Math Insight

List of all pages

• Double integrals as area
  Explanation of how double integrals could be used to represent area.
• 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 integral change of variable examples
  Examples of calculating double integrals through changing variables.
• Illustrated example of changing variables in double integrals
  An example illustrating with interactive graphics how changing variables transforms regions in the plane.
• Area calculation for changing variables in double integrals
  A derivation of how a mapping that changes variables in double integrals transforms area.
• 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.
• Double integral examples
  Examples of integrating double integrals over rectangles and triangles.
• 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 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.
• Double integrals as volume
  Explanation of how double integrals could be used to represent volume.
• Doubling time and half-life of exponential growth and decay
  How exponential growth is characterized by a doubling time and exponential decay is characterized by a half-life.
• Definition: Dynamical system definition
  A dynamical system is a system whose state evolves with time over a state space according to a fixed rule.
• The idea of a dynamical system
  The basic concept of a dynamical system as the evolution of something over time. The fundamental ideas of the state space and temporal evolution rules are illustrated with examples featuring interactive graphics.
• Initial dynamical systems exploration
  Exploring models of anteater population growth and lead decay in the bloodstream using interactive applets.
• The dynamics of competition between two species
  
• Elementary limits
  The simplest way to find a limit that works in the easiest cases.
• The ellipsoid
  Description of the ellipsoid with interactive graphics that illustrate cross sections and the effect of changing parameters.
• The elliptic paraboloid
  Description of the elliptic paraboloid with interactive graphics that illustrate cross sections and the effect of changing parameters.
• Environmental carrying capacity
  We examine a difference equation used to describe population growth in limited environments.

• Newest pages
• List of all applets
• List of all videos
• List of all images