Introduction to Calculus

# Calculus 1

How fast is an object falling? It's a deceptively simple question that puzzled scientists and mathematicians for a long time. It wasn't until the 18th century that Newton and Leibniz developed the tools needed to answer it. Those tools were the first steps in what today we call calculus. In this course, you'll get an introduction to the core concepts of differential calculus and the ways it can be applied to solve real world problems.

1. Limits and Continuity Limits are the key tool that let Newton and Leibniz side step some of the limitations faced by previous mathematicians.
1. The Derivative or its practical interpretation, the 'instantaneous rate of change', is the core concept of first semester calculus.
1. Applications of the Derivative There's a lot you can do with the derivative in a practical sense. In this section, we're going to look at a selection of those applications.
1. Antiderivatives If you think of derivatives as a functions then antiderivatives are their inverses. This is the primary topic of second semester calculus so we're only going to touch on it briefly.

## Our Approach to Teaching and Learning

Math is a little unusual in the academic world. Unlike a lot of subjects, you're expected to actually be able to do the math by the time the class is done. You can't get there by watching other people do math or reading it about it in a book. You have to get out a pencil and paper and do it for yourself. The video lectures are a good starting point for your study but you should also spend time working on the exercises and the "explorations" material. Important concepts are discussed in the Explorations material and the associated videos as well as in the main lectures. Problems in the Practice sections marked with a star are particularly important. You should try to solve those on your own based on the lecture material but it's also worth checking out the posted solutions for additional important techniques and concepts.

### Prior Knowledge

This class covers a wide range of topics at a wide variety of levels. The first four chapters are what would be covered in an introductory high school or undergraduate algebra class. The next three sections come from high school 'Algebra 2' or an undergraduate College Algebra class. The modeling and approximation material uses first and second semester calculus and a few topics from graduate level analysis.

### Time to Completion

While the class includes some practice material and questions, it's not really intended as a complete, step-by-step course. It's more useful as a supplement if you need more information on a specific topic or method that's being covered in another class.

### Technologies Used

We try to keep it simple but there are some things that we need to provide the interactive content that makes our classes special. Fortunately everything you need, including JavaScript and HTML5 compatability, is available in every modern browser.