As you can see, the gradient is perfectly well defined without coordinates. What Alice and Bob will not agree on, is the coordinate expression of their gradients.

If we are given a vector, how can we tell if that is a gradient of a vector? And how would we find the original function? I was assigned this problem, and I know how to get a gradient of a …

The analytic gradient that you've computed looks correct to me. If you look at the function in the neighborhood of (x, y) = (1, 1), it looks approximately like x + exp (something near 0, quadratic …

2 I am studying exponential functions at the moment, and this table was presented in my textbook to show that for exponential functions with increasing 'bases' the gradient of the function …

Gradient descent is ok for your problem, but does not work for all problems because it can get stuck in a local minimum. Global optimization is a holy grail of computer science: methods …

In calculus, the antiderivative (indefinite integral) can be considered as the reverse operation of a derivative. A gradient yields a vector. Is there a similar way of reversing gradient, as you d...

Jun 6, 2015 · 8 I am learning about gradient. I understand how gradient is a vector that represents the sum of the rates of change for each component variable of a function. I am able to follow …

In sum, the gradient is a vector with the slope of the function along each of the coordinate axes whereas the directional derivative is the slope in an arbitrary specified direction.

Imagine a function $\mathbb R^2 \to \mathbb R$. Let us prescribe any non-closed (importante!) contour of gradient orthogonal to the direction of the contour with $\nabla g = \|\nabla g\|\hat …

What is the gradient of $|\vec {x}|^2$? Is it simply $2\vec {x}$, or does the answer get expressed using absolute value notation?