Math Insight

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• Green's theorem examples
  Examples of using Green's theorem to calculate line integrals
• Using Green's theorem to find area
  A trick to use Green's theorem to calculate the area of a region
• The idea behind Green's theorem
  Introduction to Green's theorem, based on the intuition of microscopic and macroscopic circulation of a vector field.
• Green's theorem with multiple boundary components
  How Green's theorem applies even to regions with holes in them
• Other ways of writing Green's theorem
  Small variations in the way you can write Green's theorem
• When Green's theorem applies
  A discussion of situations where you are allowed to use Green's theorem.
• Harvest of natural populations
  Optimizing the yield when harvesting a population that is growing according to a discrete logistic equation.
• Harvest of natural populations exercise answers
  Answers to selected exercises on optimizing the yield when harvesting a population.
• Harvest of natural populations exercises
  Exercises on optimizing the yield when harvesting a population.
• Historical and theoretical comments: Mean Value Theorem
  Comments on the traditional way that Taylor polynomials are taught as inextricably linked with issues about infinite series.
• How large an interval with given tolerance for a Taylor polynomial?
  Given a Taylor polynomial expanded around a point, on how large an interval around the point does it achieve a required tolerance?
• The hyperbolic paraboloid
  Description of the hyperbolic paraboloid with interactive graphics that illustrate cross sections and the effect of changing parameters.
• The hyperboloid of one sheet
  Description of the hyperboloid of one sheet with interactive graphics that illustrate cross sections and the effect of changing parameters.
• The hyperboloid of two sheets
  Description of the hyperboloid of two sheets with interactive graphics that illustrate cross sections and the effect of changing parameters.
• The idea of the derivative of a function
  The derivative of a function as the slope of the tangent line.
• Implicit differentiation
  Differenting a function that is defined implicitly in terms of a relation between two variables.
• Developing intuition about the indefinite integral
  An intuitive exploration into the properties of the indefinite integral, illustrated by interactive graphics.
• Definition: Independent variable definition
  An independent variable is a variable that represents a quantity that is being manipulated in an experiment. In the context of a function, the independent variable is the input to the function.
• Introduction to an infectious disease model
  
• An infectious disease model with immunity
  

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