Proving F = grad(f) with 3 Variables - Physics Forums
2010年10月4日 · For two variables, F = grad(f) if only if partial P / partial y is equal to partial Q / partial x where, P and Q represent the x, y function, P(x,y) and Q(x,y) For example: F(x,y) = P(x,y) + Q(x,y) Now the question is, for three variables, I have P + Q + R. Is proving partial P / partial y = partial Q / partial x enough to say that F = grad(f)?
Proof: curl curl f = grad (div (f)) - grad^2 - Physics Forums
2011年11月19日 · Try evaluating the del x F first using the determinant representation, and then use the result of that and then use del x result to get your final result. It will probably be a little messy, but it shouldn't take you too long I think to expand out the LHS.
Gradient vector as Normal vector - Physics Forums
2008年5月21日 · In the context of functions of two variables, where the maximums and minimums of a function f(x, y) are subject to the constraint g(x, y) = 0, the extrema occur where grad(f) is parallel to grad(g) in the xy-plane, that is, where the level curves of f(x, y) = (some constant) and g(x, y) = 0 are tangent to one another.
What is the relationship between the gradient and the normal …
2010年11月16日 · The gradient vector, of a function, at a given point, is, as Office Shredder says, normal to the tangent plane of the graph of the surface defined by f(x, y, z)= constant. We can write the "directional derivative", the rate of change of the function f in the direction that makes angles [itex]\theta[/itex], [itex]\phi[/itex], and [itex]\psi ...
Understanding Scalar Fields: Div, Curl, RotGrad & DivGrad
2010年6月14日 · What does div(f) curl(f) rotgrad(f) divgrad(f) stand for? I need to know if a scalar field can have the meanings of roration and diverge like a vector field if f is a scalar field, then grad(f) is a vector fields
Solve Gradient Squared: ((grad(f(x,y,z))))^2 - Physics Forums
2012年9月26日 · How do you solve ((grad(f(x,y,z))))^2? Insights Blog -- Browse All Articles -- Physics Articles Physics Tutorials Physics Guides Physics FAQ Math Articles Math Tutorials Math Guides Math FAQ Education Articles Education Guides Bio/Chem Articles Technology Guides Computer Science Tutorials
Show that grad f(x) = 0 when x is a local minimum of f - Physics …
2016年8月17日 · Show that f'(x) grad f(x) is positive. Aug 18, 2016; Replies 5 Views 2K. Prove that this series converges ...
Prove F=-grad(U): Euler-Lagrange Equation Theorem - Physics …
2008年9月16日 · Hi, all. A friend challenged me to prove that F = -grad(U), and now that I did, I'm thinking of submitting it to the university I'm applying to. Before I do so, I want to see if this is right. Theorem: For a particle in a conservative force field, F = -grad(U). Proof: In a conservative...
Solving Grad f and Grad g for Math Problem - Physics Forums
2008年3月27日 · Decide an equation for tangent plane to the surface z=f (x, y) in the point (a, b, ab). Use differential to f in order to calculate a close value to f (9a/10, 6b/5). In which points, key planet is to the surface z=f (x, y) horizontal?
Gradient theorem, why F=-grad(U) - Physics Forums
2012年12月24日 · If we put them into a common context, then F is a force field. A line integral of F represents the work done by the force field on a free particle that traverses that path. The amount of work done is equal to the particle's gain in kinetic energy, which is equal to its loss of potential energy.