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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.

Der Screenshot zeit eine Animation zum Thema der Differentialrechnung.

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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

Die Animation zeigt ein Dreieck, das interaktiv verändert werden kann.
Geometric relations on the triangle

Die Animation zeigt ein Objekt, dass sich entsprechend einer Positions-Funktion bewegt. Die Funktion kann interaktiv verändert werden.
Basic principles of differential and integral calculus

Die Animationn zeigt ein rechtwickliges Dreieck. Ein Eckpunkt kann verschoben werden. Die Quadrate, die aus den drei Seiten gebildet werden, passen sich automatisch an.
Pythagorean theorem

Die Animation zeigt ein rechtwickliges Dreieck. Der Eckpunkt kann entlang eines Kreises verschoben werden. Die entsprechenden Funktionswerte werden auf der Sinus- und Kosinuskirve markiert.
Sine and cosine theorem

Die Animation zeigt eine Kurve, deren Form mit der Maus verändert werden kann. Die Ober- und Untersumme wird automatisch im Bereich des Integrals eingezeichnet.
Basis of the integral calculus

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