College Algebra : A Graphing Approach

by Williams,Gareth

• ISBN13: 9780534462161
• ISBN10: 0534462162
• Edition: 2nd
• Format: Hardcover
• Copyright: 2004-02-11
• Publisher: Brooks Cole

Summary

Williams offers a refreshing and innovative approach to college algebra, motivating the topics with a variety of creative applications and thoroughly integrating the graphing calculator. Written in a clear and friendly voice that speaks to students with varying algebra skills, with a rich array of pedagogical devices to support their learning, this text teaches students to look at math from both algebraic and geometric viewpoints. Williams focuses on the underlying concepts, introducing and using the graphing calculator as an integral means, not an end. This new edition is complemented by an outstanding array of innovative supplements (including online tutorials, video lessons on CD-ROM, and powerful course management and testing resources) that facilitate teaching and enhance learning.

Table of Contents

Preface	xi
Review of Basic Algebra	1	(78)
Application: Understanding the Universe in Which We Live	2	(1)
Real Numbers and Their Properties	3	(13)
Rational Exponents, Scientific Notation, and Doses of Medicine	16	(14)
Polynomials	30	(8)
Factoring	38	(11)
Rational Expressions	49	(9)
Equations, Traffic Flow, and Fermat's Last Theorem	58	(21)
Chapter Project: Space--Time Travel	71	(2)
Highlights	73	(2)
Review Exercises	75	(3)
Chapter Test	78	(1)
Interplay between Algebra and Geometry	79	(110)
Application: Skeleton Sizes	80	(1)
Equations, Graphs, and Data Analysis	80	(10)
Functions, Tables, and Skeleton Sizes	90	(15)
Lines, Least-Squares Fit, and Analysis of Tuition Costs	105	(22)
Linear Functions, Reservoir Monitoring, and Location Evaluation	127	(13)
Parabolas and Quadratic Equations	140	(9)
Quadratic Functions, Learning German, and Fluid Flow	149	(12)
Distances, Circles, and Typesetting	161	(28)
Chapter Project: Real and Subjective Times	179	(2)
Highlights	181	(2)
Review Exercises	183	(4)
Chapter Test	187	(2)
Solving Equations and Inequalities	189	(66)
Application: Motion under Gravity	190	(1)
Quadratic Equations	190	(13)
Further Types of Equations	203	(10)
Equations, Variation, Architecture, Navigation, and Ecology	213	(12)
Inequalities, Temperature Range of a Computer, and Spread of a Disease	225	(15)
Equations and Inequalities with Absolute Values	240	(15)
Chapter Project: Algorithms for Finding Roots and Solving Equations	248	(2)
Highlights	250	(1)
Review Exercises	251	(2)
Chapter Test	253	(1)
Cumulative Test: Chapters R-2	254	(1)
Further Development of Functions	255	(109)
Application: Tracking an Asteroid	256	(1)
Polynomial Functions	256	(9)
Construction of Functions, Optimization, and Drug Administration	265	(13)
Special Functions, Symmetry, and Consumer Awareness	278	(15)
Shifting and Stretching Graphs and Supply and Demand for Wheat	293	(20)
Rational Functions and Queuing Theory	313	(13)
Operations on Functions and an Introduction to the Theory of Chaos	326	(15)
Inverse Functions, One-to-One Functions, and Cryptography	341	(23)
Chapter Project: Recalling Ability	357	(1)
Highlights	358	(2)
Review Exercises	360	(3)
Chapter Test	363	(1)
Further Theory of Polynomials	364	(36)
Application: Fracial Geometry	365	(1)
Synthetic Division, Zeros, and Factors	365	(6)
Complex Numbers and the Mandelbrot Set	371	(10)
Complex Zeros, Complex Factors, and the Fundamental Theorem of Algebra	381	(8)
Computing Zeros of Polynomials	389	(11)
Chapter Project: Julia Sets	396	(1)
Highlights	397	(1)
Review Exercises	398	(1)
Chapter Test	399	(1)
Exponential and Logarithmic Functions	400	(65)
Application: The Bacterium Escherichia coli	401	(1)
Exponential Functions and the Growth of Escherichia coli	402	(13)
The Natural Exponential Function and Color Television	415	(11)
Logarithmic Functions and Seismography	426	(11)
Logarithmic Equations, Dating of Artifacts, and the Learning Curve Effect	437	(14)
Exponential Regression and Intravenous Drug Administration	451	(14)
Chapter Project: Simulating the Government Model for World Population	459	(1)
Highlights	460	(1)
Review Exercises	461	(2)
Chapter Test	463	(1)
Cumulative Test: Chapters 3--5	464	(1)
Systems of Equations and Inequalities	465	(60)
Application: Manufacturing Calculators	466	(1)
Systems of Linear Equations in Two Variables	467	(11)
Systems of Linear Equations in Three Variables	478	(13)
Gauss-Jordan Elimination and Electrical Networks	491	(7)
Systems of Nonlinear Equations	498	(6)
Systems of Linear Inequalities	504	(6)
Linear Programming and Optimal Use of Resources	510	(15)
Chapter Project: Linear Programming	519	(1)
Highlights	520	(2)
Review Exercises	522	(2)
Chapter Test	524	(1)
Matrices	525	(62)
Application: Group Relationships in Sociology	526	(1)
Matrices and Group Relationships in Sociology	526	(15)
Multiplication of Matrices and Population Movements	541	(11)
The Inverse of a Matrix, Color Graphics, and Interdependence of Industries	552	(11)
Determinants and Cramer's Rule	563	(10)
Symmetric Matrices and Archaeology	573	(14)
Chapter Project: Influence within a Group	580	(1)
Highlights	581	(2)
Review Exercises	583	(2)
Chapter Test	585	(2)
Sequences and Series	587	(49)
Application: Accumulation of Email Messages	588	(1)
Sequences, Series, and the Fibonacci Sequence	588	(7)
Arithmetic Sequences	595	(10)
Geometric Sequences, Bacteria Counts, and the Flaw in the Pentium Chip	605	(14)
Mathematical Induction	619	(6)
The Binomial Theorem	625	(11)
Chapter Project: Email Messages	631	(1)
Highlight	632	(1)
Review Exercises	633	(2)
Chapter Test	635	(1)
Permutations, Combinations, and Probability	636
Application: Blood Donors	637	(1)
Permutations and Combinations	638	(9)
Probability and Blood Groups	647
Chapter Project: Traffic Flow	663	(1)
Highlights	664	(1)
Review Exercises	665	(2)
Chapter Test	667	(1)
Cumulative Test: Chapters 6-9	668
Appendix A Conic Sections: Parabolas, Ellipses, and Hyperbolas	1	(12)
Conic Sections	1	(1)
Parabolas	2	(2)
Ellipses	4	(2)
Hyperbolas	6	(7)
Appendix B Calculator Reference	13	(7)
General Calculations	13	(1)
TI-83/83 Plus Reference	14	(6)
Answers to Odd-Numbered Exercises	20	(43)
Index of Applications	63	(3)
Index	66