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Beginning Pre-Calculus for Game Developers

Book Description

Successful game programming requires at least a rudimentary understanding of central math topics. While most books neglect the point-by-point details that are necessary to truly hone these skills, Beginning Pre-Calculus for Game Developers tackles each task head on, using easy-to-understand, hands-on exercises. You will conquer the basics of these essential math topics and will then learn how to specifically apply each skill to the field of game programming. Whether you are searching for an entertaining, engaging way to improve your math skills or you wish to develop the background skills necessary to boost your game programming, Beginning Pre-Calculus for Game Developers serves as the step-by-step guide that will help you tackle pre-calculus with confidence.

Table of Contents

  1. Copyright
  2. Acknowledgments
  3. About the Authors
  4. Introduction
  5. About Pre-Calculus
    1. Talk of Math
    2. Most People
    3. Places for Games
    4. Computer Games and Classrooms
    5. Visual Formula
    6. A Part of Life
    7. Disorganized Territory
    8. Algebra and Trigonometry
    9. Additional Reading
  6. Number Systems and Properties
    1. Number Systems
    2. Properties
    3. Multiplication and Division
    4. Using Visual Formula
    5. Conclusion
  7. Sets, Exponents, Roots, and Radicals
    1. Sets
    2. Venn Diagrams
    3. Exponents
    4. Scientific Notation
    5. A Few Worked Problems
    6. Absolute Values
    7. Radicals and Roots
    8. A Few Worked Problems
    9. Using Visual Formula
    10. Conclusion
  8. Expressions, Relations, and Functions
    1. Basic Factoring
    2. Order of Operations
    3. More on Sets
    4. Correspondence Between Sets
    5. Domain and Range
    6. Cartesian Coordinates
    7. Functions
    8. Non-Functional Relationship
    9. Designating Functions
    10. Using Visual Formula
    11. Conclusion
  9. Functions and More Functions
    1. Thinking About Equations
    2. More on Absolute Values
    3. Inequalities
    4. Conclusion
  10. Lines, Slopes, and Functions
    1. Reviewing Domain and Range
    2. Linear Functions
    3. What Makes a Function Linear?
    4. Slopes That Do Change
    5. Points, Intercepts, and Slopes
    6. The Point-Slope Equation
    7. Using Visual Formula
    8. Conclusion
  11. Distances and Other Things
    1. More Slopes
    2. The Distance Between Points
    3. Depicting Absolute Values
    4. Translation and Shift
    5. Inverses Generally
    6. Using Visual Formula
    7. Conclusion
  12. Polynomial Equations
    1. Polynomials
    2. Working with Polynomials
    3. Solving Equations
    4. Addition and Subtraction Activities
    5. Multiplication and Division Activities
    6. Monomial and Binomial Expressions
    7. Sums, Differences, and Squares
    8. FOIL Strategies
    9. Polynomial Multiplication
    10. Reviewing Long Division
    11. Long Division in Algebra
    12. Using Visual Formula
    13. Conclusion
  13. Quadratic Equations
    1. Quadratic Equations
    2. Translation Along the x and y Axes
    3. Arbitrary Vertex Positions
    4. Standard Forms
    5. Completing the Square
    6. The Quadratic Formula
    7. The Discriminant
    8. Using Visual Formula
    9. Conclusion
  14. Visual Formula, Important Graphs, Inequalities, and Other Things
    1. Compare and Contrast
    2. Linear Graphs
    3. Lines that Parallel the x and y Axes
    4. Absolute Values
    5. Nonlinear Absolute Values
    6. Even and Odd Exponential Values
    7. Roots
    8. Graphs of Inverses
    9. Varieties of Translation
    10. Flipping Across the Axis
    11. Inverting and Shifting Parabolas
    12. Conclusion
  15. Systems and Matrices
    1. Shared Solutions
    2. Substitution
    3. Systems Solved by Adding and Multiplying
    4. Variations on Themes
    5. Systems with No Solutions
    6. An Infinite Number of Solutions
    7. Systems with Three Variables
    8. Matrices
    9. Conclusion
  16. Trigonometry
    1. The Ratios of Trigonometry
    2. Degrees and Radians
    3. Trigonometric Ratios
    4. Ratios and Degrees
    5. Rotation
    6. Rotation and the Unit Circle
    7. Plotting Sine Values
    8. Negative Values
    9. Plotting Cosine Values
    10. Defining Tangents and Cotangents
    11. Plotting Tangent Values
    12. Plotting Cotangent Values
    13. Plotting Secant Values
    14. Plotting Cosecant Values
    15. Using Visual Formula
    16. Conclusion
  17. Answers to the Exercise Sets