Articles containing proofs | Theorems in calculus
The gradient theorem, also known as the fundamental theorem of calculus for line integrals, says that a line integral through a gradient field can be evaluated by evaluating the original scalar field at the endpoints of the curve. The theorem is a generalization of the second fundamental theorem of calculus to any curve in a plane or space (generally n-dimensional) rather than just the real line. For φ : U ⊆ Rn → R as a differentiable function and γ as any continuous curve in U which starts at a point p and ends at a point q, then where ∇φ denotes the gradient vector field of φ. The gradient theorem implies that line integrals through gradient fields are path-independent. In physics this theorem is one of the ways of defining a conservative force. By placing φ as potential, ∇φ is a conservative field. Work done by conservative forces does not depend on the path followed by the object, but only the end points, as the above equation shows. The gradient theorem also has an interesting converse: any path-independent vector field can be expressed as the gradient of a scalar field. Just like the gradient theorem itself, this converse has many striking consequences and applications in both pure and applied mathematics. (Wikipedia).
Gradient theorem | Lecture 43 | Vector Calculus for Engineers
Derivation of the gradient theorem (or fundamental theorem of calculus for line integrals, or fundamental theorem of line integrals). The gradient theorem shows that the line integral of the gradient of a function is path independent, and only depends on the starting and ending points. J
From playlist Vector Calculus for Engineers
Download the free PDF http://tinyurl.com/EngMathYT A basic tutorial on the gradient field of a function. We show how to compute the gradient; its geometric significance; and how it is used when computing the directional derivative. The gradient is a basic property of vector calculus. NOT
From playlist Engineering Mathematics
This video explains what information the gradient provides about a given function. http://mathispower4u.wordpress.com/
From playlist Functions of Several Variables - Calculus
What is Gradient, and Gradient Given Two Points
"Find the gradient of a line given two points."
From playlist Algebra: Straight Line Graphs
Find the Gradient Vector Field of f(x,y)=ln(2x+5y)
This video explains how to find the gradient of a function. It also explains what the gradient tells us about the function. The gradient is also shown graphically. http://mathispower4u.com
From playlist The Chain Rule and Directional Derivatives, and the Gradient of Functions of Two Variables
Introduction to the Gradient Theory and Formulas
Introduction to the Gradient Theory and Formulas If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)
From playlist Calculus 3
Example on gradient identities for functions of two variables.
From playlist Engineering Mathematics
Ex: Find the Gradient of the Function f(x,y)=xy
This video explains how to find the gradient of a function of two variables. The meaning of the gradient is explained and shown graphically. Site: http://mathispower4u.com
From playlist The Chain Rule and Directional Derivatives, and the Gradient of Functions of Two Variables
Find the Gradient Vector Field of f(x,y)=x^3y^5
This video explains how to find the gradient of a function. It also explains what the gradient tells us about the function. The gradient is also shown graphically. http://mathispower4u.com
From playlist The Chain Rule and Directional Derivatives, and the Gradient of Functions of Two Variables
We introduce the implicit function theorem ansatz, as a way for solving optimization problems with equality constraints.
From playlist There and Back Again: A Tale of Slopes and Expectations (NeurIPS-2020 Tutorial)
22: Gradient Theorem - Valuable Vector Calculus
Video on directional derivatives: https://youtu.be/v98uipDYuqU Explanation of the fundamental theorem of calculus for line integrals, also known as the gradient theorem. The gradient theorem is important because it gives us information about path-independent vector fields and the integral
From playlist Valuable Vector Calculus
Fundamental theorem of line integrals. Chris Tisdell UNSW
This lecture discusses the "fundamental theorem of line integrals for gradient fields". The topic is motivated and the theorem is stated and proved. A number of examples are presented to illustrate the theory.
From playlist Vector Calculus @ UNSW Sydney. Dr Chris Tisdell
The Fundamental Theorem of Line Integrals // Big Idea & Proof // Vector Calculus
Back in 1st year calculus we have seen the Fundamental Theorem of Calculus II, which loosely said that integrating the derivative of a function just gave the difference of the function at the endpoints. That is, what happened in the middle did not matter. In this video we upgrade to the Fu
The Tartar's method of oscillating test functions and correctors (Lecture 2) by Patrizia Donato
PROGRAM: MULTI-SCALE ANALYSIS AND THEORY OF HOMOGENIZATION ORGANIZERS: Patrizia Donato, Editha Jose, Akambadath Nandakumaran and Daniel Onofrei DATE: 26 August 2019 to 06 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Homogenization is a mathematical procedure to understa
From playlist Multi-scale Analysis And Theory Of Homogenization 2019
On the structure of measures constrained by linear PDEs – Guido De Philippis – ICM2018
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From playlist Partial Differential Equations
PHYS 102 | The Gradient 3 - Fundamental Theorem of the Gradient
The Fundamental Theorem of Calculus can be applied to the Gradient. Here we also introduce the del operator. -----Differential Maxwell's Eqns playlist - https://www.youtube.com/playlist?list=PL9_sR6QqqcymvpKToRdhxjmQgCIU5xlDM -----Use the channel, or take the courses at edX - https://www.
From playlist PHYS 102 | Differential Form of Maxwell's Equations
Line integrals: Fundamental theorem
Free ebook http://tinyurl.com/EngMathYT A basic lecture on the fundamental theorem of line integrals, which involves only the end-points of the path of integration. Such an idea is a generalization of the fundamental theorem of calculus for functions of one variable. Plenty of examples a
From playlist Engineering Mathematics
Tensor Calculus 2b: Two Geometric Gradient Examples (Torricelli's and Heron's Problems)
This course will eventually continue on Patreon at http://bit.ly/PavelPatreon Textbook: http://bit.ly/ITCYTNew Errata: http://bit.ly/ITAErrata McConnell's classic: http://bit.ly/MCTensors Table of Contents of http://bit.ly/ITCYTNew Rules of the Game Coordinate Systems and the Role of Te
From playlist Introduction to Tensor Calculus