# Multivariable calculus

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**Multivariable calculus** is the study of calculus as it applies to functions of multiple independent variables. It is usually studied in the third semester of calculus.

While it is sometimes used synonymously with vector calculus, it is a slightly broader field as it also covers non vector-related topics, such as partial derivatives and multiple integrals.

## Topics in multivariable calculus

- Limits and continuity in higher dimensions
- Total and partial derivatives
- Gradient, divergence, and curl
- Jacobian matrices, coordinate transformations, and integrals in spherical and cylindrical coordinates
- Parametric functions in higher dimensions, curvature, radius of curvature, and torsion of a function, parametrization of functions
- Lagrange multipliers
- Directional derivatives
- Multiple integrals
- Flux
- Line and surface integrals
- Laplace operators