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What is the physical interpretation of gradient of a scalar field and directional derivative and what are its applications?
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∙ 13y ago
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∙ 13y ago
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The derivative finds the of a curve?
The gradient of the tangents to the curve.
What is a gradient in maths?
The gradient of a function, in a given direction, is the change in the value of the function per unit change in the given direction. It is, thus, the rate of change of the function, with respect to the direction. It is generally found by calculating the derivative of the function along the required direction. For a straight line, it is simply the slope. That is the "Rise" divided by the "Run".
How do you work out the gradient of a perpendicular line?
basically the reciprocal of the original lines gradient is going to be the gradient for the perpendicular line (remember the signs should switch). For example if i had a line with the gradient of 3, then the gradient of the perpendicular line will be -1over3. But if the line had the gradient of -3, then the line perpendicular to that line will have the gradient 1over3.
How do you find the gradient of two points?
If A = (xa, ya) and B = (xb, yb) and xa is not equal to xb, then gradient of AB = (ya - yb)/(xb - xb).If xa = xb then the gradient is undefined.
What is the gradient temperature for 15 C and 20 C?
A gradient requires two variables. There is information on only one.
What is the physical interpretation of gradient of a scalar field and directional derivative and its application?
If you think of it as a hill, then the gradient points toward the top of the hill. With the same analogy, directional derivatives would tell the slope of the ground in a direction.
What is the physical interpretation of gradient of a scalar field and directional derivative?
The elevation of points on a hill is a scalar 'field'. It can have a different value at every point, but each one is a scalar value. Imagine a lumpy bumpy irregular hill, and pick a point to talk about, say, somewhere on the side of the hill. At that point, the directional derivative of the elevation is the rate at which the elevation changes leaving the point in that direction. It has different values in different directions: If you're looking up the hill, then the d.d. is positive in that direction; if you're looking down the hill, the d.d. is negative in that direction. If you're looking along the side of the hill, the d.d. could be zero, because the elevation doesn't change in that particular direction. The directional derivative is a vector. The direction is whatever direction you're talking about, and the magnitude is the rate of change in that direction. The gradient is the vector that's simply the greatest positive directional derivative at that point. Its direction is the direction of the steepest rise, and its magnitude is the rate of rise in that direction. If your hill is, say, a perfect cone, and you're on the side, then the gradient is the vector from you straight toward the top, with magnitude equal to the slope of the side of the cone. Any other vector is a directional derivative, with a smaller slope, and it isn't the gradient.
Why the second derivative negative for Maxima?
When you solve for the 2nd derivative, you are determining whether the function is concave up/down. If you calculated that the 2nd derivative is negative, the function is concave down, which means you have a relative/absolute maximum, given that the 1st derivative equals 0. To understand why this is, think about the definition of the 2nd derivative. It is a measure of the rate of change of the gradient. At a maximum, the gradient starts positive, becomes 0 at the maximum itself and then becomes negative, so it is decreasing. If the gradient is going down, then its rate of change, the 2nd derivative, must be negative.
The derivative finds the of a curve?
The gradient of the tangents to the curve.
What is the derivative of -1?
The derivative of a linear function is always its gradientIn the function y = x-1, the gradient is 1 as 1 is the co-efficient of 1x.
What is the derivative of 1/x?
The derivative of a linear function is always its gradientIn the function y = x-1, the gradient is 1 as 1 is the co-efficient of 1x.
What is the derivative of x-1?
The derivative of a linear function is always its gradientIn the function y = x-1, the gradient is 1 as 1 is the co-efficient of 1x.
How do you Find derivative to get the slope?
the deivative of a function is the gradient, at a point if you can sub in the x coordinate for that point
What does gradient mean in physics?
Gradient means the vector derivative (Del) of a scalar quantity, e.g. for the Gravity Potenttial/scalar energy, Del-mGm/r= mw2R.
What is the gradient of the tangent to the curve at x equals 2 if Y equals x2?
Gradient to the curve at any point is the derivative of y = x2 So the gradient is d/dx of x2 = 2x. When x = 2, 2x = 4 so the gradient of the tangent at x = 2 is 4.
Define term gradient give definition of fick's law?
Fick's laws of diffusion describe diffusion and can be used to solve for the diffusion, the concentration gradient (spatial derivative), or in simplistic terms the concept.
What are some applications for the calculus?
Calc. has many applications. A few of them are calculating: work, area, volume, gradient, center of mass, surface area...
