Dynamic Calculus

A collection of interactive learning objects for teaching calculus

1. Introduction

Modern opinion credits Isaac Newton and Gottfried Leibniz with jointly and independently developing the branch of mathematics known as calculus. In the late 17th century and early 18th century, however, debate raged as to which of these esteemed mathematicians first invented calculus. Click here to learn more about the 'calculus controversy'.

2. The gradient function

Calculate the average gradient of a curve.

Find the limiting position of the secant PQ as Q approaches P.

Explore the relationship between the gradient of a curve and the gradient of the tangent.

Discover the geometric relationship between the tangent and the normal to a curve.

Determine the geometric significance of the formal definition of the derivative by examining the graph of a parabola.

Determine the geometric significance of the formal definition of the derivative by examining the graph of a cubic function.

Given a linear function, examine the graph of its derived function.

Given a quadratic function, examine the graph of its derived function.

Given a cubic function, examine the graph of its derived function.

Given a polynomial function, examine the graph of its derived function.

Determine the maximum height reached by a golf ball.

3. Curve sketching and problems on maxima and minima

Find the stationary points and points of inflexion on the graph of a polynomial function.

Sketch four ‘mystery’ curves by observing the values of the first and second derivatives.

Sketch a harder set of four ‘mystery’ curves by observing the values of the first and second derivatives.

Calculate the dimensions of a chicken-run that will give the maximum area for a farmer’s chickens.

Determine the maximum possible volume of a cylinder.

Determine where to cut a length of wire so that the sum of the areas of the shapes formed is a minimum.

Graph a polynomial function and its derived function.

4. Integral calculus

Draw the graph of a function, given its derived function.

Calculate the revenue received from the sale of a product.

Estimate the population of a town ten years from now.

Approximate the area enclosed by a curve and the x-axis.

Examine the relationship between the area under a curve and the areas of the ‘upper’ and ‘lower’ rectangles.

Examine the geometric significance of the definite integral.

Graph a polynomial function and calculate the value of a definite integral.

Calculate the area bounded by a curve and the x-axis.

Calculate the area bounded by a cubic curve and the x-axis.

Explore the relationship between the area bounded by a curve and the x-axis and the value of the definite integral.

Calculate the area bounded by a curve and the y-axis.

Calculate the area between two curves.

Use a numerical method to approximate the area bounded by a curve and the x-axis.

Calculate the work done in stretching a spring beyond its natural length.

Calculate the volume of the solid generated by rotating an area about the x-axis.

Calculate the volume of the solid generated by rotating an area about the y-axis.

2018 Update

In 2018, the platform tha Dynamic Calculus was hosted on, will be retired. Due to some aspects of Dynamic Calculus using Flash and concerns about accessibility, Dynamic Calculus was not getting migrated.

With the help of James Rudd, Dynamic Calculus is published here with no reliance on the Java version of GeoGebra and no use of Flash.

There are some parts of this resource that look a little broken, and I will work on fixing them. If you notice anything in particular, feel free to contact me.