Math Insight

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• Scale-free networks
  Scale-free networks are those that have a power law degree distribution.
• The second and higher derivatives
  Taking derivatives multiple times to calculate the second or higer derivative.
• Definition: Definition of the set membership symbol
  The symbol $\in$ indicates set membership and means “is an element of” so that the statement $x \in A$ means that $x$ is an element of the set $A$.
• Definition: Simple curve definition
  A simple curve is a curve that does not cross itself.
• A simple spiking neuron model
  An introduction to the Fitzhugh Nagumo model of a spiking neuron, including basic phase plane analysis.
• The simplest integration substitutions
  Reversing a simple chain rule application to compute integrals.
• One of the simplest types of networks
  An introduction and motivation behind one of the simplest types of networks, the Erd
• Definition: Simply connected definition
  A simply connected domain is a path-connected domain where one can continuously shrink any simple closed curve into a point while remaining in the domain.
• Solutions to single autonomous differential equation problems
  Solutions to sample problems involving analysis of a single autonomous differential equation.
• Single autonomous differential equation problems
  Sample problems involving analysis of a single autonomous differential equation.
• Small world networks
  Small world networks are those that have a relative small mean path length but high transitivity.
• More details on solving linear discrete dynamical systems
  
• Examples of solving linear discrete dynamical systems
  Examples demonstrating how the solution to a linear discrete dynamical system is an exponential.
• Solving linear discrete dynamical systems
  One can solve a linear discrete dynamical system analytically. The result is an exponential function of the time step.
• Solving single autonomous differential equations using graphical methods
  Using graphical methods, one can observe where the rate of change is positive or negative and determine the behavior of a solution to a differential equation.
• Spherical coordinates
  Illustration of spherical coordinates with interactive graphics.
• Spruce budworm outbreak model
  A graphical analysis of a differential equation model reveals how the spruce budworm could devastate forests every 40 years.
• The stability of the asynchronous state as function of largest eigenvalue
  The network influences the stability of the asynchronous state through the largest eigenvalue of the adjacency matrix.
• The stability of equilibria of a differential equation
  Identifying stable and unstable equilibria of a differential equation by graphically solving the equation for nearby initial conditions.
• The standard unit vectors
  The standard unit vectors are the vectors of length one that point along the positive coordinates axes.

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