简介
Williams offers a refreshing and innovative approach to college algebra, motivating the topics with a variety of applications and thoroughly integrating the graphing calculator. Written in a clear and friendly voice that speaks to students with weak algebra skills, 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. New applications examples and exercises from a variety of fields motivate the key ideas and show students why math is useful and powerful. Packaged free with every new copy of the text, an ELECTRONIC COMPANION TO COLLEGE ALGEBRA CD-ROM is a dynamic and interactive college algebra tutorial. It covers key concepts through multiple representations: graphic, numerical, algebraic, and verbal. "Review Topics" boxes present the main ideas of the course and "Test Yourself" problems test student understanding. A workbook of additional examples and exercises is built into the CD-ROM.
目录
Table Of Contents:
Preface xiii
Supplements xxi
Walkthrough xxv
Index of Applications xxxiii
Review of Basic Algebra 1(84)
Real Numbers and Their Properties 3(13)
Rational Exponents, Scientific Notation, and Doses of Medicine 16(14)
Polynomials 30(7)
Factoring 37(7)
Rational Expressions 44(7)
Equations, Variation, Scuba Diving, and Fermat's Last Theorem 51(13)
Functions, Tables, and Skeleton Sizes 64(21)
Chapter Project: Space-Time Travel 77(2)
Highlights 79(2)
Review Exercises 81(3)
Test 84(1)
Interplay Between Algebra and Geometry 85(77)
Coordinate Systems and Graphs 86(9)
Lines, Least-Squares Fit, and the Year 2000 Problem 95(18)
Linear Functions, Reservoir Monitoring, and Cost-Volume Analysis 113(9)
Parabolas and Quadratic Equations 122(7)
Quadratic Functions, Learning German, and Fluid Flow 129(10)
Distances, Circles, and Typesetting 139(23)
Chapter Project: Real and Subjective Times 154(2)
Highlights 156(1)
Review Exercises 157(3)
Test 160(2)
Solving Equations and Inequalities 162(55)
Quadratic Equations 163(12)
Applications of Quadratic Equations Including Motion and Architecture 175(7)
Further Types of Equations 182(9)
Inequalities, Temperature Range of a Computer, and Spread of a Disease 191(13)
Equations and Inequalities with Absolute Values 204(13)
Chapter Project: Algorithms for Finding Roots and Solving Equations 210(2)
Highlights 212(1)
Review Exercises 213(1)
Test 214(1)
Cumulative Test 215(2)
Further Development of Functions 217(106)
Polynomial Functions 218(8)
Construction of Functions, Optimization, and Drug Administration 226(14)
Special Functions, Symmetry, and Consumer Awareness 240(15)
Shifting and Stretching Graphs, Supply and Demand for Wheat 255(20)
Rational Functions 275(11)
Operations on Functions and an Introduction to the Field of Chaos 286(14)
Inverse Functions, One-to-One, and Cryptography 300(23)
Chapter Project: Recalling Ability 315(2)
Highlights 317(1)
Review Exercises 318(3)
Test 321(2)
Further Theory of Polynomials 323(35)
Synthetic Division, Zeros, and Factors 324(6)
Complex Numbers and the Mandelbrot Set 330(11)
Complex Zeros, Complex Factors, and the Fundamental Theorem of Algebra 341(6)
Computing Zeros of Polynomials 347(11)
Chapter Project: Julia Sets 354(1)
Highlights 355(1)
Review Exercises 356(1)
Test 357(1)
Exponential and Logarithmic Functions 358(62)
Exponential Functions and the Growth of Escherichia coli 360(14)
The Natural Exponential Function and Solving Exponential Equations 374(10)
Logarithmic Functions and Seismography 384(9)
Properties of Logarithms and Solving Logarithmic Equations 393(11)
Exponential Regression and Intravenous Drug Administration 404(16)
Chapter Project: Simulating the Government Model for World Population 414(1)
Highlights 415(1)
Review Exercises 416(1)
Test 417(1)
Cumulative Test 418(2)
Systems of Equations and Inequalities 420(56)
Systems of Linear Equations in Two Variables 422(11)
Systems of Linear Equations in Three Variables 433(12)
Gauss-Jordan Elimination and Electrical Networks 445(7)
Systems of Nonlinear Equations 452(6)
Systems of Linear Inequalities 458(6)
Linear Programming and Optimal Use of Resources 464(12)
