Page 13 - Calculus Workbook For Dummies

Table of Contents

Introduction .................................................................................1

About This Book.........................................................................................................................1
Conventions Used in This Book ...............................................................................................1
How to Use This Book ...............................................................................................................2
Foolish Assumptions .................................................................................................................2
How This Book Is Organized.....................................................................................................2
Part I: Pre-Calculus Review .............................................................................................2
Part II: Limits and Continuity..........................................................................................3
Part III: Differentiation .....................................................................................................3
Part IV: Integration and Infinite Series...........................................................................3
Part V: The Part of Tens...................................................................................................3
Icons Used in This Book............................................................................................................4
Where to Go from Here..............................................................................................................4

Part I: Pre-Calculus Review ...........................................................5

Chapter 1: Getting Down the Basics: Algebra and Geometry ........................................7

Fraction Frustration...................................................................................................................7
Misc. Algebra: You Know, Like Miss South Carolina..............................................................9
Geometry: When Am I Ever Going to Need It?......................................................................12
Solutions for This Easy Elementary Stuff..............................................................................15
Chapter 2: Funky Functions and Tricky Trig.....................................................................19
Figuring Out Your Functions...................................................................................................19
Trigonometric Calisthenics ....................................................................................................22
Solutions to Functions and Trigonometry............................................................................25

Part II: Limits and Continuity ......................................................29

Chapter 3: A Graph Is Worth a Thousand Words: Limits and Continuity....................31
Digesting the Definitions: Limit and Continuity...................................................................31
Taking a Closer Look: Limit and Continuity Graphs............................................................34
Solutions for Limits and Continuity.......................................................................................37
Chapter 4: Nitty-Gritty Limit Problems..............................................................................39
Solving Limits with Algebra....................................................................................................39
Pulling Out Your Calculator: Useful “Cheating” ...................................................................44
Making Yourself a Limit Sandwich .........................................................................................46
Into the Great Beyond: Limits at Infinity...............................................................................47
Solutions for Problems with Limits .......................................................................................50

Part III: Differentiation ...............................................................57

Chapter 5: Getting the Big Picture: Differentiation Basics ..........................................59
The Derivative: A Fancy Calculus Word for Slope and Rate...............................................59
The Handy-Dandy Difference Quotient ................................................................................61
Solutions for Differentiation Basics .......................................................................................64