Matrices, Vectors, and 3D Math

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Matrices, Vectors, and 3D Math: A Game Programming Approach with MATLAB®
Scott Stevens– Champlain College

ISBN-10: 0-9842071-8-X
ISBN-13: 978-0-9842071-8-3
254 Pages
©2019 Worldwide Center of Mathematics, LLC

Digital | $9.95
Print | $29.95

 

Features

 

contents

 

Supplements

Introduction

Written for undergraduate students, Matrices, Vectors, and 3D Math: A Game Programming Approach with MATLAB provides a resource to learn standard topics in linear algebra and vector calculus in a single course within the context of game programming applications and projects. Topics presented in this text are constructed to enable students to succeed after completing a single college-level calculus course.  

MATLAB is used to solve numerous examples in the book. In addition, a supplemental set of MATLAB code files is available for download here.


Features

  • The text contains standard topics in Linear Algebra followed by a selection of topics usually found in a Calculus III course including vector geometry, differential calculus, and surfaces.

  • Applications are drawn from an interesting collection of game programming objectives such as collision detection, realistic trajectories, and collision response.
         
  • Most applications involve graphical depictions and animations written in MATLAB®. 

  • All example code found in the text is available for student download from the associated website.  These can be used as ‘starter code’ for many of the homework assignments.

  • Homework problems consist of standard ‘pencil and paper’ problems as well as MATLAB® assignments. 

  • Detailed solutions to about half of the homework problems are presented in the back of the student version - not just the answers.

  • There is an appendix for trigonometry review with a collection of homework problems.

  • There is an appendix for using MATLAB® which includes a simple project to get students started using the software along with starter code for the project. 

  • Each instructor gets a full electronic PDF copy of the student version for presentation purposes.
     
  • Each instructor gets a full PDF copy of an instructor’s version, which has detailed solutions to all homework problems inserted within the text.

  • Instructors can also receive the MATLAB® code for answers to all of the problems requiring it.  

Contents

  • 1.1 Systems of Linear Equations - Row Reduction
  • 1.2 Matrices and Vectors
  • 1.3 Inverses and Determinants
  • 1.4 Vector Spaces: R2 and R3
  • 1.5 Linear Independence, Span, Basis, Dimension
  • 1.6 Change of Basis
  • 1.7 Matrix Transformations
  • 2.1 Vectors in the Plane
  • 2.2 Vectors in Space
  • 2.3 The Dot Product
  • 2.4 The Cross Product
  • 2.5 Lines in 2D and 3D
  • 2.6 Planes
  • 2.7 Collision Detection and Response: Lines and Planes
  • 3.1 Vector-Valued Functions and Curves
  • 3.2 Differentiation of Vector-Valued Functions
  • 3.3 Projectiles
  • 3.4 Euler's Method
  • 3.5 Bouncing Around in 2D
  • 4.1 Surfaces: z = f(x; y)
  • 4.2 Partial Derivatives, Gradients, and Normal Vectors
  • 4.3 Bouncing Around in 3D

 

 

Supplements

 

Web Technology Pages:

MATLAB® files are available for each chapter: http://www.StevensMV3D.com