The Gradient Vector

University
Massachusetts Institute of Technology
Course
Multivariable Calculus
Pages

1

Academic year

2022
Author

Sporkz
Views

13

p {margin: 0; padding: 0;} .ft00{font-size:20px;font-family:Arial;color:#000000;} .ft01{font-size:18px;font-family:Arial;color:#000000;} .ft02{font-size:18px;font-family:ArialMT;color:#000000;} .ft03{font-size:18px;line-height:22px;font-family:Arial;color:#000000;} .ft04{font-size:18px;line-height:22px;font-family:ArialMT;color:#000000;} The gradient ● A gradient vector is a vector that is used to describe the direction and magnitude of a uniform change in a scalar quantity (e.g. temperature, pressure, or density). Thegradient of a function at a point is the directional derivative of that function in theneighborhood of that point. Let's summarize what we learned. We found an equation that allows us to find the normalvector of a level curve at any point on the curve. The negative 4, 2 were the coefficients of the x and y in the linear approximation.Moreover, the coefficients of the delta x and delta y were the same. So the equations were just x derivatives and y derivatives. So, if I take the derivative of f at a point (vector, x derivative, y derivative), the vectorformed by that derivative is perpendicular to the level curves at that point. The vector (f sub x, f sub y) is called the gradient of f. We'll study it next.