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Introduction to differential and integral calculus

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

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

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

Der Screenshot zeit eine Animation zum Thema der Differentialrechnung.

Start App

The app has been specifically designed for mobile devises. The layout of the app will adapt to the appropriate format. The app can also be used on a regular PC or Mac.

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 shows the fundamentals of differential calculus in relationship to position, velocity and acceleration.

When the animation starts, the curve shows the position of the object in meters in dependency to time.

You can change the shape of the curve with your mouse or your finger on a touch screen. To do so, first set the drag points. There are two circles shown at the beginning and at the end of the curve. These points are used to specify the initial / final position and slope.

For you to use the animation on mobile devices, the adjustable markers are slightly enlarged.

Display the speed to show the 1st derivative curve. The acceleration is the 2nd derivative.

When changing the shape of the curve you can observe the effects on the two derivatives.

Background information: The curve relating to the position is a third-degree polynomial function. With the aid of different start and end points various curved shapes can be created.

Further animations for smartphones/tablets


Calculation of the outer circle of a triangle


Calculation of the inner circle of a triangle


Calculation of the center of gravity on a triangle


Geometric relationships on a square

Further 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.
Fundamentals of the integral calculus

Sources

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