Math Insight

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• Tangent and normal lines
  How to compute the tangent and normal lines to the graph of a function.
• Taylor polynomial introduction
  An introduction to the Taylor polynomial, focusing on the quadratic polynomial
• Multivariable Taylor polynomial example
  Example of a calculating a second-degree multivariable Taylor polynomial.
• Quadratic Taylor polynomial examples
  Examples of calculating quadratic Taylor polynomials.
• Taylor polynomials: formulas
  Different ways of writing Taylor's formula with remainder term.
• Introduction to Taylor's theorem for multivariable functions
  Development of Taylor's polynomial for functions of many variables.
• Definition: Trajectory definition
  In dynamical systems, a trajectory is the set of points in state space that are the future states resulting from a given initial state.
• Definition: Definition of the transitivity of a graph
  The transitivity of a graph is three times the ratio between the number of triangles and the number of connected triples of nodes in a graph.
• Translation, rescaling, and reflection
  An illustration using interactive graphics how to translate, rescale, and reflect graphs of functions of two variables.
• Trigonometric integrals
  Using trigonometric identities to calculate integrals involving trigonometric functions.
• Trigonometric substitution
  Using trigonometric substitution to simplify integrals involving square roots.
• Triple integral change of variable examples
  Examples of changing variables in triple integrals.
• Introduction to changing variables in triple integrals
  Introduction to the concepts behind a change of variables in triple integrals.
• Triple integral change of variables story
  Story illustrating the process of changing variables in triple integrals.
• Volume calculation for changing variables in triple integrals
  A derivation of how a mapping that changes variables in triple integrals transforms volume.
• The cross section method for determining triple integral bounds
  Explanation of the cross section method for turning a triple integral into a double integral combined with a single integral in order to compute the limits of integration.
• Triple integral examples
  Examples showing how to calculate triple integrals, including setting up the region of integration and changing the order of integration.
• Introduction to triple integrals
  An introduction to the definition of triple integrals as well as their formulation as iterated integrals.
• The shadow method for determining triple integral bounds
  Explanation of the shadow method for turning a triple integral into a double integral combined with a single integral in order to compute the limits of integration.
• Solutions to two dimensional autonomous differential equation problems
  Solutions to sample problems involving analysis of a two coupled autonomous differential equations.

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