gradient variations
manipulates the magnetic field in a + or – linear fashion allowing one slice to remain at the true magnetic strength
The gradient is a mathematical concept in calculus that measures the rate of change of a function at a given point. It provides information about the direction in which the function is increasing or decreasing the most rapidly at that point. Variations in the gradient of a function can occur when different values are plugged in for the input or independent variable.
For example, if we take the function f(x) = x^2, the gradient at any given point would be 2x. If we plug in x=1, we get a gradient of 2. However, if we plug in x=2, we get a gradient of 4. This means that the function is increasing more rapidly at x=2 than at x=1.
Additionally, the gradient may also vary depending on the direction in which we are measuring the change. This is known as directional derivatives. The directional derivative measures how much a function changes in a particular direction. For example, if we have a function f(x,y) and measure the directional derivative in the x-direction (meaning that we are only considering the change in the x-variable), we would take the partial derivative with respect to x, denoted by ∂f/∂x. Similarly, if we measure the directional derivative in the y-direction, we would take the partial derivative with respect to y, denoted by ∂f/∂y.
In summary, variations in the gradient of a function can occur depending on the input or independent variable, the direction of measurement, and the nature of the function itself.
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