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# Calculus II For Dummies by Mark Zegarelli

## Calculus II Contents

Part I: Introduction to Integration

• Chapter 1: An Aerial View of the Area Problem
• Chapter 2: Dispelling Ghosts from the Past: A Review of Pre-Calculus and Calculus I
• Chapter 3: From Definite to Indefinite: The Indefinite Integral

Part II: Indefinite Integrals

• Chapter 4: Instant Integration: Just Add Water (And C)
• Chapter 5: Making a Fast Switch: Variable Substitution
• Chapter 6: Integration by Parts
• Chapter 7: Trig Substitution: Knowing All the (Tri)Angles
• Chapter 8: When All Else Fails: Integration with Partial Fractions

Part III: Intermediate Integration Topics

• Chapter 9: Forging into New Areas: Solving Area Problems
• Chapter 10: Pump up the Volume: Using Calculus to Solve 3-D Problems

Part IV: Infinite Series

• Chapter 11: Following a Sequence, Winning the Series
• Chapter 12: Where Is This Going? Testing for Convergence and Divergence
• Chapter 13: Dressing up Functions with the Taylor Series

• Chapter 14: Multivariable Calculus
• Chapter 15: What’s So Different about Differential Equations?

Part VI: The Part of Tens

• Chapter 16: Ten “Aha!” Insights in Calculus II
• Chapter 17: Ten Tips to Take to the Test

## Introduction to Calculus II For Dummies

Calculus is the great Mount Everest of math. Most of the world is content to just gaze upward at it in awe. But only a few brave souls attempt the ascent. Or maybe not.

In recent years, calculus has become a required course not only for math, engineering, and physics majors, but also for students of biology, economics, psychology, nursing, and business. Law schools and MBA programs welcome students who’ve taken calculus because it requires discipline and clarity of mind.

Even more and more high schools are encouraging the students to study calculus in preparation for the Advanced Placement (AP) exam. So, perhaps calculus is more like a well-traveled Vermont mountain, with lots of trails and camping spots, plus a big ski lodge on top.

You may need some stamina to conquer it, but with the right guide (this book, for example!), you’re not likely to find yourself swallowed up by a snowstorm half a mile from the summit.

### About Calculus II For Dummies

You, too, can learn calculus. That’s what this book is all about. In fact, as you read these words, you may well already be a winner, having passed a course in Calculus I.

If so, then congratulations and a nice pat on the back are in order. Having said that, I want to discuss a few rumors you may have heard about Calculus II:

Calculus II is harder than Calculus I. Calculus II is harder, even, than either Calculus III or Differential Equations.

Calculus II is more frightening than having your home invaded by zombies in the middle of the night and will result in emotional trauma requiring years of costly psychotherapy to heal.

Now, I admit that Calculus II is harder than Calculus I. Also, I may as well tell you that many — but not all — math students find it to be harder than the two semesters of math that follow.

(Speaking personally, I found Calc II to be easier than Differential Equations.) But I’m holding my ground that the long- term psychological effects of a zombie attack far outweigh those awaiting you in any one-semester math course.

The two main topics of Calculus II are integration and infinite series. Integration is the inverse of differentiation, which you study in Calculus I.

(For practical purposes, integration is a method for finding the area of unusual geometric shapes.) An infinite series is a sum of numbers that goes on forever, like 1 + 2 + 3 + … or 2 1 + 4 1 + 8 1 + …. Roughly speaking, most teachers focus on integration for the first two-thirds of the semester and infinite series for the last third.

This book gives you a solid introduction to what’s covered in a college course in Calculus II. You can use it either for self-study or while enrolled in a Calculus II course. So feel free to jump around.

Whenever I cover a topic that requires information from earlier in the book, I refer you to that section in case you want to refresh yourself on the basics.

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