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Calculus For Dummies

ISBN: 978-0-7645-2498-1
384 pages
September 2003
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The mere thought of having to take a required calculus course is enough to make legions of students break out in a cold sweat. Others who have no intention of ever studying the subject have this notion that calculus is impossibly difficult unless you happen to be a direct descendant of Einstein.

Well, the good news is that you can master calculus. It's not nearly as tough as its mystique would lead you to think. Much of calculus is really just very advanced algebra, geometry, and trig. It builds upon and is a logical extension of those subjects. If you can do algebra, geometry, and trig, you can do calculus.

Calculus For Dummies is intended for three groups of readers:

  • Students taking their first calculus course – If you're enrolled in a calculus course and you find your textbook less than crystal clear, this is the book for you. It covers the most important topics in the first year of calculus: differentiation, integration, and infinite series.
  • Students who need to brush up on their calculus to prepare for other studies – If you've had elementary calculus, but it's been a couple of years and you want to review the concepts to prepare for, say, some graduate program, Calculus For Dummies will give you a thorough, no-nonsense refresher course.
  • Adults of all ages who'd like a good introduction to the subject – Non-student readers will find the book's exposition clear and accessible. Calculus For Dummies takes calculus out of the ivory tower and brings it down to earth.

This is a user-friendly math book. Whenever possible, the author explains the calculus concepts by showing you connections between the calculus ideas and easier ideas from algebra and geometry. Then, you'll see how the calculus concepts work in concrete examples. All explanations are in plain English, not math-speak. Calculus For Dummies covers the following topics and more:

  • Real-world examples of calculus
  • The two big ideas of calculus: differentiation and integration
  • Why calculus works
  • Pre-algebra and algebra review
  • Common functions and their graphs
  • Limits and continuity
  • Integration and approximating area
  • Sequences and series

Don't buy the misconception. Sure calculus is difficult – but it's manageable, doable. You made it through algebra, geometry, and trigonometry. Well, calculus just picks up where they leave off – it's simply the next step in a logical progression.

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Introduction.

Part I: An Overview of Calculus.

Chapter 1: What Is Calculus?

Chapter 2: The Two Big Ideas of Calculus: Differentiation and Integration.

Chapter 3: Why Calculus Works.

Part II: Warming Up with Calculus Prerequisites.

Chapter 4: Pre-Algebra and Algebra Review.

Chapter 5: Funky Functions and Their Groovy Graphs.

Chapter 6: The Trig Tango.

Part III: Limits.

Chapter 7: Limits and Continuity.

Chapter 8: Evaluating Limits.

Part IV: Differentiation.

Chapter 9: Differentiation Orientation.

Chapter 10: Differentiation Rules — Yeah, Man, It Rules.

Chapter 11: Differentiation and the Shape of Curves.

Chapter 12: Your Problems Are Solved: Differentiation to the Rescue!

Part V: Integration and Infinite Series.

Chapter 13: Intro to Integration and Approximating Area.

Chapter 14: Integration: It’s Backwards Differentiation.

Chapter 15: Integration Techniques for Experts.

Chapter 16: Forget Dr. Phil: Use the Integral to Solve Problems.

Chapter 17: Infinite Series.

Part VI: The Part of Tens.

Chapter 18: Ten Things to Remember.

Chapter 19: Ten Things to Forget.

Chapter 20: Ten Things You Can’t Get Away With.

Index.

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Mark Ryan has taught pre-math through calculus for more than a decade. He is a member of the National Council of Teachers of Mathematics.
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