Ads
related to: multivariable calculus example problems worksheet 1educator.com has been visited by 10K+ users in the past month
Search results
Results from the WOW.Com Content Network
Multivariable calculus is used in many fields of natural and social science and engineering to model and study high-dimensional systems that exhibit deterministic behavior. In economics , for example, consumer choice over a variety of goods, and producer choice over various inputs to use and outputs to produce, are modeled with multivariate ...
where the expression between bars on the right-hand side is the magnitude of the cross product of the partial derivatives of r(s, t), and is known as the surface element (which would, for example, yield a smaller value near the poles of a sphere, where the lines of longitude converge more dramatically, and latitudinal coordinates are more ...
The image of a function f(x 1, x 2, …, x n) is the set of all values of f when the n-tuple (x 1, x 2, …, x n) runs in the whole domain of f.For a continuous (see below for a definition) real-valued function which has a connected domain, the image is either an interval or a single value.
Two other well-known examples are when integration by parts is applied to a function expressed as a product of 1 and itself. This works if the derivative of the function is known, and the integral of this derivative times is also known. The first example is (). We write this as:
In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices.It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate function with respect to a single variable, into vectors and matrices that can be treated as single entities.
Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations. A simple example of such a problem is to find the curve of shortest length connecting two points. If there are no constraints, the solution is a straight line between the points. However, if the curve is constrained to ...
In multivariable calculus, an initial value problem [a] (IVP) is an ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given point in the domain. Modeling a system in physics or other sciences frequently amounts to
Here the final equality follows by the gradient theorem, since the function f(x) = | x | α+1 is differentiable on R n if α ≥ 1. If α < 1 then this equality will still hold in most cases, but caution must be taken if γ passes through or encloses the origin, because the integrand vector field | x | α − 1 x will fail to be defined there.
Ads
related to: multivariable calculus example problems worksheet 1educator.com has been visited by 10K+ users in the past month