Mathematics and Physics for Programmers

✍ Scribed by John Patrick Flynt, Danny Kodicek

• Publisher: Cengage Learning
• Year: 2012
• Tongue: English
• Leaves: 689
• Series: Course Technology PTR
• Edition: 2
• Category: Library

✦ Table of Contents

Cover
Table of Contents
Part I: Essential Topics in Mathematics
Chapter 1 Numbers
Overview
Numbers as Written
How Computers Represent Numbers
Exercises
Summary
You Should Now Know
Chapter 2 Arithmetic
Overview
Fractions
Proportions, Ratios, and Percentages
Exponentials
Logarithms
Exercises
Summary
You Should Now Know
Chapter 3 Algebra
Overview
Basic Algebra
Working with Equations
Factoring and Solving Quadratic Equations
Functions and Graphs
Exercises
Summary
You Should Now Know
Chapter 4 Geometry and Trigonometry
Overview
Angles
Triangles
Calculations with Triangles
Rotations and Reflections
Exercises
Summary
You Should Now Know
Chapter 5 Vectors
Overview
Getting from Here to There
Vector Motion
Vector Calculations
Matrices
Exercises
Summary
You Should Now Know
Chapter 6 Calculus
Overview
Differentiation and Integration
Differential Equations
Approximation Methods
Exercises
Summary
You Should Now Know
Part II: Essential Topics in Physics
Chapter 7 Acceleration, Mass, and Energy
Overview
Ballistics
Mass and Momentum
Energy
Exercises
Summary
You Should Now Know
Chapter 8 Detecting Collisions Between Simple Shapes
Overview
Ground Rules
When Circles Collide
When Squares Collide
When Ellipses Collide
When Things Collide
Exercises
Summary
You Should Now Know
Chapter 9 Collision Resolution
Overview
Resolving a Single Collision
Multiple Collisions
Exercises
Summary
You Should Now Know
Chapter 10 Detecting Collisions Between Complex Shapes
Overview
Problems with Complex Shapes
Some Reasonable Problems
Built-In Solutions
Exercises
Summary
You Should Now Know
Chapter 11 A Simple Pool Game
Overview
Primary Elements of a Simulation
Taking a Shot
Exercises
Summary
You Should Now Know
Part III: Complex Motion
Chapter 12 Force and Newton’s Laws
Overview
Force
Gravity
Rockets and Satellites
Exercise
Summary
You Should Now Know
Chapter 13 Angular Motion
Overview
The Physics of a Lever
Spin
Spinning Collisions
Spin Applied to the Pool Game
Exercises
Summary
You Should Now Know
Chapter 14 Friction
Overview
How Friction Works
Friction and Angular Motion
Exercise
Summary
You Should Now Know
Chapter 15 Strings, Pulleys, and Conveyor Belts
Overview
Pulling Things Around
Continuous Momentum
Exercise
Summary
You Should Now Know
Chapter 16 Oscillations
Overview
Springs
Simple Harmonic Motion
Damped Harmonic Motion
Complications of Springs
Calculating Spring Motion
Waves
Exercise
Summary
You Should Now Know
Part IV: 3-D Mathematics
Chapter 17 3-D Geometry
Overview
3-D Vectors
Rendering
Casting a Ray
Exercise
Summary
You Should Now Know
Chapter 18 Transforms
Overview
Describing Locations in Space
Applying Transforms
Exercise
Summary
You Should Now Know
Chapter 19 3-D Collision Detection
Overview
Colliding Worlds
Colliding Footballs
Colliding Boxes
Colliding Cans
Varieties of Collisions
Resolving Collisions in Three Dimensions
Exercise
Summary
You Should Now Know
Chapter 20 Lighting and Textures
Overview
Light
Materials
Shading
Exercises
Summary
You Should Now Know
Chapter 21 Modeling Techniques
Overview
Mathematical 3-D Modeling
Animated Surfaces
Bone Animations
Exercises
Summary
You Should Now Know
Part V: Game Algorithms
Chapter 22 Speeding Things Up
Overview
Cheap and Expensive Calculations
Pseudo-Physics
Culling
Exercises
Summary
You Should Now Know
Chapter 23 Tile-Based Games
Overview
Generating a Game from Bits
Advanced Tiling
Exercises
Summary
You Should Now Know
Chapter 24 Mazes
Overview
Classifying Mazes
Creating Mazes
Navigating Within Mazes
Exercises
Summary
You Should Now Know
Chapter 25 Game Theory and Artificial Intelligence
Overview
Introduction to Game Theory
Tactical AI
Top-Down AI
Bottom-Up AI
Exercises
Summary
You Should Now Know
Chapter 26 Search Techniques
Overview
Problem Solving
Case Study
Genetic Algorithms
Exercises
Summary
You Should Now Know
Appendix A: Glossary of Mathematical Terms
Appendix B: Code References
Appendix C: The Greek Alphabet
Appendix D: Learning Resources
Appendix E: Answers to Exercises
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
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W
Z