Flash Applets for Math Students and Instructors:
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Multivariable Calculus Applets

  • NEW!   Contour Diagram Plotter and 3D Function Grapher Applets Combined This applet combines a contour diagram plotter and a 3D function grapher, and allows the user to toggle between the two. Since both contour maps and 3D graphs are very sensitive to the choice of x and y ranges, it is often very hard to interpret a contour diagram without seeing the corresponding 3D graph. This applet gives an opportunity to compare these two ways to visualize functions of two variables.
     
  • NEW!   Implicit Equations Grapher This applet graphs user-defined implicit equations of the form f(x,y)=g(x,y) in a user-defined x,y ranges. The syntax used for input is the same as graphing calculator syntax and the applet is very easy to use. The results are comparable with those provided by CAS like Maple.
     
  • 3D Function Graphers  Enter a formula for f(x,y) in terms of x and y, the ranges for x and y, and the graphers display the graph of the function of two variables f(x,y) in 3D. You can rotate the graph in real time and change its transparency to see the surface clearly.
     
  • Parametric Surfaces in Rectangular Coordinates  Enter parametric formulas for the x, y, and z coordinates, and the grapher will display the corresponding surface in 3D. You can rotate the graph in real time and change its transparency for better understanding of the surface.
     
  • Parametric Surfaces in Spherical Coordinates  Enter parametric formulas for the theta, phi, and rho coordinates, and the grapher will display the corresponding surface in 3D. You can rotate the graph in real time and change its transparency of the surface. You can use the next applet below to gain a better understanding of spherical coordinates.
     
  • Spherical Coordinates Presented Interactively  Move a point in 3D and see its spherical coordinates change. Many multiple choice practice problems will help you gain an insight into spherical coordinates. Especially that pesky phi coordinate!
     
  • Parametric Surfaces in Cylindrical Coordinates  Enter parametric formulas for the theta, r, and z cylindrical coordinates, and the grapher will display the corresponding surface in 3D. You can rotate the graph in real time and change its transparency of the surface.
     
  • Double Integrals in Rectangular and Polar Coordinates  Enter the limits of integration in double integrals and see the planar region that they describe. Practice finding limits in Cartesian and in polar coordinates that correspond to a given region on the plane.
     
  • Parametric Curves in 3D and Motion in 3D  Enter parametric formulas for the x, y, and z coordinates in terms of the parameter t. The applet will graph the corresponding parametric curve in 3D. The curve can be traced while the velocity and the acceleration vectors are displayed together with their approximate values. The curve can be rotated in real time with the mouse.

 

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