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Essay giving very brief biography of l'Hospital, the history of his and Johann Bernoulli's rule, and a slightly modernized diagram for and version of the proof he and Bernoulli gave.

History of Calculus

Timeline of Calculus History

Timeline of contributors to formulation of the Calculus with biographies: Click on the historical figure's image to see his biography and two links to further online information.

History of Calculus

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

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

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

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

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

The Product Rule

Wolfram's demo for the product rule, with dropdown menus for the functions. Users can download the free Mathematica Player to play a live version of the demo.

Differentiation: Calculation Rules

Taylor Polynomials - Exponential Functions

This granular application shows the graph of exp(x) and interactively displays the Taylor polynomial approximations at any point and up to very high orders. It comes with a short explanation.

Infinite Limits: Sequences and Series

Banchoff's Multivariable Calculus Labs

A very large colleciton of labs with interactive applets, covering nearly every topic in a typical multivariable calculus course.

General Collections of Applets, General Tools