multivariable function

Let us assume that we wish to integrate a multivariable function f over a region A.

High-dimensional model representation is a finite expansion for a given multivariable function.

The general equation for the linearization of a multivariable function at a point is:

Here is a version for discontinuous multivariable functions.

The vertex operators may also be written as a functional of a multivariable function f as:

In next section, we will show that, if the multivariable function is continuous, so are all these univariable functions, but the converse is not necessarily true.

For more on the treatment of row vectors and column vectors of multivariable functions, see matrix calculus.

What Captain Saxtorph decides-has decided to do is a multivariable function of the logic of the situation and of his personality.

Partial differential equations - differential equation that contains unknown multivariable functions and their partial derivatives.

This is because the total derivative of a multivariable function has to record much more information than the derivative of a single-variable function.

Our problem is to find the minimum af a linear multivariable function with the constrain that all the solutions must be integer and minimum in one norm.

In other words, the Jacobian for a scalar-valued multivariable function is the gradient and that of a scalar-valued function of single variable is simply its derivative.

Usually, although not in all cases, the partial derivative is taken in a multivariable function, (i.e., the function has three or more variables, whether independent or dependent variables).

A domain of a real smooth function can be the real coordinate space (which yields a real multivariable function), a topological vector space, an open subset of them, or a smooth manifold.

Coordinate descent is based on the idea that the minimization of a multivariable function can be achieved by minimizing it along one direction at a time, i.e., solving univariate (or at least much simpler) optimization problems in a loop.

Multivariable functions of real variables arise inevitably in engineering and physics, because observable physical quantities are real numbers (with associated units and dimensions), and any one physical quantity will generally depend on a number of other quantities.

With the definitions of multiple integration and partial derivatives, key theorems can be formulated, including the fundamental theorem of calculus in several real variables (namely Stokes' theorem), integration by parts in several real variables, and Taylor's theorem for multivariable functions.