# CALCULUS GLOSSARY

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Title Description
Calculus Calculus is the branch of mathematics concerned with the rates of changes between variables (derivatives) as well as areas under curves that represent functions (integrals).
Chain Rule The Chain Rule is a basic rule in calculus to find the derivative of a composite function.
Continuous A function is considered Continuous if its graph has no gaps, no holes, no steps, and no cusps or discontinuities.
Continuous Function When the graph of a function has no holes, no gaps, no steps, or no discontinuities, then it is considered Continuous.
It may have cusps.
Continuously Differentiable When a function is Continuously Differentiable it is both continuous and smooth.
Convergence To approach a limit is to experience Convergence.
Mathematical series experience convergence when the sum of their expanded terms reaches a boundary or limit.
Convergent Series A series is said to be Convergent when its sum approaches a limit.
Critical Number While there are many ways to define Critical Numbers, depending on the circumstances, most generally we're interested in places where a function generates either an extreme value or a discontinuity.
Curve Beware that mathematicians consider straight lines to be Curves!
Cusp When the graph of a function comes to a sharp point, we say that point on the graph is a Cusp.
Cylindrical Shell A method for volumetric calculations especially for rotated bodies around an axis.
The small thickness of the shell is typically the differential "dx" (or dy or whatever differential represents the incremental thickness of the cylinder).

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