Multivariable Calculus Apps:

  • CalcPlot3D – a multivariable calculus visual exploration tool that allows the user to graph points, vectors, curves, surfaces, vector fields, and more.  It also works with redblue or redcyan 3D glasses.
  • CalcPlot3D (en español) – This version of CalcPlot3D is completely in Spanish!
  • Projection of Vectors Exploration – this simple app allows the user to grab the tips of the two displayed vectors and vary them, observing the projection of the green vector onto the blue one.

Differential Equations Apps:

  • Direction Field Explorer – an app designed to allow you to visually verify the general solution of a 1st-order differential equation.  You can enter the differential equation, solved for dy/dx (or whatever variables it involves, setting these in the app).  You can also enter the general solution using the independent variable and C as the parameter.  This parameter C can then be varied either with the scrollbar or by entering a value to see if the resulting solution curve fits nicely in the direction field or not.  If the vectors/slope segments are not tangent to the path of the curve at all points, the general solution is not correct.  That is, if for some value of C, the solution curve does not go with the flow of the vectors in the direction field, then the general solution is incorrect.

Linear Algebra Apps:

  • LinAlg4x4 – a simplified version of CalcPlot3D that allows the user to apply a 4 x 4 transformation matrix to a 3D surface and the containing box to see its effect.  The matrix can then be varied or left unchanged and applied to the view, multiple times.