Table Of ContentMathematics
and Physics
for Programmers
Second Edition
John Patrick Flynt
Danny Kodicek
Course Technology PTR
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Programmers, Second Edition
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The first edition of this book was dedicated to
Tony Revel and David Hepburne-Scott, two teachers sadly missed.
The second edition of this book is dedicated to its readers.
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Acknowledgments
The First Edition
For the production of the book, Danny Kodicek conveys his gratitude to Dave Pallai,
Jennifer Blaney, Ania Wieckowski, Bryan Davidson, and Meg Dunkerley. Likewise, to
James Newton and Pim, and Robert Tweed. For web-based tutorials, Jim Andrews, Jonas
Beckeman, Thomas Higgins, Martin Kloss, Lucas Meijer, Allen Partridge, Ben Pitt
(RobotDuck), Simeon Rice (NoiseCrime), Barry Swan, and Alex (Zav) Zavatone. For
mathematical and other grounding, Michael Davies, John Field, Jim Cogan, Jonathan Katz,
and Tony Revell. For physics grounding, David Hepburne-Scott. And to his children Anna
and Matthew for letting him snooze on the sofa in the morning, to his wife Catherine for
putting up with this huge endeavor for so long and her unfailing support, and to his mother
and father for their encouragement and advice.
The Second Edition
For the production of the book, John Flynt conveys his gratitude to Danny Kodicek,
Emi Smith, Kim Benbow, Lisa Staib, Judith Littlefield, and others at Cengage Learning.
For technical concerns, to Ben Sherman, Toby Jones, John Hart, Kevin Claver, and Rob
Johnson. For a general perspective, thanks go to Jim Curry and the prospect of doing
more math. And to his family, Marcia, for being amazing, and to Amy and Adrian, for
being equally amazing. And to Java for being Java and guarding the door: Woof-Woof!
v
About the Authors
John Flyntis the author and co-author of several books on programming, math, software
engineering, and game development. Among his books are Software Engineering for
Game Developers; In the Mind of a Game; Perl Power!: The Comprehensive Guide; Java
Programming for the Absolute Beginner, Second Edition; Beginning Math Concepts for
Game Developers; and Java ME Game Programming, Second Edition.
Danny Kodicek works with Sunflower Learning in the UK developing science simula-
tions and tools for schools. His software has been translated into over fifteen languages
and is sold worldwide. As a freelancer, his previous clients include the BBC and the
Royal Air Force, and he was co-creator of the award-winning TimeHunt website.
vi
Table of Contents
Part I Essential Topics in Mathematics............................... 1
Chapter 1 Numbers..................................................................... 3
Overview...................................................................................... 3
Numbers as Written.................................................................... 4
How Computers Represent Numbers........................................ 9
Exercises....................................................................................... 20
Summary...................................................................................... 21
You Should Now Know.............................................................. 21
Chapter 2 Arithmetic................................................................... 23
Overview...................................................................................... 23
Fractions...................................................................................... 24
Proportions, Ratios, and Percentages........................................ 35
Exponentials................................................................................ 43
Logarithms................................................................................... 47
Exercises....................................................................................... 51
Summary...................................................................................... 52
You Should Now Know.............................................................. 52
Chapter 3 Algebra....................................................................... 53
Overview...................................................................................... 53
Basic Algebra............................................................................... 53
Working with Equations............................................................ 59
Factoring and Solving Quadratic Equations............................. 64
Functions and Graphs................................................................. 76
vii
viii Table of Contents
Exercises....................................................................................... 87
Summary...................................................................................... 88
You Should Now Know.............................................................. 88
Chapter 4 Geometry and Trigonometry ................................... 89
Overview...................................................................................... 89
Angles.......................................................................................... 89
Triangles...................................................................................... 94
Calculations with Triangles........................................................ 105
Rotations and Reflections.......................................................... 110
Exercises....................................................................................... 118
Summary...................................................................................... 118
You Should Now Know.............................................................. 119
Chapter 5 Vectors........................................................................121
Overview...................................................................................... 121
Getting from Here to There....................................................... 121
Vector Motion............................................................................. 130
Vector Calculations..................................................................... 138
Matrices....................................................................................... 147
Exercises....................................................................................... 155
Summary...................................................................................... 155
You Should Now Know.............................................................. 156
Chapter 6 Calculus.......................................................................157
Overview...................................................................................... 157
Differentiation and Integration................................................. 157
Differential Equations................................................................ 170
Approximation Methods............................................................ 173
Exercises....................................................................................... 179
Summary...................................................................................... 180
You Should Now Know.............................................................. 180
Part II Essential Topics in Physics.........................................181
Chapter 7 Acceleration, Mass, and Energy...............................183
Overview...................................................................................... 183
Ballistics....................................................................................... 183
Mass and Momentum................................................................. 190
Energy.......................................................................................... 192
Exercises....................................................................................... 196
Summary...................................................................................... 197
You Should Now Know.............................................................. 198
Table of Contents ix
Chapter 8 Detecting Collisions Between Simple Shapes.........199
Overview...................................................................................... 199
Ground Rules............................................................................... 200
When Circles Collide................................................................... 201
When Squares Collide................................................................. 211
When Ellipses Collide.................................................................. 220
When Things Collide................................................................... 226
Exercises....................................................................................... 227
Summary...................................................................................... 228
You Should Now Know.............................................................. 228
Chapter 9 Collision Resolution...................................................229
Overview...................................................................................... 229
Resolving a Single Collision........................................................ 230
Multiple Collisions...................................................................... 238
Exercises....................................................................................... 242
Summary...................................................................................... 243
You Should Now Know.............................................................. 243
Chapter 10 Detecting Collisions Between Complex Shapes......245
Overview...................................................................................... 245
Problems with Complex Shapes................................................. 246
Some Reasonable Problems....................................................... 259
Built-In Solutions......................................................................... 273
Exercises....................................................................................... 274
Summary...................................................................................... 274
You Should Now Know.............................................................. 275
Chapter 11 A Simple Pool Game..................................................277
Overview...................................................................................... 277
Primary Elements of a Simulation............................................. 278
Taking a Shot.............................................................................. 285
Exercises....................................................................................... 293
Summary...................................................................................... 294
You Should Now Know.............................................................. 294
Part III Complex Motion........................................................295
Chapter 12 Force and Newton’s Laws.........................................297
Overview...................................................................................... 297
Force............................................................................................ 298
Gravity......................................................................................... 302
Rockets and Satellites................................................................. 305
