Q:
# How Do You Determine the Gradient in Spherical Coordinates?

The spherical coordinate system is the method of giving the specific direction of a point in a three dimensional space. The coordinates are represented by rho, theta and phi. The coordinates are first changed into rectangular coordinates. This is done in order to simplify the initial equation. The equation is then partially differentiated to determine the gradient.

Continue Reading
Credit:
Peter Dazeley
Photographer's Choice
Getty Images

The gradient is a concept used to generalize a function’s derivative in one dimension to a function in numerous dimensions. The spherical coordinate system is more convenient in the creation of points in three dimensional space. Rho is the measured distance from the origin to the point, theta is the angle from the origin on the x axis to the line connecting the point, and phi is the angle between the point and the point from the z axis. The partial derivatives are then multiplied by specific vectors in the coordinate systems. These vectors are the simple directions from the point of origin to the given specified point through any of the three axes in the dimension space. The unit vector in most cases is assumed to be u.

The multiplication by the unit vector is the final step towards obtaining the gradient in a spherical coordinate system.

Learn more about Geometry-
Q:
## How Do You Convert Polar Coordinates to Rectangular Coordinates?

A: There are two formulas to convert polar coordinates to rectangular coordinates. The cosine of the angle times the radius determines the rectangular x-coord... Full Answer >Filed Under: -
Q:
## How Do You Draw a Plane in Geometry?

A: Plane geometry is the sub-category of geometry that deals with flat surfaces and the coordinates, lines and shapes on them. To draw a plane, use grid or gr... Full Answer >Filed Under: -
Q:
## What Is the Definition of the Term "vector Quantity"?

A: A vector quantity is a quantity of something which possesses both magnitude and direction. Magnitude is simply the size or amount of the quantity. For exam... Full Answer >Filed Under: -
Q:
## How Do You Draw a Rectangular Prism?

A: To draw a rectangular prism, determine what direction you want it to face, draw the two ends and connect them with lines using the vanishing point and othe... Full Answer >Filed Under: