Math Insight

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• Definition: State space definition
  The state space of a dynamical system is the set of all possible states of the system.
• Definition: State variable definition
  A state variable is one of the variables used to describe the state of a dynamical system.
• A stochastic process introduction
  
• Stokes' theorem examples
  Examples illustrating how to use Stokes' theorem.
• The idea behind Stokes' theorem
  Introduction to Stokes' theorem, based on the intuition of microscopic and macroscopic circulation of a vector field and illustrated by interactive graphics.
• Proper orientation for Stokes' theorem
  The importance of orientating the surface and its boundary correctly when using Stokes' theorem.
• Definition: Definition of subset
  A set $A$ is a subset of another set $B$ if all elements of the set $A$ are elements of the set $B$. The subset relationship is denoted as $A \subset B$.
• Definition: Definition of the summation symbol
  The symbol `\sum` indicates summation and is used as a shorthand notation for the sum of terms that follow a pattern.
• Definition: Definition of superset
  A set $A$ is a superset of another set $B$ if all elements of the set $B$ are elements of the set $A$. The superset relationship is denoted as $A \supset B$.
• Cross sections of a surface
  A sketch of how to determine the cross sections of surfaces and use them to understand the shape of a surface.
• Surfaces defined implicitly
  Graphing surfaces defined implicitly through an equation.
• Surfaces as graphs of functions
  Illustration of how the graph of a scalar-valued function of two variables is a surface.
• Scalar surface integral examples
  Examples of calculating the integral of scalar functions over parametrized surfaces.
• Introduction to a surface integral of a scalar-valued function
  How to define the integral of a scalar-valued function over a parametrized surface.
• Vector surface integral examples
  Examples of calculating the integral of vector fields over parametrized surfaces.
• Introduction to a surface integral of a vector field
  How to define the integral of a vector field over a parametrized surface, illustrated by interactive graphics.
• Surfaces of revolution
  A description of how surfaces of revolutions are graphs of functions of two variables that depend only on the radius.
• Definition: Symmetric matrix definition
  A matrix A is symmetric if it is equal to its transpose, i.e., $A=A^T$.
• The idea of synchrony of phase oscillators
  The concepts of a phase oscillator and synchronization of a collection of phase oscillators are introduced through interactive applets.
• The tangent line as a linear approximation
  How the tangent line to the graph of a function is a linear approximation to the function close by the tangent point.

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