Pages similar to: Polar coordinates mapping
- Determinants and linear transformations
A description of how a determinant describes the geometric properties of a linear transformation. - Polar coordinates
Illustration of polar coordinates with interactive graphics. - Linear transformations
Definition of a linear transformation of Euclidean spaces. - Area calculation for changing variables in double integrals
A derivation of how a mapping that changes variables in double integrals transforms area. - Spherical coordinates
Illustration of spherical coordinates with interactive graphics. - Cartesian coordinates
Illustration of Cartesian coordinates in two and three dimensions. - Cylindrical coordinates
Illustration of cylindrical coordinates with interactive graphics. - How linear transformations map parallelograms and parallelepipeds
Why linear transformations map parallelograms onto parallelograms and parallelepipeds onto parallelepipeds. - 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. - Matrices and linear transformations
A description of how every matrix can be associated with a linear transformation. - Double integrals as area
Explanation of how double integrals could be used to represent area. - Using Green's theorem to find area
A trick to use Green's theorem to calculate the area of a region - Surface area of parametrized surfaces
An introduction to surface area of parametrized surfaces, illustrated by interactive graphics. - 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. - Length, area, and volume factors
A summary of the expansion factors that arise from mappings in integrals of multivariable calculus. - Lines (and other items in Analytic Geometry)
How to describe the equation for a line in terms of horizontal and vertical coordinates. - Area and definite integrals
Integrating to find the area under a curve or the area between two curves. - The elliptic paraboloid
Description of the elliptic paraboloid with interactive graphics that illustrate cross sections and the effect of changing parameters.
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