Vectors and Their Applications

Vectors and Their Applications

by Anthony J. Pettofrezzo

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Overview

Geared toward undergraduate students, this text illustrates the use of vectors as a mathematical tool in plane synthetic geometry, plane and spherical trigonometry, and analytic geometry of two- and three-dimensional space. Its rigorous development includes a complete treatment of the algebra of vectors in the first two chapters.
Among the text's outstanding features are numbered definitions and theorems in the development of vector algebra, which appear in italics for easy reference. Most of the theorems include proofs, and coordinate position vectors receive an in-depth treatment. Key concepts for generalized vector spaces are clearly presented and developed, and 57 worked-out illustrative examples aid students in mastering the concepts. A total of 258 exercise problems offer supplements to theories or provide the opportunity to reinforce the understanding of applications, and answers to odd-numbered exercises appear at the end of the book.

Product Details

ISBN-13: 9780486445212
Publisher: Dover Publications
Publication date: 09/08/2005
Series: Dover Books on Mathematics Series
Pages: 144
Product dimensions: 6.12(w) x 9.25(h) x (d)

Table of Contents

1. Elementary Operations
1.1 Scalars and Vectors
1.2 Equality of Vectors
1.3 Vector Addition and Subtraction
1.4 Multiplication of a Vector by a Scalar
1.5 LInear Dependence of Vectors
1.6 Applications of Linear Dependence
1.7 Position Vectors
2. Products of Vectors
2.1 The Scalar Product
2.2 Applications of the Scalar Product
2.3 Circles and Lines on a Coordinate Plane
2.4 Translation and Rotation
2.5 Orthogonal Bases
2.6 The Vector Product
2.7 Applications of the Vector Product
2.8 The Scalar Triple Product
2.9 The Vector Triple Product
2.10 Quadruple Products
2.11 Quaternions
3. Planes and Lines in Space
3.1 Direction Cosines and Numbers
3.2 Equation of a Plane
3.3 Equation of a Sphere
3.4 Angle Between Two Planes
3.5 Distance Between a Point and a Plane
3.6 Equation of a Line
3.7 Skew Lines
3.8 Distance Between a Point and a Line
Bibliography for Reference
Answers for Odd-Numbered Exercises
Index

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