Pages similar to: Orienting surfaces
- A Möbius strip is not orientable
Explanation why a Möbius strip cannot be oriented by choosing a normal vector to point to one side. - An introduction to parametrized surfaces
An introduction to how a vector-valued function of two variables can be viewed as parametrizing a surface. Interactive graphics illustrate the way in which the function maps a planar region onto a surface. - Surface area of parametrized surfaces
An introduction to surface area of parametrized surfaces, illustrated by interactive graphics. - Normal vector of parametrized surfaces
How to calculate the normal vector from the parametrization of a surface. - Parametrized surface examples
Examples showing how to parametrize surfaces as vector-valued functions of two variables. - Calculation of the surface area of a parametrized surface
A calculation deriving the expression for the surface area of a parametrized surface. - Parametrized surface area example
An example of calculating the surface area of a parametrized surface. - 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. - 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. - Derivatives of parameterized curves
The derivative of the vector-valued function parameterizing a curve is shown to be a vector tangent to the curve. - Tangent lines to parametrized curves
The tangent vector given by the derivative of a parametrized curve forms the basis for the equation of a line tangent to the curve. - Tangent line to parametrized curve examples
Examples showing how to calculate the tangent line to a parameterized curve from the derivative of the underlying vector-valued function. - Parametrized curve and derivative as location and velocity
Description of a parametrization of a curve as the position of a particle and the derivative as the particle's velocity. Illustrated with animated graphics. - 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. - Parametrization of a plane
Introduction to how one can parametrize a plane. Interactive graphics illustrate basic concepts. - Plane parametrization example
Example showing how to parametrize a plane. - 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. - Scalar surface integral examples
Examples of calculating the integral of scalar functions over parametrized surfaces.
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