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Suppose f(x,y,z) = Ax2 + Bxy + Cxyz2.   What is ▽f?

Suppose f(x,y,z) = Ax2 + Bxy + Cxyz2.   What is ▽f?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Suppose f(x,y,z) = Ax2 + Bxy + Cxyz2.   What is ▽f?

Near the surface of Earth F direction (up) We can also write this as F - (mgy) • = "Del" = â+ŷ³y + 2 ºz = a measure of how something changes in space. дz ● grav ə ду ● ● - (mgy) =-ŷ (mgy) = -mgŷ What is the meaning of f(x,y,z)?? grav ● = : -mgŷ where ŷ is unit vector that points in the y- is called "Del" or "Gradient" is an operator that converts a scalar function into a vector. If f(x,y,z) is some general function of position, f(x,y,z) is a vector that points in the direction that the function f(x,y,z) increases the fastest. Conservative forces are related to changes in potential energy: • In general, Fcons = −(PE) A conservative force points in the direction that the associated potential energy decreases the fastest. Golden Rule: Nature runs downhill! Left on her own, Nature tries to minimize the potential energy. Problem : Suppose f(x,y,z) = Ax² + Bxy + Cxyz². What is f?
Transcribed Image Text:Near the surface of Earth F direction (up) We can also write this as F - (mgy) • = "Del" = â+ŷ³y + 2 ºz = a measure of how something changes in space. дz ● grav ə ду ● ● - (mgy) =-ŷ (mgy) = -mgŷ What is the meaning of f(x,y,z)?? grav ● = : -mgŷ where ŷ is unit vector that points in the y- is called "Del" or "Gradient" is an operator that converts a scalar function into a vector. If f(x,y,z) is some general function of position, f(x,y,z) is a vector that points in the direction that the function f(x,y,z) increases the fastest. Conservative forces are related to changes in potential energy: • In general, Fcons = −(PE) A conservative force points in the direction that the associated potential energy decreases the fastest. Golden Rule: Nature runs downhill! Left on her own, Nature tries to minimize the potential energy. Problem : Suppose f(x,y,z) = Ax² + Bxy + Cxyz². What is f?
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