Efnisyfirlit

• Cover
• Introduction
  • About This Book
  • Foolish Assumptions
  • Icons Used in This Book
  • Beyond the Book
  • Where to Go from Here
• Part 1: Getting Started with Pre-Calculus
  • Chapter 1: Pre-Pre-Calculus
    • Pre-Calculus: An Overview
    • All the Number Basics (No, Not How to Count Them!)
    • Visual Statements: When Math Follows Form with Function
    • Get Yourself a Graphing Calculator
  • Chapter 2: Playing with Real Numbers
    • Solving Inequalities
    • Variations on Dividing and Multiplying: Working with Radicals and Exponents
  • Chapter 3: The Building Blocks of Pre-Calculus Functions
    • Qualities of Special Function Types and Their Graphs
    • Dealing with Parent Functions and Their Graphs
    • Graphing Functions That Have More Than One Rule: Piece-Wise Functions
    • Setting the Stage for Rational Functions
    • Putting the Results to Work: Graphing Rational Functions
  • Chapter 4: Operating on Functions
    • Transforming the Parent Graphs
    • Sharpen Your Scalpel: Operating on Functions
    • Turning Inside Out with Inverse Functions
  • Chapter 5: Digging Out and Using Roots to Graph Polynomial Functions
    • Understanding Degrees and Roots
    • Factoring a Polynomial Expression
    • Finding the Roots of a Factored Equation
    • Cracking a Quadratic Equation When It Won’t Factor
    • Solving Unfactorable Polynomials with a Degree Higher Than Two
    • Put It in Reverse: Using Solutions to Find Factors
    • Graphing Polynomials
  • Chapter 6: Exponential and Logarithmic Functions
    • Exploring Exponential Functions
    • Logarithms: The Inverse of Exponential Functions
    • Base Jumping to Simplify and Solve Equations
    • Growing Exponentially: Word Problems in the Kitchen
• Part 2: The Essentials of Trigonometry
  • Chapter 7: Circling in on Angles
    • Introducing Radians: Circles Weren’t Always Measured in Degrees
    • Trig Ratios: Taking Right Triangles a Step Further
    • Understanding How Trig Ratios Work on the Coordinate Plane
    • Building the Unit Circle by Dissecting the Right Way
    • Digesting Special Triangle Ratios
    • Triangles and the Unit Circle: Working Together for the Common Good
    • Measuring Arcs: When the Circle Is Put in Motion
  • Chapter 8: Simplifying the Graphing and Transformation of Trig Functions
    • Drafting the Sine and Cosine Parent Graphs
    • Graphing Tangent and Cotangent
    • Putting Secant and Cosecant in Pictures
    • Transforming Trig Graphs
  • Chapter 9: Identifying with Trig Identities: The Basics
    • Keeping the End in Mind: A Quick Primer on Identities
    • Lining Up the Means to the End: Basic Trig Identities
    • Tackling Difficult Trig Proofs: Some Techniques to Know
  • Chapter 10: Advanced Identities: Your Keys to Success
    • Finding Trig Functions of Sums and Differences
    • Doubling an Angle and Finding Its Trig Value
    • Taking Trig Functions of Common Angles Divided in Two
    • A Glimpse of Calculus: Traveling from Products to Sums and Back
    • Eliminating Exponents with Power-Reducing Formulas
  • Chapter 11: Taking Charge of Oblique Triangles with the Laws of Sines and Cosines
    • Solving a Triangle with the Law of Sines
    • Conquering a Triangle with the Law of Cosines
    • Filling in the Triangle by Calculating Area
• Part 3: Analytic Geometry and System Solving
  • Chapter 12: Plane Thinking: Complex Numbers and Polar Coordinates
    • Understanding Real versus Imaginary
    • Combining Real and Imaginary: The Complex Number System
    • Graphing Complex Numbers
    • Plotting Around a Pole: Polar Coordinates
  • Chapter 13: Creating Conics by Slicing Cones
    • Cone to Cone: Identifying the Four Conic Sections
    • Going Round and Round: Graphing Circles
    • Riding the Ups and Downs with Parabolas
    • The Fat and the Skinny on the Ellipse
    • Pair Two Curves and What Do You Get? Hyperbolas
    • Expressing Conics Outside the Realm of Cartesian Coordinates
  • Chapter 14: Streamlining Systems, Managing Variables
    • A Primer on Your System-Solving Options
    • Algebraic Solutions of Two-Equation Systems
    • Solving Systems with More than Two Equations
    • Decomposing Partial Fractions
    • Surveying Systems of Inequalities
    • Introducing Matrices: The Basics
    • Simplifying Matrices to Ease the Solving Process
    • Making Matrices Work for You
  • Chapter 15: Sequences, Series, and Expanding Binomials for the Real World
    • Speaking Sequentially: Grasping the General Method
    • Difference between Terms: Arithmetic Sequences
    • Ratios and Consecutive Paired Terms: Geometric Sequences
    • Creating a Series: Summing Terms of a Sequence
    • Expanding with the Binomial Theorem
  • Chapter 16: Onward to Calculus
    • Scoping Out the Differences between Pre-Calculus and Calculus
    • Understanding Your Limits
    • Finding the Limit of a Function
    • Operating on Limits: The Limit Laws
    • Calculating the Average Rate of Change
    • Exploring Continuity in Functions
• Part 4: The Part of Tens
  • Chapter 17: Ten Polar Graphs
    • Spiraling Outward
    • Falling in Love with a Cardioid
    • Cardioids and Lima Beans
    • Leaning Lemniscates
    • Lacing through Lemniscates
    • Roses with Even Petals
    • A Rose Is a Rose Is a Rose
    • Limaçon or Escargot?
    • Limaçon on the Side
    • Bifolium or Rabbit Ears?
  • Chapter 18: Ten Habits to Adjust before Calculus
    • Figure Out What the Problem Is Asking
    • Draw Pictures (the More the Better)
    • Plan Your Attack — Identify Your Targets
    • Write Down Any Formulas
    • Show Each Step of Your Work
    • Know When to Quit
    • Check Your Answers
    • Practice Plenty of Problems
    • Keep Track of the Order of Operations
    • Use Caution When Dealing with Fractions
• Index
• About the Author
• Advertisement Page
• Connect with Dummies
• End User License Agreement

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