Applications and Uses
Techniques of multivariable calculus are used to study many objects of interest in the mental world. In particular,
| Domain/Range | Applicable techniques | ||
|---|---|---|---|
| Curves | Lengths of curves, line integrals, and curvature. | ||
| Surfaces | Areas of surfaces, surface integrals, flux through surfaces, and curvature. | ||
| Scalar fields | Maxima and minima, Lagrange multipliers, directional derivatives. | ||
| Vector fields | Any of the operations of vector calculus including gradient, divergence, and curl. |
Multivariable calculus can be applied to analyze deterministic systems that have multiple degrees of freedom. Functions with independent variables corresponding to each of the degrees of freedom are often used to model these systems, and multivariable calculus provides tools for characterizing the system dynamics.
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. Non-deterministic, or stochastic systems can be studied using a different kind of mathematics, such as stochastic calculus. Quantitative analysts in finance also often use multivariate calculus to predict future trends in the stock market.
Read more about this topic: Multivariable Calculus