# Animations

### Using The Materials

There are already various applets available for demonstrating mathematical ideas and so it is fair to ask, why more? First, it is now not hard to come across an animation of data in the media, which are often difficult to follow without some experience. These animations have been created with this in mind to provide students with experience reading quantitative information. Hopefully these help with quantitative literacy. Second, the animations each have two versions. There is an html version which allows the user to control the animation with start, stop, forward, backward, and speed controls. This has the advantage of using the animations as an exercise allowing assignments such as explaining or calculating something on a particular frame (there are frame numbers on the animations), as well as, comparing frames. The gif version has the advantage of portability so, for example, they can be placed in PowerPoint slides. On the downside they don't have the controls of the html version. Overall, these animations are created with the idea of being part of a lesson plan or homework assignment and less as a stand means to learn material. Comments and suggestions are welcome.

NOTE: When you click on an html animation it will be stopped. You will need to either click play or advance slide by slide with the arrows.

### Zoom in on a Tangent Line

• HTML or GIF
• Pay particular attention to the values along both axis during this animation.

### No Derivative

• HTML or GIF
• This is an example of a function that doesn't have a derivative at a point. It is also an example of what can go wrong using a secant line that straddles a point to estimate the slope of the tangent line. Notice how the secant line that straddles the point always has the same slope.

### Secant Approximation Tangent

• HTML or GIF
• Secant lines to the left and the right zoom in on the tangent line. Note the changing values along the axis.

### Computation - Product Rule

• HTML1  GIF1
• HTML2 GIF2
• These two animations provide examples on computing the product rule.

### Computation - Quotient Rule

• HTML1  GIF1
• HTML2 GIF2
• These two animations provide examples on computing the quotient rule.

### Left Riemann Sum

• HTML1  GIF1
• HTML2  GIF2
• For the first animation the function is positive. The second animation the function crosses the x-axis.

### Right Riemann Sum

• HTML1  GIF1
• HTML2  GIF2
• For the first animation the function is positive. The second animation the function crosses the x-axis.

### Midpoint Riemann Sum

• HTML1 GIF1
• HTML2 GIF2
• For the first animation the function is positive. The second animation the function crosses the x-axis.

### The Limit of Riemann Boxes

• HTML or GIF
• Note the connection between the main graph and the sub graph in this animation, as well as how the number of boxes increases.

### Euler's Method

• HTML1 GIF1
• HTML2 GIF2
• The first example has more details of the calculations then the second.

### Increase Mean Increase Tail Probability

• HTML or GIF
• This animation demonstrates how the tail probability increases drastically with a shift of the mean. A real world application of this is an increase in global mean temperature greatly increases the chances of "extreme" temperatures. For example, see this post from Yale Climate Change.

### Increase Sd Increase Tail Probability

• HTML or GIF
• This animation demonstrates how the tail probability increases drastically with an increase of the standard deviation. A real world application of this is an increase in global temperature variability greatly increases the chances of "extreme" temperatures. See Climate Communication and a more scientific article in Nature on increased variability in precipitation.

### Increase Mean/Sd Increase Tail Prob

• HTML or GIF
• The animation explores the increase in the tail probability if both the mean and the standard deviation are increased. In climate change we are seeing both an increase in the average temperature as well as the  variation. See this post from Climate Communications.

### The Central Limit Theorem

• HTML1 or GIF1
• HTML2 or GIF2
• This is a simulation to illustrate the central limit theorem. Note that the y-axis values change.

### Regression - Leverage

• HTML or GIF
• This is an example of how a point can exert leverage on a regression line.

### The Sample Max

• HTML1 or GIF1
• HTML2 or GIF2
• This animation provides an example of a sample distribution, the sample max, as a comparison to the central limit theorem.

### Regression - R-sq and P-value

• HTML1 GIF1
• HTML2 GIF2
• These two animations illustrate the relationship between R-squared and the P-value.