Math Insight

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• Function composition
  How composing two functions forms a new combined function.
• Function composition examples
  Examples of composing functions to form a new combined function.
• Function examples
  Basic examples of functions illustrating the definition of a function.
• Definition: Function iteration form definition
  A discrete dynamical system is in function iteration form when it is written so that the new value of the state variable is a function of the previous value of the state variable.
• The function machine
  The function machine metaphor helps explain the definition and properties of a function.
• Function machine composition
  Composing two functions simply means connecting together their respective function machines.
• The function machine inverse
  The inverse of a function is represented by running its function machine backwards.
• Function machine parameters
  Illustrating function parameters as dials that influence the behavior of a function machine.
• Function notation
  A description of how we denote functions.
• Functions and inequalities worksheet
  Worksheet on evaluating functions and manipulating inequalities.
• The fundamental theorems of vector calculus
  A summary of the four fundamental theorems of vector calculus and how the link different integrals.
• Generating networks with a desired degree distribution
  Overview of algorithms that allow one to generate networks with a prescribed degree distribution
• Generating networks with a desired second order motif frequency
  An approach to generating networks with given frequency of second order connection motifs.
• The gradient theorem for line integrals
  A introduction to the gradient theorem for conservative or path-independent line integrals.
• A simple example of using the gradient theorem
  An example of using the gradient theorem to calculate the line integral of a conservative, or path-independent, vector field.
• The gradient vector
  The gradient vector is the matrix of partial derivatives of a scalar valued function viewed as a vector.
• Definition: Graph definition
  By one definition, a graph is network, i.e., a set of objects (called vertices or nodes) that are connected together. A graph can also refer to a function graph, i.e., a plot of a function.
• Definition: Vertex definition
  A vertex of a graph is one of the objects that are connected together.
• A graphical approach to finding equilibria of discrete dynamical systems
  By plotting the updating function and the diagonal, one can read off the equilibria from their intersections of the two graphs.
• Graphing rational functions, asymptotes
  Finding vertical and horizontal asymptotes of functions to aid in graphing them.

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