want to see more of these videos, or would like to say thanks for this one, the best way you can do that is by becoming a patron - see the link above :). And a huge thank you to all my existing patrons - you make these videos possible. Quasi-Fermi l
From playlist Electronics I: Semiconductor Physics and Devices
Charge Carrier Concentration of Doped Semiconductors
https://www.patreon.com/edmundsj If you want to see more of these videos, or would like to say thanks for this one, the best way you can do that is by becoming a patron - see the link above :). And a huge thank you to all my existing patrons - you make these videos possible. In this video
From playlist Electronics I: Semiconductor Physics and Devices
[T1 2022] Sebastian Schreiber - Coevolution of habitat choice in a stochastic world
Joint work with Alex Hening and Dang Nguyen. Species live and interact in patchy landscapes where environmental conditions vary both in time and space. In the face of this spatial-temporal heterogeneity, species may co-evolve how they select habitat patches. Under equilibrium conditions,
From playlist [T1 2022] Workshop - Mathematical models in ecology and evolution - March 21st to 25th, 2022
Reputation based information design for indusing prosocial behaviour by Rajesh Sundaresan
Program Summer Research Program on Dynamics of Complex Systems ORGANIZERS: Amit Apte, Soumitro Banerjee, Pranay Goel, Partha Guha, Neelima Gupte, Govindan Rangarajan and Somdatta Sinha DATE : 15 May 2019 to 12 July 2019 VENUE : Madhava hall for Summer School & Ramanujan hall f
From playlist Summer Research Program On Dynamics Of Complex Systems 2019
Lecture 16: Isometry invariance and spectral techniques
CS 468: Differential Geometry for Computer Science
From playlist Stanford: Differential Geometry for Computer Science (CosmoLearning Computer Science)
Lecture 15: Isometries, Rigidity, and Curvature
CS 468: Differential Geometry for Computer Science
From playlist Stanford: Differential Geometry for Computer Science (CosmoLearning Computer Science)
Using the property of equality to solve equations with exponents
π Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo
From playlist Solve Exponential Equations without a Calculator
Options Trading - Call and Put Options - Basic Introduction
This stock options trading video tutorial provides a basic introduction into call and put options. The prices of options depend on share price, volatility, and time left to expiration. The extrinsic value of all options is subject to time decay, that is, they decrease as time move forwar
From playlist Stocks and Bonds