## Calculus Online: Lab 1

Welcome to our computer lab! Our aim for today's lab is to introduce you to some of the skills which will help you take advantage of our online resources and successfully complete the subsequent labs.

Remember:

You will not receive a mark for this lab

so relax and enjoy your experience today. If you have difficulties at any point, don't hesitate to contact one of the lab assistants. Let's jump in now!

 As you read this on the computer screen, you might wonder what all the stuff on the top of the screen does. Don't worry: we'll introduce you to that later. However, we would like to show you the scroll bar on the side of the page. It looks like the picture just to the right. This can help you position the text that you want to read in the center of the screen. To use it, simply move the mouse so that the pointer is on top of the scroll bar. Now hold down the left mouse button and drag the scroll bar down and then back up. Do you notice how the text moves in the window? This will enable you to expose new text after you have read what is visible on your screen.

Since there are so many resources available to you online, we would like you to be comfortable reading a piece of text on the screen. Below are a few short paragraphs. After you read them, answer the question which follows.
 A Brief History of Calculus The subject of Calculus, as we think of it now, was independently developed by two mathematicians in the seventeenth century. One of these was Isaac Newton (shown to the right), an eccentric Englishman born in the year 1642, the year of Galileo's death. Newton was a bit of an introvert, preferring to avoid human contact as much as possible. His great work, the Principia Mathematica, is often cited as the most influential book of modern times. The other developer of Calculus was Gottfried Wilhelm von Leibniz (shown to the left), a German who lived from 1646 to 1716. In contrast to the reclusive Newton, Leibniz was out-going and gregarious and sometimes even called a "ladies' man". His accomplishments range widely: besides being a mathematician, he was also a philosopher and respected statesman. Leibniz was the first to publish his work though evidence indicates Newton had worked out many of the ideas ahead of Leibniz without publishing them. This issue of who was more deserving of credit for the discovery of Calculus began a bitter feud between the two men which was enthusiastically pursued by their fellow countrymen.

Now here is a question. To answer, move the pointer over the box next to the correct answer and click to select it. You should see the box change colour. If you change your mind, simply click beside your new answer.

#### Question

Select the statement below that is most true.
• (a) Newton was a respected statesman.
• (b) Leibniz published his work first.
• (c) Everyone got along famously.
• (d) The Principia Mathematica is a forgotten work.
• (e) Leibniz died at an early age.

Making a Selection
 Next, we'd like to ask you to choose your favourite shape from a list. To do this, position the pointer over the region below which says "Click here." As you hold the mouse button down, you will see a list of options appear. Still holding the mouse button down, drag the pointer until it lies above your choice. When you release the mouse button, the list of options should go away and your favourite shape will appear below. You can change your mind as many times as you like!

Interactive Diagrams
 What appears below is an interactive diagram of the sort we'll see frequently in our labs. Begin by making sure that Part a is selected in the diagram. You should see a line passing through the origin (the point (0,0)) and a point represented by a dot on the line (if you have a colour monitor, you'll see that the dot is red). You can change the slope of the line by moving the dot with the mouse. Use the mouse to position the pointer over the dot, hold the left mouse button down and drag the point to a new position. Remember that the slope of a line is the ratio of the change in vertical distance to the change in horizontal distance. In other words, the slope of a line measures the "steepness" of a line. Use the mouse to modify the line so that its slope of 1.5. Now select Part b in the diagram. You should see a line and two points on the line. The line may be modified by moving the points. Modify the line so that it has the equation: