### Pages similar to: Introduction to a line integral of a scalar-valued function

- 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 are independent of parametrization

Description of how the value of a line integral over a curve is independent of the parametrization of the curve. - The arc length of a parametrized curve

Introduction to the arc length of a parametrized curve. The arc length definition is illustrated with interactive graphics. - Examples of scalar line integrals

Examples demonstrating how to calculate line integrals of scalar-valued functions. - 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 line integral examples

Example of calculating line integrals of vector fields. - Introduction to changing variables in double integrals

Introduction to the concepts behind a change of variables in double integrals. The transformation is illustrated with interactive graphics. - Introduction to double integrals

The definition of a double integral is motivated through a hair density example. - Introduction to changing variables in triple integrals

Introduction to the concepts behind a change of variables in triple integrals. - Using the Forward Euler algorithm to solve pure-time differential equations

By pretending that the slope of a function is constant over small intervals, we following tangent lines to estimate the solution to pure-time differential equations. - Introduction to a surface integral of a scalar-valued function

How to define the integral of a scalar-valued function over a parametrized surface. - Introduction to a surface integral of a vector field

How to define the integral of a vector field over a parametrized surface, illustrated by interactive graphics. - An introduction to parametrized curves

An introduction to how a vector-valued function of a single variable can be viewed as parametrizing a curve. Interactive graphics illustrate the way in which the function maps an interval onto a curve. - Introduction to triple integrals

An introduction to the definition of triple integrals as well as their formulation as iterated integrals. - Double integrals as volume

Explanation of how double integrals could be used to represent volume. - Triple integral change of variables story

Story illustrating the process of changing variables in triple integrals. - Calculating the formula for circulation per unit area

A sketch of the proof for the formula for the component of the curl of a vector field. - Double integral change of variable examples

Examples of calculating double integrals through changing variables. - 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. - The gradient theorem for line integrals

A introduction to the gradient theorem for conservative or path-independent line integrals.