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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. 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 Students easy Smartphones, tablets and PCs 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 PCs Geometric relations on the triangle Basic principles of differential and integral calculus Pythagorean theorem Sine and cosine theorem Fundamentals of the integral calculus

## Sources

• Authoring tool: Adobe Animate
• JavaScript library: CreateJS

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