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College Algebra Through Modeling and Visualization,9780321015952
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College Algebra Through Modeling and Visualization

by ; ;
ISBN13:

9780321015952

ISBN10:
0321015959
Format:
Hardcover
Pub. Date:
8/1/1999
Publisher(s):
Pearson College Div

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Summary

Intended for a graphing required college algebra course, this book, offers an innovative approach to the college. It does not simply reiterate past algebra texts and courses. Rather, it consistently integrates mathematical concepts with real applications to enhance student intuition and understanding. Concentrating on broad mathematical themes, the authors emphasize the unifying concepts and skills used repeatedly in mathematics. Symbolic, graphical, numerical, and verbal skills are continually reinforced throughout the course. When introducing mathematical ideas, the authors move from the concrete to the abstract. The authors' believe that learning is enhanced when students can relate a concept to something in their lives. Hence, mathematical concepts are often introduced through applications that help make the mathematics real to students. Definitions and theorems also become more meaningful to students when they are explained and motivated from an applied perspective. Students see the importance of a topic from a practical and intuitive point of view, with models and applications playing a central part in the learning process. This approach increases both student interest and motivation. Once students are interested and motivated, symbolic concepts and abstractions become more accessible.

Table of Contents

Preface ix
Introduction to Functions and Graphs
1(100)
Data, Numbers, and Algorithms
2(12)
Visualization of Data
14(12)
Checking Basic Concepts for Sections 1.1 and 1.2
26(1)
Functions and Their Representations
26(17)
Types of Functions and Their Rates of Change
43(20)
Checking Basic Concepts for Sections 1.3 and 1.4
63(1)
Modeling Data with Functions
63(13)
Transformations of Graphs
76(25)
Checking Basic Concepts for Sections 1.5 and 1.6
95(1)
Summary
95(1)
Review Exercises
96(3)
Extended and Discovery Exercises
99(2)
Linear Functions and Equations
101(81)
Linear Equations
102(14)
Linear Inequalities
116(15)
Checking Basic Concepts for Sections 2.1 and 2.2
131(1)
Equations of Lines
131(16)
Piecewise-Defined Functions
147(16)
Checking Basic Concepts for Sections 2.3 and 2.4
163(1)
Linear Approximation
163(19)
Checking Basic Concepts for Section 2.5
176(1)
Summary
176(1)
Review Exercises
177(3)
Extended and Discovery Exercises
180(2)
Nonlinear Functions and Equations
182(114)
Quadratic Equations and Inequalities
183(17)
Nonlinear Functions and Their Graphs
200(19)
Checking Basic Concepts for Sections 3.1 and 3.2
219(1)
Polynomial Functions and Their Graphs
219(20)
Real Zeros of Polynomial Functions
239(16)
Checking Basic Concepts for Sections 3.3 and 3.4
255(1)
The Fundamental Theorem of Algebra
255(13)
Rational Functions
268(28)
Checking Basic Concepts for Sections 3.5 and 3.6
288(1)
Summary
289(1)
Review Exercises
290(3)
Extended and Discovery Exercises
293(3)
Inverse Functions
296(90)
Combining Functions
297(17)
Inverse Functions and Their Representations
314(17)
Checking Basic Concepts for Sections 4.1 and 4.2
331(1)
Exponential Functions
331(16)
Logarithmic Functions
347(19)
Checking Basic Concepts for Sections 4.3 and 4.4
366(1)
Exponential and Logarithmic Equations
366(20)
Checking Basic Concepts for Section 4.5
379(1)
Summary
380(1)
Review Exercises
380(4)
Extended and Discovery Exercises
384(2)
Systems of Equations and Inequalities
386(94)
Functions and Equations of More than One Variable
387(14)
Linear Systems of Equations and Inequalities in Two Variables
401(19)
Checking Basic Concepts for Sections 5.1 and 5.2
420(1)
Solutions of Linear Systems Using Matrices
420(14)
Properties and Applications of Matrices
434(15)
Checking Basic Concepts for Sections 5.3 and 5.4
449(1)
Inverses of Matrices
449(13)
Determinants
462(18)
Checking Basic Concepts for Sections 5.5 and 5.6
472(1)
Summary
473(1)
Review Exercises
473(4)
Extended and Discovery Exercises
477(3)
Further Topics in Algebra
480(81)
Sequences
481(14)
Series
495(14)
Checking Basic Concepts for Sections 6.1 and 6.2
509(1)
Conic Sections
509(23)
Checking Basic Concepts for Section 6.3
531(1)
Counting
532(12)
Probability
544(17)
Checking Basic Concepts for Sections 6.4 and 6.5
555(1)
Summary
556(1)
Review Exercises
557(2)
Extended and Discovery Exercises
559(2)
Bibliography 561
Answers to Selected Exercises A-1
Index of Applications I-1
Index I-7
TI-83 Graphig Calculator Appendix AP-1


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