Calculus is sometimes defined as ‘the mathematics of change’. The whole point of calculus is to take the conventional rules and principles of mathematics and apply them to dynamic situations where one or more variable is changing. In particular, calculus provides you with the tools to deal with rates of change.
There are actually two ‘big ideas’ in calculus, called differentiation and integration. These are both techniques that can be applied to algebraic expressions. As you will discover, one is the converse of the other. Algebraically, what this means is that, if you start with some function f(x) and differentiate it, then integrating the result will get you back, roughly speaking, to your original function f(x). And the same idea is true in reverse – if you first choose to integrate f(x), then differentiating the result will get you back to your original function f(x). The notation used for integration is the sign ∫, which is the oldfashioned, elongated letter ‘S’.
In the summer of 1666, Isaac Newton saw an apple fall in his garden, and promptly invented the theory of gravity. That, at least, is the story.
And, however oversimplified this version of events may be, it makes as good a starting point as any for an introduction to calculus.
Because the apple speeds up as it falls.
It even raises the whole question of what we mean, exactly, by the speed of the apple at any given moment.
Welcome to Calculus, Eleventh Edition. We are excited to offer you a new edition with even more resources that will help you understand and master calculus. This textbook includes features and resources that continue to make Calculus a valuable learning tool for students and a trustworthy teaching tool for instructors.
Calculus Workbook For Dummies, 3rd Edition, like Calculus For Dummies, is intended for three groups of readers: high school seniors or college students in their first calculus course, students who’ve taken calculus but who need a refresher to get ready for other pursuits, and adults of all ages who want to practice the concepts they learned in Calculus For Dummies or elsewhere.
This workbook is designed to help practice essential calculus techniques, especially the art of finding derivatives and performing integrals. Each chapter focuses on one main topic such as how to apply the chain rule or how to perform an integral with a trigonometric substitution.
Every chapter begins with a concise explanation of the main concept, followed by a few examples. The examples are fully solved step-by-step with explanations, and should serve as a valuable guide for solving the practice problems. The solution to every practice exercise is tabulated at the back of the book.
Precalculus provides the clear instruction, precise mathematics, and thorough coverage that you expect for your course. Additionally, this new edition provides you with free access to three companion websites:
• CalcView.com—video solutions to selected exercises
• CalcChat.com—worked-out solutions to odd-numbered exercises and access to online tutors
• LarsonPrecalculus.com—companion website with resources to supplement your learning
These websites will help enhance and reinforce your understanding of the material presented in this text and prepare you for future mathematics courses. CalcView® and CalcChat® are also available as free mobile apps.