College Algebra: A View of the World Around Us / Edition 1

College Algebra: A View of the World Around Us / Edition 1

by David Wells, Lynn Schmitt
     
 

ISBN-10: 0135710197

ISBN-13: 9780135710197

Pub. Date: 03/28/1997

Publisher: Prentice Hall Professional Technical Reference

This book places mathematics into a concrete, real- world setting. Designed to emphasize problem solving-skills, it introduces new concepts in the context of physical situations to show how algebra can be applied to solve physical problems. The book provides analytical, graphical, and numerical approaches to all major topics. Readers

Overview

This book places mathematics into a concrete, real- world setting. Designed to emphasize problem solving-skills, it introduces new concepts in the context of physical situations to show how algebra can be applied to solve physical problems. The book provides analytical, graphical, and numerical approaches to all major topics. Readers who find one approach to a topic most natural can use that approach to enhance their understanding of the other two. It includes regular use of Polya problem solving strategies. By frequently identifying Polya strategies used in the exposition, the book provides readers with a large number of examples of how each strategy can be used effectively. The use of graphing calculators is incorporated where appropriate as well as discussions of the advantages and limitations of technology. A valuable reference book for any reader who needs a greater understanding of the real-world problem-solving capabilities of algebra.

Product Details

ISBN-13:
9780135710197
Publisher:
Prentice Hall Professional Technical Reference
Publication date:
03/28/1997
Pages:
539
Product dimensions:
8.20(w) x 10.22(h) x 1.02(d)

