Cantarella - Petersons eggheads guide to calculus

This eggheads Guide was designed to help you learn calculus in a fun and easy way. well, boring. well, boring.

It can also be confusing at times. If it wasnt, wed all have straight As, right? As your guide through the adventure of education, Im here to make things a bit more enjoyable. I studied the boring books so you dont have to. I got straight As and lived to tell about it. I understand this stuff, and you can, too. In this guide, Ill show you what you need to learn to get to the next level.

Wherever I can, I explain things in pictures and stories. I break concepts down and teach them step by step. I try to stick with words that you know. I give examples from real life that you can relate to.

In this book, well work together to improve your calculus skills and build your confidence. Confidence is very important, and it comes from trust.

You can trust me as your guide, and most important, you can trust yourself. If your calculus knowledge isnt strong enough, lets do something about it!

This book contains nine chapters. We recommend you read them in order. Chapter 1 provides a review of algebra. In order to solve calculus problems, youll need to use algebra often. This chapter reviews basic algebra concepts, such as multiplying and dividing polynomials, factoring polynomials, and absolute value.

Here well also explain interval notation. Chapter 2 discusses graphing. This chapter covers the coordinate plane, graphing linear equations, finding the slope of a line, the slope-intercept formula, and graphing quadratic equations. Chapter 3 defines functions. Here we review the basic concept of a function and discuss domain and range. We also explain functional notation, composite functions, and piecewise functions.

Chapter 4 addresses trigonometry. Along with algebra, graphing, and functions, trigonometry is used throughout calculus. In this chapter, we review the Pythagorean Theorem and how to find sine, cosine, and tangent. We also address inverse trigonometric functions and the concept of the unit circle. Chapter 5 introduces the concept of limits. Here we learn about the properties of limits and how to take limits of polynomials, rational functions, composite functions, and trig functions.

Infinite limits are also addressed. Chapter 6 deals with differentiation. This chapter introduces one of the two main contributions of calculus, the process of differentiation. We address how to understand differentiation and how to work with derivatives. Chapter 7 focuses on applications of differentiation. The process of differentiation has many varied applications.

This chapter presents several key applications and shows how to use differentiation to solve specific types of problems. Chapter 8 explains integration. This chapter focuses on the second main contribution of calculus, the process of integration. We discuss how to understand integration and how to solve problems using integrals. Chapter 9 concludes with definite integrals and the Fundamental Theorem of Calculus. The related processes of differentiation and integration are tied together by connections shown through the Fundamental Theorem of Calculus.

This chapter explains the connections and shows how the Fundamental Theorem assists calculus problem-solving. As you read each chapter, youll find practice exercises along the way. Complete the exercises to practice what youve learned. The more you use your skills, the better they will stick in your mind. To Learn More Ready for more practice? After youve finished this book, visit the egghead website at www.petersonspublishing.com. Click the egghead link for additional practice exercises.

This book will get you off to a great start. The website can give you that extra calculus boost! Petersons Books Along with producing the eggheads Guides, Petersons publishes many types of books. These can help you prepare for tests, choose a college, and plan your career. They can even help you obtain financial aid. Look for Petersons books at your schools guidance office or library, your local library or bookstore, or at www.petersonsbooks.com. Many Petersons eBooks are also online! We welcome any comments or suggestions you may have about this book.

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The discipline of calculus was developed through the cumulative work of many mathematicians and scientists over hundreds of years. Before such key contributors as Sir Isaac Newton and Gottfried Leibniz, the scientific community was unable to solve many problems that had vexed scholars for ages. As the tools of calculus became more developed and refined, mathematicians were able to achieve solutions that had once been out of reach. With this mathematical advancement came a surge in technological progress, creating much of the capacity that we now have today. Many of the problems that calculus helps to solve concern motion and change.