Page 14 - Calculus Workbook For Dummies

xii Calculus Workbook For Dummies

Chapter 6: Rules, Rules, Rules: The Differentiation Handbook....................................69
Rules for Beginners..................................................................................................................69
Giving It Up for the Product and Quotient Rules .................................................................72
Linking Up with the Chain Rule..............................................................................................75
What to Do with Ys: Implicit Differentiation.........................................................................78
Getting High on Calculus: Higher Order Derivatives...........................................................80
Solutions for Differentiation Problems..................................................................................82

Chapter 7: Analyzing Those Shapely Curves with the Derivative ...............................91
The First Derivative Test and Local Extrema .......................................................................91
The Second Derivative Test and Local Extrema ..................................................................95
Finding Mount Everest: Absolute Extrema ...........................................................................98
Smiles and Frowns: Concavity and Inflection Points.........................................................102
The Mean Value Theorem: Go Ahead, Make My Day.........................................................106
Solutions for Derivatives and Shapes of Curves................................................................108
Chapter 8: Using Differentiation to Solve Practical Problems...................................123
Optimization Problems: From Soup to Nuts.......................................................................123
Problematic Relationships: Related Rates..........................................................................127
A Day at the Races: Position, Velocity, and Acceleration .................................................131
Make Sure You Know Your Lines: Tangents and Normals.................................................134
Looking Smart with Linear Approximation.........................................................................138
Solutions to Differentiation Problem Solving .....................................................................140

Part IV: Integration and Infinite Series.......................................157

Chapter 9: Getting into Integration..................................................................................159
Adding Up the Area of Rectangles: Kid Stuff ......................................................................159
Sigma Notation and Reimann Sums: Geek Stuff .................................................................162
Close Isn’t Good Enough: The Definite Integral and Exact Area ......................................166
Finding Area with the Trapezoid Rule and Simpson’s Rule..............................................168
Solutions to Getting into Integration...................................................................................171
Chapter 10: Integration: Reverse Differentiation..........................................................177
The Absolutely Atrocious and Annoying Area Function...................................................177
Sound the Trumpets: The Fundamental Theorem of Calculus ........................................179
Finding Antiderivatives: The Guess and Check Method...................................................183
The Substitution Method: Pulling the Switcheroo.............................................................185
Solutions to Reverse Differentiation Problems ..................................................................188
Chapter 11: Integration Rules for Calculus Connoisseurs ..........................................193
Integration by Parts: Here’s How u du It.............................................................................193
Transfiguring Trigonometric Integrals................................................................................196
Trigonometric Substitution: It’s Your Lucky Day!..............................................................198
Partaking of Partial Fractions...............................................................................................201
Solutions for Integration Rules.............................................................................................205
Chapter 12: Who Needs Freud? Using the Integral to Solve Your Problems...........219
Finding a Function’s Average Value .....................................................................................219
Finding the Area between Curves........................................................................................220
Volumes of Weird Solids: No, You’re Never Going to Need This......................................222
Arc Length and Surfaces of Revolution...............................................................................227
Getting Your Hopes Up with L’Hôpital’s Rule .....................................................................229