Book Details
| Print ISBN | 9781119357483 |
| eText ISBN | 9781119357506 |
| Publisher | For Dummies |
| Publishing Year | 2018 |
| Edition | 3rd Edition |
| Language | English |
| Pages | 336 |
Calculus Workbook For Dummies, 3rd Edition, provides targeted exercises designed to reinforce core mathematical procedures through hands-on practice. The volume supports students seeking extra coursework assistance or preparing for calculus exams.
Coverage spans essential topics including limits, continuity, differentiation, integration, and infinite series. Additional problem sets address foundational algebra and geometry, trigonometric functions, vectors, conic sections, and natural logarithms.
Author Mark Ryan pairs hundreds of practice problems with detailed solutions and access to online chapter quizzes. The exercises are structured for use as an in-class supplement or alongside a tutor.
Table of Contents
Chapter Introduction: Introduction
- • About This Book
- • Foolish Assumptions
- • Icons Used in This Book
- • Beyond the Book
- • Where to Go from Here
Chapter 1: Getting Down to Basics: Algebra and Geometry
- • Fraction Frustration
- • Misc. Algebra: You Know, Like Miss South Carolina
- • Geometry: When Am I Ever Going to Need It?
- • Solutions for This Easy, Elementary Stuff
Chapter 2: Funky Functions and Tricky Trig
- • Figuring Out Your Functions
- • Trigonometric Calisthenics
- • Solutions to Functions and Trigonometry
Chapter 3: A Graph Is Worth a Thousand Words: Limits and Continuity
- • Digesting the Definitions: Limit and Continuity
- • Taking a Closer Look: Limit and Continuity Graphs
- • Solutions for Limits and Continuity
Chapter 4: Nitty-Gritty Limit Problems
- • Solving Limits with Algebra
- • Pulling Out Your Calculator: Useful “Cheating”
- • Making Yourself a Limit Sandwich
- • Into the Great Beyond: Limits at Infinity
- • Solutions for Problems with Limits
Chapter 5: Getting the Big Picture: Differentiation Basics
- • The Derivative: A Fancy Calculus Word for Slope and Rate
- • The Handy-Dandy Difference Quotient
- • Solutions for Differentiation Basics
Chapter 6: Rules, Rules, Rules: The Differentiation Handbook
- • Rules for Beginners
- • Giving It Up for the Product and Quotient Rules
- • Linking Up with the Chain Rule
- • What to Do with Y’s: Implicit Differentiation
- • Getting High on Calculus: Higher Order Derivatives
- • Solutions for Differentiation Problems
Chapter 7: Analyzing Those Shapely Curves with the Derivative
- • The First Derivative Test and Local Extrema
- • The Second Derivative Test and Local Extrema
- • Finding Mount Everest: Absolute Extrema
- • Smiles and Frowns: Concavity and Inflection Points
- • The Mean Value Theorem: Go Ahead, Make My Day
- • Solutions for Derivatives and Shapes of Curves
Chapter 8: Using Differentiation to Solve Practical Problems
- • Optimization Problems: From Soup to Nuts
- • Problematic Relationships: Related Rates
- • A Day at the Races: Position, Velocity, and Acceleration
- • Solutions to Differentiation Problem Solving
Chapter 9: Even More Practical Applications of Differentiation
- • Make Sure You Know Your Lines: Tangents and Normals
- • Looking Smart with Linear Approximation
- • Calculus in the Real World: Business and Economics
- • Solutions to Differentiation Problem Solving
Chapter 10: Getting into Integration
- • Adding Up the Area of Rectangles: Kid Stuff
- • Sigma Notation and Riemann Sums: Geek Stuff
- • Close Isn’t Good Enough: The Definite Integral and Exact Area
- • Finding Area with the Trapezoid Rule and Simpson’s Rule
- • Solutions to Getting into Integration
Chapter 11: Integration: Reverse Differentiation
- • The Absolutely Atrocious and Annoying Area Function
- • Sound the Trumpets: The Fundamental Theorem of Calculus
- • Finding Antiderivatives: The Guess-and-Check Method
- • The Substitution Method: Pulling the Switcheroo
- • Solutions to Reverse Differentiation Problems
Chapter 12: Integration Rules for Calculus Connoisseurs
- • Integration by Parts: Here’s How u du It
- • Transfiguring Trigonometric Integrals
- • Trigonometric Substitution: It’s Your Lucky Day!
- • Partaking of Partial Fractions
- • Solutions for Integration Rules
Chapter 13: Who Needs Freud? Using the Integral to Solve Your Problems
- • Finding a Function’s Average Value
- • Finding the Area between Curves
- • Volumes of Weird Solids: No, You’re Never Going to Need This
- • Arc Length and Surfaces of Revolution
- • Solutions to Integration Application Problems
Chapter 14: Infinite (Sort of) Integrals
- • Getting Your Hopes Up with L’Hôpital’s Rule
- • Disciplining Those Improper Integrals
- • Solutions to Infinite (Sort of) Integrals
Chapter 15: Infinite Series: Welcome to the Outer Limits
- • The Nifty nth Term Test
- • Testing Three Basic Series
- • Apples and Oranges . . . and Guavas: Three Comparison Tests
- • Ratiocinating the Two “R” Tests
- • He Loves Me, He Loves Me Not: Alternating Series
- • Solutions to Infinite Series
Chapter 16: Ten Things about Limits, Continuity, and Infinite Series
- • The 33333 Mnemonic
- • First 3 over the “l”: 3 parts to the definition of a limit
- • Fifth 3 over the “l”: 3 cases where a limit fails to exist
- • Second 3 over the “i”: 3 parts to the definition of continuity
- • Fourth 3 over the “i”: 3 cases where continuity fails to exist
- • Third 3 over the “m”: 3 cases where a derivative fails to exist
- • The 13231 Mnemonic
- • First 1: The nth term test of divergence
- • Second 1: The nth term test of convergence for alternating series
- • First 3: The three tests with names
- • Second 3: The three comparison tests
- • The 2 in the middle: The two R tests
Chapter 17: Ten Things You Better Remember about Differentiation
- • The Difference Quotient
- • The First Derivative Is a Rate
- • The First Derivative Is a Slope
- • Extrema, Sign Changes, and the First Derivative
- • The Second Derivative and Concavity
- • Inflection Points and Sign Changes in the Second Derivative
- • The Product Rule
- • The Quotient Rule
- • Linear Approximation
- • “PSST,” Here’s a Good Way to Remember the Derivatives of Trig Functions
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