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This applet is designed to build the student's visual intuition about the line tangent to a curve at a point being the limit of the secant lines through that point.

Differentiation: Definition and Elementary Application

Moving Secant Line

This animation shows how a secant line approximates the tangent line at a fixed point when its other intersection with the curve is forced toward the fixed one. This is a Quick Time movie.

Differentiation: Definition and Elementary Application

Measuring Slope and Plotting the Derivative

This animation shows how to use the slope of a curve to plot the derivative for that curve.

Differentiation: Definition and Elementary Application

Functions and Derivatives

This GeoGebra applet plots the first and second derivative on the same graph. The tangent line to the graph of a function at a point is drawn.

Differentiation: Definition and Elementary Application

Five-in-One Calculus Applet: Mean Value Theorem

This applet encompasses five different applets on different topics and at different levels.

Numerical Integration, Integration: Motivation and Definition, Differentiation: Definition and Elementary Application, Functions In General, Graphers and Definitions, Theoretical Issues

Beginning the Year with Local Linearity

An article on how to teach tangent lines, the derivative, and local linearity through experimentation and exploration by students.

Differentiation: Definition and Elementary Application

Systems of Differential Equations

The mathlet graphs solution functions \(x(t)\) and \(y(t)\) to the system of differential equations \(x' = f(x,y)\) and \(y' = g(x,y)\), with initial values given by \( x(t_0)=x_0\) and \(y(t_0)=y

Differential Equations

Numerical Methods for Differential Equations

Graphic Methods, Ordinary Differential Equations

Differential Equations and Initial Value Problems

Graphs solution functions \(y(x)\) to the differential equation \(y'=f (x,y)\), with initial value given by \(y(x_0)=y_0\). The student can zoom in and out of the graphs.

Differential Equations, One-Variable Calculus

The Enigmatic Number \(e\): A History in Verse and Its Uses in the Mathematics Classroom

History of Calculus, One-Variable Calculus