Understanding Math - Introduction to Calculus

by Brian Boates, Isaac Tamblyn

In this book, we introduce the concept of calculus derivatives, discuss their basic properties, and show how to evaluate them for a wide variety of single-variable functions. We introduce the derivative using the idea of slopes and use this approach to reach the formal definition of the derivative. Many rules of differentiation are introduced with several examples of each, including the power rule, product rule, quotient rule, and chain rule. We also discuss the derivatives of several common special functions, such as trigonometric functions, exponentials, and logarithms. The goal of this book is to teach students a practical way of thinking about what derivatives are and how they work, in an approach suitable for all. Many examples are given throughout to aid in the understanding and execution of new concepts; we strongly believe in teaching by examples, and that repetition is the best way to internalize new ideas. Each example intends to guide the student through the thinking process without skipping steps and touches on all of the new material presented.

51 pages, Kindle Edition

First published November 4, 2011