List of all pages
- Introduction to Calculus Refresher
Introduction describing the Calculus Refresher notes. - Definition: Inverse function definition
An inverse function is a function that undoes the action of the another function. - Inverse function examples
Examples of forming an inverse function that does undoes the action of another function. - Length, area, and volume factors
A summary of the expansion factors that arise from mappings in integrals of multivariable calculus. - Length of curves
An integral to find the length of a curve. - Level set examples
Examples demonstrating how to calculate level curves and level surfaces. - Level sets
A introduction to level sets. Illustrates level curves and level surfaces with interactive graphics. - L'Hospital's rule
A way to simplify evaluation of limits when the limit is an indeterminate form. - Limits with cancellation
Calculating limits of a fraction my canceling factors from the numerator and denominator. - Limits of exponential functions at infinity
Calculating limits of exponential functions as a variable goes to infinity. - Limits at infinity
Calculating limits as a variable goes to infinity. - Line integrals as circulation
Definition of circulation as the line integral of a vector field around a closed curve. - Line integrals are independent of parametrization
Description of how the value of a line integral over a curve is independent of the parametrization of the curve. - Examples of scalar line integrals
Examples demonstrating how to calculate line integrals of scalar-valued functions. - Introduction to a line integral of a scalar-valued function
Introduction with interactive graphics illustrating the line integral of a scalar-valued function and informally deriving the formula for calculating the integral from the parametrization of the curve. - Alternate notation for vector line integrals
An alternative notation for the line integral of a vector field is introduced. - Vector line integral examples
Example of calculating line integrals of vector fields. - Introduction to a line integral of a vector field
The concepts behind the line integral of a vector field along a curve are illustrated by interactive graphics representing the work done on a magnetic particle. The graphics motivate the formula for the line integral. - Parametrization of a line
Introduction to how one can parametrize a line. Interactive graphics illustrate basic concepts. - Parametrization of a line examples
Examples demonstrating how to calculate parametrizations of a line.
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