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## Book Description

Slay the calculus monster with this user-friendly guide

Calculus For Dummies, 2nd Edition makes calculus manageable—even if you're one of the many students who sweat at the thought of it. By breaking down differentiation and integration into digestible concepts, this guide helps you build a stronger foundation with a solid understanding of the big ideas at work. This user-friendly math book leads you step-by-step through each concept, operation, and solution, explaining the "how" and "why" in plain English instead of math-speak. Through relevant instruction and practical examples, you'll soon learn that real-life calculus isn't nearly the monster it's made out to be.

Calculus is a required course for many college majors, and for students without a strong math foundation, it can be a real barrier to graduation. Breaking that barrier down means recognizing calculus for what it is—simply a tool for studying the ways in which variables interact. It's the logical extension of the algebra, geometry, and trigonometry you've already taken, and Calculus For Dummies, 2nd Edition proves that if you can master those classes, you can tackle calculus and win.

• Includes foundations in algebra, trigonometry, and pre-calculus concepts

• Explores sequences, series, and graphing common functions

• Instructs you how to approximate area with integration

• Features things to remember, things to forget, and things you can't get away with

• Stop fearing calculus, and learn to embrace the challenge. With this comprehensive study guide, you'll gain the skills and confidence that make all the difference. Calculus For Dummies, 2nd Edition provides a roadmap for success, and the backup you need to get there.

1. Introduction
2. Part I: An Overview of Calculus
1. Chapter 1: What Is Calculus?
2. Chapter 2: The Two Big Ideas of Calculus: Differentiation and Integration — plus Infinite Series
1. Defining Differentiation
2. Investigating Integration
3. Sorting Out Infinite Series
3. Chapter 3: Why Calculus Works
1. The Limit Concept: A Mathematical Microscope
2. What Happens When You Zoom In
3. Two Caveats, or Precision, Preschmidgen
3. Part II: Warming Up with Calculus Prerequisites
1. Chapter 4: Pre-Algebra and Algebra Review
2. Absolute Value — Absolutely Easy
4. Rooting for Roots
5. Logarithms — This Is Not an Event at a Lumberjack Competition
6. Factoring Schmactoring — When Am I Ever Going to Need It?
2. Chapter 5: Funky Functions and Their Groovy Graphs
1. What Is a Function?
2. What Does a Function Look Like?
3. Common Functions and Their Graphs
4. Inverse Functions
5. Shifts, Reflections, Stretches, and Shrinks
3. Chapter 6: The Trig Tango
1. Studying Trig at Camp SohCahToa
2. Two Special Right Triangles
3. Circling the Enemy with the Unit Circle
4. Graphing Sine, Cosine, and Tangent
5. Inverse Trig Functions
6. Identifying with Trig Identities
4. Part III: Limits
1. Chapter 7: Limits and Continuity
1. Take It to the Limit — NOT
3. The 33333 Limit Mnemonic
2. Chapter 8: Evaluating Limits
1. Easy Limits
2. The “Real Deal” Limit Problems
3. Evaluating Limits at Infinity
5. Part IV: Differentiation
1. Chapter 9: Differentiation Orientation
1. Differentiating: It’s Just Finding the Slope
2. The Derivative: It’s Just a Rate
3. The Derivative of a Curve
4. The Difference Quotient
5. Average Rate and Instantaneous Rate
6. To Be or Not to Be? Three Cases Where the Derivative Does Not Exist
2. Chapter 10: Differentiation Rules — Yeah, Man, It Rules
1. Basic Differentiation Rules
2. Differentiation Rules for Experts — Oh, Yeah, I’m a Calculus Wonk
3. Differentiating Implicitly
4. Getting into the Rhythm with Logarithmic Differentiation
5. Differentiating Inverse Functions
6. Scaling the Heights of Higher Order Derivatives
3. Chapter 11: Differentiation and the Shape of Curves
1. Taking a Calculus Road Trip
2. Finding Local Extrema — My Ma, She’s Like, Totally Extreme
3. Finding Absolute Extrema on a Closed Interval
4. Finding Absolute Extrema over a Function’s Entire Domain
5. Locating Concavity and Inflection Points
6. Looking at Graphs of Derivatives Till They Derive You Crazy
7. The Mean Value Theorem — GRRRRR
4. Chapter 12: Your Problems Are Solved: Differentiation to the Rescue!
1. Getting the Most (or Least) Out of Life: Optimization Problems
2. Yo-Yo a Go-Go: Position, Velocity, and Acceleration
3. Related Rates — They Rate, Relatively
5. Chapter 13: More Differentiation Problems: Going Off on a Tangent
1. Tangents and Normals: Joined at the Hip
2. Straight Shooting with Linear Approximations
6. Part V: Integration and Infinite Series
1. Chapter 14: Intro to Integration and Approximating Area
2. Finding the Area Under a Curve
3. Approximating Area
4. Getting Fancy with Summation Notation
5. Finding Exact Area with the Definite Integral
6. Approximating Area with the Trapezoid Rule and Simpson’s Rule
2. Chapter 15: Integration: It’s Backwards Differentiation
1. Antidifferentiation
2. Vocabulary, Voshmabulary: What Difference Does It Make?
3. The Annoying Area Function
4. The Power and the Glory of the Fundamental Theorem of Calculus
5. The Fundamental Theorem of Calculus: Take Two
6. Finding Antiderivatives: Three Basic Techniques
7. Finding Area with Substitution Problems
3. Chapter 16: Integration Techniques for Experts
1. Integration by Parts: Divide and Conquer
2. Tricky Trig Integrals
3. Your Worst Nightmare: Trigonometric Substitution
4. The As, Bs, and Cxs of Partial Fractions
4. Chapter 17: Forget Dr. Phil: Use the Integral to Solve Problems
1. The Mean Value Theorem for Integrals and Average Value
2. The Area between Two Curves — Double the Fun
3. Finding the Volumes of Weird Solids
4. The Washer Method
5. Analyzing Arc Length
6. Surfaces of Revolution — Pass the Bottle ’Round
5. Chapter 18: Taming the Infinite with Improper Integrals
1. L’Hôpital’s Rule: Calculus for the Sick
2. Improper Integrals: Just Look at the Way That Integral Is Holding Its Fork!
6. Chapter 19: Infinite Series
1. Sequences and Series: What They’re All About
2. Convergence or Divergence?That Is the Question
3. Alternating Series
4. Keeping All the Tests Straight
7. Part VI: The Part of Tens
1. Chapter 20: Ten Things to Remember
2. Chapter 21: Ten Things to Forget
3. Chapter 22: Ten Things You Can’t Get Away With