Converge enables students to:

Learn how to plot points and how to connect them to get a graph. Also, to make decisions about how the axes should be scaled and when enough points have been plotted.

Generate tables of values, sign graphs, and plot points in preparation for drawing graphs with or without a rectangular or polar grid.

Graph polar functions in a demo mode, where you can step through the graphing point by point, with the terminal side of drawn at each point.

Learn how to row reduce matrices step by step.

Learn the general steps for solving triangles.

Improve their understanding of operations with 2 and 3 dimensional vectors by diagramming vector operations (including cross products).

See the convergence involved in the limit of a function, Bisection Method, the Secant Method, and Newton's Method both graphically and numerically, while zooming in during the convergence.

Use the sign graphs of the first two derivatives of a function to determine the graph of the function.

Develop their comprehension of limits by observing the convergence of all types of limits of functions, limits of sequences and series, limits involving the ratio and root test for sequences and series, even limits of recursive sequences.  (See Labs in Converge.)

Greatly increase their understanding of the definitions of Left and Right Hand Derivative, Definite Integral, Arc Length, Simpson's Rule, the Trapezoidal Rule, the area between two curves, the area under a polar curve, the area between two polar curves, and the volumes of different types of solids of revolution by observing the convergence (or non-convergence) related to these definitions both graphically and numerically.  (See Labs in Converge.)

Visualize and experiment with the application of the Definition of the Limit of a Function and the Mean Value Theorem.  (See Labs in Converge.)

Better understand the relationship between function and derivatives by tracing graphs with appropriate tangent lines drawn and tables of values generated.  (See Labs in Converge.)

Observe the graphing of an antiderivative of a function and relate this graph to the simultaneously displayed graph of the function.

Increase their understanding of solutions of first order differential equations by graphing direction fields and multiple solutions corresponding to different initial conditions for such equations.  (See Labs in Converge.)

Improve their comprehension of partial derivatives by observing the graphs Z=F(X,Y) and X=c (or Y=c) on one set of axes, as well as a graph of their intersection and values of corresponding partial derivatives and tangent lines on the same screen.

Greatly increase their understanding of how Taylor polynomials can be used to estimate functions by overlaying graphs of Taylor polynomials of degrees up to 100.  (See Labs in Converge.)

Better understand linear correlation by entering any linear correlation coefficient and then viewing the scatter diagram for the paired data with this correlation that is randomly generated by Converge.  (See Labs in Converge.)

Increase their understanding of curve fitting and polynomial interpolation by conveniently entering data with a mouse and fitting the data with a curve and/or interpolating the data via a polynomial.  (See Labs in Converge.)

Watch graphs of parametric equations in 3-dimensions drawn in a special demo mode where an animated right triangle helps them visualize the 3-dimensional locations of plotted points on the graphs.

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(P(Partial derivative)