Math Insight

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• Elementary discrete dynamical systems problems, part 2
  More sample problems illustrating discrete dynamical systems.
• Discrete dynamical systems as function iteration
  The simplest versions of discrete dynamical systems can be viewed as evolving due to iterating a function repeatedly.
• An introduction to discrete dynamical systems
  Overview of discrete dynamical systems, focusing on the simplest one-dimensional case, where the dynamics are given by iterating a function.
• Discrete dynamical system iteration examples
  Examples of iterating discrete dynamical system models.
• A discrete SIR infectious disease model
  
• Distance from point to plane
  A derivation, aided by an interactive graphic, of the formula for the distance from a point to a plane.
• Distance from point to plane example
  An example of calculating the distance from a point to a plane.
• Divergence and curl example
  An example problem of calculating the divergence and curl of a vector field.
• Divergence and curl notation
  Different ways to denote divergence and curl.
• The idea of the divergence of a vector field
  Intuitive introduction to the divergence of a vector field. Interactive graphics illustrate basic concepts.
• Subtleties about divergence
  Counterexamples illustrating how the divergence of a vector field may differ from the intuitive appearance of the expansion of a vector field.
• Divergence theorem examples
  Examples of using the divergence theorem.
• The idea behind the divergence theorem
  Introduction to divergence theorem (also called Gauss's theorem), based on the intuition of expanding gas.
• Definition: Domain definition
  The domain of a function is the set of its possible inputs.
• Domain of functions
  How to determine the domain of a function.
• The dot product
  Introduction to the dot product with a focus on its basic geometric properties.
• Dot product examples
  Examples of calculating the dot product of two- and three-dimensional vectors.
• The formula for the dot product in terms of vector components
  Derivation of the component formula for the dot product, starting with its geometric definition based on projection of vectors.
• Dot product in matrix notation
  How to view the dot product between two vectors as a product of matrices.
• The double cone
  Description of the double cone with interactive graphics that illustrate cross sections and the effect of changing parameters.

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