Related Subjects

Table of Contents

PREFACE XIII
CHAPTER 1 MODELING AND PROBLEM SOLVING
1(28)
1-1 A Case for Algebra
1(6)
Algebra Is an Analytical Tool
4(1)
Algebra Is Rich in Concepts and Contexts
4(1)
Algebra Is Part of Our Intellectual Heritage
5(1)
You May Actually Use Algebra!
5(1)
Some Suggestions for Feeling at Home with This Book
5(2)
1-2 Models of Quantitative Relationships
7(12)
Three Types of Model
7(1)
Information Provided by the Three Types of Model
8(1)
Creating One Model from Another
9(10)
1-3 Problem-Solving Strategies
19(8)
First Step: Understand the Problem
20(1)
Second Step: Devise a Plan
21(1)
Third Step: Carry Out the Plan
22(1)
Fourth Step: Look Back
23(4)
Chapter Review
27(2)
CHAPTER 2 FUNCTIONS
29(44)
2-1 Three Views of Functions
29(11)
The Definition of Function
29(2)
A Numerical View of Functions
31(1)
An Analytical View of Functions
32(1)
A Graphical View of Functions
33(3)
Reasons to Study Functions and Their Models
36(4)
2-2 The Concept of Function As Process
40(11)
Functional Notation
41(1)
Combining Functions
42(9)
2-3 Domain and Range
51(14)
Domain and Range of Abstract Functions
52(3)
Domain and Range of Functions in a Physical Context
55(2)
Sequences
57(2)
Dynamic Behavior: Increasing and Decreasing Functions
59(6)
2-4 Solving Equations and Inequalities Graphically
65(6)
Solving Equations Graphically
66(2)
Solving Inequalities Graphically
68(3)
Chapter Review
71(2)
CHAPTER 3 LINEAR FUNCTIONS
73(42)
3-1 Three Views of Linear Functions
73(10)
A Numerical View of Linear Functions
73(4)
A Graphical View of Linear Functions
77(1)
An Analytical View of Linear Functions
78(2)
Summary
80(3)
3-2 Modeling and Problem Solving with Linear Functions
83(8)
Modeling of Linear Relationships
83(2)
Linear Variation
85(1)
Arithmetic Sequences
86(5)
3-3 Linear Modeling of Nonlinear Relationships
91(10)
Linearization
91(2)
Average Rate of Change
93(8)
3-4 Piecewise Linear Functions
101(12)
Three Views of Piecewise Linear Functions
102(2)
Three Views of Linear Absolute Value Functions
104(5)
Solving Linear Absolute Value Inequalities
109(4)
Chapter Review
113(2)
CHAPTER 4 LINEAR SYSTEMS
115(34)
4-1 Systems of Linear Equations
115(10)
Methods of Solving 2 X 2 Systems
115(2)
Methods of Solving 3 X 3 Systems
117(2)
Numbers of Solutions to 2 X 2 and 3 X 3 Systems
119(6)
4-2 Matrix Solutions of Systems of Linear Equations
125(14)
Augmented Matrix of a System
125(1)
Matrix Row Operations
126(2)
Gauss-Jordan Elimination
128(2)
Reduced Row-Echelon Matrices
130(1)
Matrices and Numbers of Solutions
131(5)
Summary: Matrix Versus Nonmatrix Methods
136(3)
4-3 Systems of Linear Inequalities and Linear Programming
139(8)
Graphs of Linear Inequalities in Two Variables
139(2)
Graphs of Systems of Linear Inequalities in Two Variables
141(1)
Linear Programming
142(5)
Chapter Review
147(2)
CHAPTER 5 QUADRATIC FUNCTIONS
149(28)
5-1 Three Views of Quadratic Functions
149(17)
A Graphical View of Quadratic Functions
150(4)
An Analytical View of Quadratic Functions
154(6)
A Numerical View of Quadratic Functions
160(6)
5-2 Modeling and Problem Solving with Quadratic Functions
166(9)
Optimization Problems
166(2)
Solving Quadratic Inequalities
168(2)
Fitting a Quadratic Function to a Table
170(5)
Chapter Review
175(2)
CHAPTER 6 QUADRATIC RELATIONS
177(74)
6-1 Relations
177(10)
Three Views of Relations
179(5)
Implicit Functions
184(3)
6-2 A Graphical View of Conic Sections
187(15)
A Graphical View of Parabolas
189(1)
A Graphical View of Ellipses
190(5)
A Graphical View of Hyperbolas
195(5)
Exceptional Graphs
200(2)
6-3 Graphical Transformations
202(15)
Stretches and Compressions
203(2)
Shifts
205(1)
Reflections
206(2)
Applying a Sequence of Transformations
208(3)
Summary
211(6)
6-4 An Analytical View of Conic Sections
217(15)
An Analytical View of Parabolas
217(4)
An Analytical View of Ellipses
221(4)
An Analytical View of Hyperbolas
225(7)
6-5 Square Root Functions
232(6)
6-6 Systems of Quadratic Equations and Inequalities
238(11)
Solving Systems of Quadratic Equations Analytically
239(2)
Solving Systems of Quadratic Equations Graphically
241(2)
Solving Systems of Quadratic Inequalities
243(6)
Chapter Review
249(2)
CHAPTER 7 POLYNOMIAL FUNCTIONS
251(44)
7-1 Power Functions
251(8)
Basic Power Functions and Their Graphs
251(2)
Graphical Transformations
253(1)
Polynomial Variation
254(5)
7-2 An Analytical View of Polynomial Functions
259(8)
Factors and Zeros
260(2)
The Fundamental Theorem of Algebra
262(5)
7-3 A Graphical View of Polynomial Functions
267(14)
Points of Interest
268(5)
End Behavior
273(3)
Symmetry
276(5)
7-4 A Numerical View of Polynomial Functions
281(6)
nth-Order Differences
281(1)
Fitting a Polynomial Function to a Table
282(1)
A Numerical Method for Finding Zeros
283(2)
A Comparison of Methods for Finding Zeros
285(2)
7-5 Solving Polynomial Inequalities
287(6)
Solving Polynomial Inequalities Graphically
287(2)
Solving Polynomial Inequalities Analytically
289(4)
Chapter Review
293(2)
CHAPTER 8 RATIONAL FUNCTIONS
295(28)
8-1 Reciprocal Power Functions
295(5)
Three Views of Reciprocal Power Functions
296(2)
Inverse Variation
298(2)
Graphical Transformations
300(4)
8-2 Discontinuities and End Behavior of Rational Functions
304(10)
Discontinuities and Vertical Asymptotes
305(3)
End Behavior and Horizontal Asymptotes
308(6)
8-3 Solving Rational Inequalities
314(6)
A Graphical Method
316(1)
The Test-Value Method
316(1)
The Scan Method
317(3)
Chapter Review
320(3)
CHAPTER 9 EXPONENTIAL AND LOGARITHMIC FUNCTIONS
323
9-1 Exponential Functions
323(15)
A Numerical View of Exponential Functions
324(2)
An Analytical View of Exponential Functions
326(3)
A Graphical View of Exponential Functions
329(3)
Geometric Sequences and Series
332(6)
9-2 The Special Number e
338(7)
The Definition of e
338(3)
Using the Base e to Express Exponential Functions
341(4)
9-3 Inverse Functions
345(13)
One-to-One Functions
346(2)
Finding Inverses of One-to-One Functions
348(10)
9-4 Logarithmic Functions
358(16)
A Numerical View of Logarithmic Functions
360(3)
A Graphical View of Logarithmic Functions
363(2)
An Analytical View of Logarithmic Functions
365(9)
9-5 Curve Fitting
374(14)
Fitting Linear Functions to Data
375(3)
Fitting Logarithmic Functions to Data
378(2)
Fitting Exponential Functions to Data
380(1)
Fitting Power Functions to Data
381(2)
Curve Fitting on Your Calculator
383(5)
Chapter Review
388
APPENDIX A BASIC ALGEBRA REFERENCE A1
A-1 Accuracy and Precision A1
A-2 Linear Equations A4
A-3 The Coordinate Plane A5
A-4 The Pythagorean Theorem and the Distance Formula A7
A-5 Basic Graphing Techniques A8
A-6 Graphing Linear Equations A11
A-7 Intervals A15
A-8 Linear Inequalities A17
A-9 Absolute Value Equations and Inequalities A19
A-10 Systems of Linear Equations A22
A-11 The Laws of Exponents A26
A-12 Factoring A28
A-13 Quadratic Equations A32
A-14 Operations with Complex Numbers A36
A-15 Division and Synthetic Division of Polynomials A38
A-16 Algebraic Fractions A41
A-17 Equations with Algebraic Fractions A48
A-18 Radicals and Rational Exponents A49
A-19 Equations with Radicals A54
APPENDIX B TIPS FOR GRAPHING FUNCTIONS WITH A CALCULATOR B1
B-1 The Viewing Window B1
B-2 Graphing Linear Functions B6
B-3 Graphing Quadratic Functions B7
B-4 Graphing Quadratic Relations B9
B-5 Graphing Polynomial Functions B11
B-6 Graphing Rational Functions B14
ANSWERS TO ODD-NUMBERED EXERCISES ANS 1
INDEX 11

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