List of all pages
- Numerical integration
Methods to approximate the value of definite integrals and estimate the error in the approximations. - Definition: Open curve definition
An open curve is a curve where the beginning and end points are different. - An introduction to ordinary differential equations
An introduction using simple examples explaining what an ordinary differential equation is and how one might solve them. - Ordinary differential equation examples
Simple examples of solving ordinary differential equation. - Solving linear ordinary differential equations using an integrating factor
Illustration of the procedure to find an integrating factor that allows integration of a first order linear ordinary differential equation. - Examples of solving linear ordinary differential equations using an integrating factor
Examples of finding an integrating factor and integrating first order linear ordinary differential equations. - Definition: Oriented curve definition
An oriented curve is a curve where a consistent direction is defined along the curve. - Definition: Parallelepiped definition
A parallelepiped is a three-dimensional geometric solid with six faces that are parallelograms. - Definition: Parallelogram definition
A parallelogram is a quadrilateral that has two pairs of parallel sides. - Definition: Parameter definition
A parameter is a quantity that influences the output or behavior of a mathematical object but is viewed as being held constant. - 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. - Parametrized curve arc length examples
Examples of calculating the arc length of parametrized curves. - Derivatives of parameterized curves
The derivative of the vector-valued function parameterizing a curve is shown to be a vector tangent to the curve. - 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. - 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. - Orienting curves
Orienting curves by choosing a tangent vector. - 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. - 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.
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