Pages similar to: Alternate notation for vector line integrals
- 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. - Line integrals as circulation
Definition of circulation as the line integral of a vector field around a closed curve. - Vector line integral examples
Example of calculating line integrals of vector fields. - 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. - 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. - The idea behind Green's theorem
Introduction to Green's theorem, based on the intuition of microscopic and macroscopic circulation of a vector field. - The integrals of multivariable calculus
A summary of the integrals of multivariable calculus, including calculation methods and their relationship to the fundamental theorems of vector calculus. - Vector field overview
An overview introducing the basic concept of vector fields in two or three dimensions. - Vector fields as fluid flow
Interpretation of vector fields as velocity fields of fluids. - Function notation
A description of how we denote functions. - Introduction to double integrals
The definition of a double integral is motivated through a hair density example. - Double integrals as iterated integrals
A description of how to convert double integrals into two single integrals. - Double integral examples
Examples of integrating double integrals over rectangles and triangles. - Double integrals as volume
Explanation of how double integrals could be used to represent volume. - Examples of changing the order of integration in double integrals
Examples illustrating how to change the order of integration (or reverse the order of integration) in double integrals. - Double integrals as area
Explanation of how double integrals could be used to represent area. - Double integrals where one integration order is easier
Illustration of a region where integrating a double integral in one order is must easier than integrating in the other order. - Introduction to triple integrals
An introduction to the definition of triple integrals as well as their formulation as iterated integrals. - Triple integral examples
Examples showing how to calculate triple integrals, including setting up the region of integration and changing the order of integration.