# Introduction to differential and integral calculus

The following interactive app presents the fundamentals of the differential and integral calculus using the example of a moving body.

The first function refers to the position of the moving object. The shape of the curve can be interactively changed with the mouse (or the finger on a touch screen).

The first derivative (speed function) and the second derivative (acceleration function) adjust automatically.

Start App

The app has been specifically designed for mobile phones and tablets. The layout of the app can adapt to different display formats. The app can also be played on a normal PC or Macintosh.

Title: | Introduction to differential and integral calculus |

Target group: | Students |

Level: | easy |

Platforms (primary): | Smartphones, tablets and PCs |

Online/Offline: | Internet connection is required. |

The animation is the basis of the differential calculus by the example of the relationship between position, velocity and acceleration.

When the animation is started, the curve is shown which shows the position of the object in meters as a function of time.

The shape of this curve can be changed interactively with the mouse, or the finger on a touch screen. To do so, first set the drag points. Two circles are shown at the beginning and at the end of the curve. These points are used to specify the initial and final positions and the slopes.

The dots are displayed somewhat large, so that even with a finger on a mobile phone display is possible.

To display the 1st derivative curve, display the speed. The acceleration is the 2nd derivative.

Change the shape of the position curve and observe the effects on the two derivatives.

Background information: The curve relating to the position is a three-degree, fully-rational function. Various curve shapes can be created by using the start and end points. The curve can be roughly the shape of a parabola or the shape of a straight line.

## Further animations for smartphones / tablets

Calculation of the outer circle at the triangle

Calculation of the inner circle at the triangle

Calculation of the center of gravity of a triangle

Geometric relationships at the quadrangle

## Advanced animations for PCs

Geometric relations on the triangle

Basic principles of differential and integral calculus

Pythagorean theorem

Sine and cosine theorem

Basis of the integral calculus

## Sources

- Authoring tool: Adobe Animate
- JavaScript library: CreateJS

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