You are previewing Master Math: Pre-Calculus.
O'Reilly logo
Master Math: Pre-Calculus

Book Description

Get ready to master the principles and formulas of pre-calculus! Master Math: Pre-Calculus is a comprehensive reference guide that explains and clarifies pre-calculus and introductory calculus principles in a simple, easy-to-follow style and format. Beginning with the most basic fundamental topics and progressing through to the more advanced topics that will help prepare you for introductory calculus, the book helps clarify pre-calculus using step-by-step procedures and solutions, along with examples and applications. A complete table of contents and a comprehensive index enable you to quickly find specific topics, and the approachable style and format facilitate an understanding of what can be intimidating and tricky skills. Perfect for both students who need some extra help or rusty professionals who want to brush up on their basic math skills, Master Math: Pre-Calculus will help you master everything from sets and functions to derivatives and integrals.

Table of Contents

  1. Copyright
  2. Acknowledgments
  3. About the Author
  4. Introduction
  5. 1. Geometry
    1. 1.1. Lines and Angles
    2. 1.2. Polygons
    3. 1.3. Triangles
    4. 1.4. Quadrilaterals (Four-Sided Polygons)
    5. 1.5. Circles
    6. 1.6. Perimeter and Area of Planar Two-Dimensional Shapes
      1. Triangle
      2. Square
      3. Rectangle
      4. Regular Hexagon
      5. Circle
      6. Triangle
      7. Square
      8. Rectangle
      9. Parallelogram
      10. Trapezoid
      11. Circle
    7. 1.7. Volume and Surface Area of Three-Dimensional Objects
    8. 1.8. Vectors
  6. 2. Trigonometry
    1. 2.1. Introduction
    2. 2.2. General Trigonometric Functions
    3. 2.3. Addition, Subtraction, and Multiplication of Two Angles
    4. 2.4. Oblique Triangles
      1. Law of Sines
      2. Law of Cosines
      3. Law of Tangents
    5. 2.5. Graphs of Cosine, Sine, Tangent, Secant, Cosecant, and Cotangent
    6. 2.6. Relationship Between Trigonometric and Exponential Functions
    7. 2.7. Hyperbolic Functions
  7. 3. Sets and Functions
    1. 3.1. Sets
    2. 3.2. Functions
  8. 4. Sequences, Progressions, and Series
    1. 4.1. Sequences
    2. 4.2. Arithmetic Progressions
    3. 4.3. Geometric Progressions
    4. 4.4. Series
    5. 4.5. Infinite Series: Convergence and Divergence
    6. 4.6. Tests for Convergence of Infinite Series
      1. The Comparison Test for Convergence
      2. The Ratio Test for Convergence
      3. Tests for Series with Positive and Negative Terms
      4. Integral Test for Convergence
    7. 4.7. The Power Series
    8. 4.8. Expanding Functions into Series
    9. 4.9. The Binomial Expansion
  9. 5. Limits
    1. 5.1. Introduction to Limits
    2. 5.2. Limits and Continuity
  10. 6. Introduction to the Derivative
    1. 6.1. Definition
    2. 6.2. Evaluating Derivatives
    3. 6.3. Differentiating Multivariable Functions
    4. 6.4. Differentiating Polynomials
    5. 6.5. Derivatives and Graphs of Functions
    6. 6.6. Adding and Subtracting Derivatives of Functions
    7. 6.7. Multiple or Repeated Derivatives of a Function
    8. 6.8. Derivatives of Products and Powers of Functions
    9. 6.9. Derivatives of Quotients of Functions
    10. 6.10. The Chain Rule for Differentiating Complicated Functions
    11. 6.11. Differentiation of Implicit vs. Explicit Functions
    12. 6.12. Using Derivatives to Determine the Shape of the Graph of a Function (Minimum and Maximum Points)
      1. Minimum and Maximum Points
    13. 6.13. Other Rules of Differentiation
    14. 6.14. An Application of Differentiation: Curvilinear Motion
  11. 7. Introduction to the Integral
    1. 7.1. Definition of the Antiderivative or Indefinite Integral
    2. 7.2. Properties of the Antiderivative or Indefinite Integral
    3. 7.3. Examples of Common Indefinite Integrals
    4. 7.4. Definition and Evaluation of the Definite Integral
    5. 7.5. The integral and the Area Under the Curve in Graphs of Functions
      1. Area of Functions That Extend Below the X-Axis
    6. 7.6. Integrals and Volume
    7. 7.7. Even Functions, Odd Functions, and Symmetry
    8. 7.8. Properties of the Definite Integral
    9. 7.9. Methods for Evaluating Complex Integrals: Integration by Parts, Substitution, and Tables
      1. Integral Tables