Chapter Project: Linear Programming 471(1)
Highlights 472(1)
Review Exercises 473(2)
Test 475(1)
Matrices 476(59)
Matrices and Group Relationships in Sociology 477(15)
Multiplication of Matrices and Population Movements 492(11)
The Inverse of a Matrix and the Interdependence of Industries 503(9)
Determinants and Cramer's Rule 512(10)
Symmetric Matrices and Archaeology 522(13)
Chapter Project: Influence Within a Group 528(2)
Highlights 530(1)
Review Exercises 531(2)
Test 533(2)
Sequences and Series 535(47)
Sequences, Series, and the Fibonacci Sequence 536(8)
Arithmetic Sequences 544(8)
Geometric Sequences, Count of Bacteria, and the Flaw in the Pentium Chip 552(14)
Mathematical Induction 566(1)
The Binomial Theorem 567(15)
Chapter Project: E-Mail Messages 576(2)
Highlights 578(1)
Review Exercises 579(1)
Test 580(2)
Permutations, Combinations, and Probability 582(32)
Permutations and Combinations 583(9)
Probability and Blood Groups 592(22)
Chapter Project: Traffic Flow 607(1)
Highlights 608(1)
Review Exercises 609(2)
Test 611(1)
Cumulative Test 612(2)
Conic Sections 614(12)
TI-82/TI-83 Calculator Reference 626(7)
Answers to Odd-Numbered Exercises 633(42)
Index 675
Preface xiii
Supplements xxi
Walkthrough xxv
Index of Applications xxxiii
Review of Basic Algebra 1(84)
Real Numbers and Their Properties 3(13)
Rational Exponents, Scientific Notation, and Doses of Medicine 16(14)
Polynomials 30(7)
Factoring 37(7)
Rational Expressions 44(7)
Equations, Variation, Scuba Diving, and Fermat's Last Theorem 51(13)
Functions, Tables, and Skeleton Sizes 64(21)
Chapter Project: Space-Time Travel 77(2)
Highlights 79(2)
Review Exercises 81(3)
Test 84(1)
Interplay Between Algebra and Geometry 85(77)
Coordinate Systems and Graphs 86(9)
Lines, Least-Squares Fit, and the Year 2000 Problem 95(18)
Linear Functions, Reservoir Monitoring, and Cost-Volume Analysis 113(9)
Parabolas and Quadratic Equations 122(7)
Quadratic Functions, Learning German, and Fluid Flow 129(10)
Distances, Circles, and Typesetting 139(23)
Chapter Project: Real and Subjective Times 154(2)
Highlights 156(1)
Review Exercises 157(3)
Test 160(2)
Solving Equations and Inequalities 162(55)
Quadratic Equations 163(12)
Applications of Quadratic Equations Including Motion and Architecture 175(7)
Further Types of Equations 182(9)
Inequalities, Temperature Range of a Computer, and Spread of a Disease 191(13)
Equations and Inequalities with Absolute Values 204(13)
Chapter Project: Algorithms for Finding Roots and Solving Equations 210(2)
Highlights 212(1)
Review Exercises 213(1)
Test 214(1)
Cumulative Test 215(2)
Further Development of Functions 217(106)
Polynomial Functions 218(8)
Construction of Functions, Optimization, and Drug Administration 226(14)
Special Functions, Symmetry, and Consumer Awareness 240(15)
Shifting and Stretching Graphs, Supply and Demand for Wheat 255(20)
Rational Functions 275(11)
Operations on Functions and an Introduction to the Field of Chaos 286(14)
Inverse Functions, One-to-One, and Cryptography 300(23)
Chapter Project: Recalling Ability 315(2)
Highlights 317(1)
Review Exercises 318(3)
Test 321(2)
Further Theory of Polynomials 323(35)
Synthetic Division, Zeros, and Factors 324(6)
Complex Numbers and the Mandelbrot Set 330(11)
Complex Zeros, Complex Factors, and the Fundamental Theorem of Algebra 341(6)
Computing Zeros of Polynomials 347(11)
Chapter Project: Julia Sets 354(1)
Highlights 355(1)
Review Exercises 356(1)
Test 357(1)
Exponential and Logarithmic Functions 358(62)
Exponential Functions and the Growth of Escherichia coli 360(14)
The Natural Exponential Function and Solving Exponential Equations 374(10)
Logarithmic Functions and Seismography 384(9)
Properties of Logarithms and Solving Logarithmic Equations 393(11)
Exponential Regression and Intravenous Drug Administration 404(16)
Chapter Project: Simulating the Government Model for World Population 414(1)
Highlights 415(1)
Review Exercises 416(1)
Test 417(1)
Cumulative Test 418(2)
Systems of Equations and Inequalities 420(56)
Systems of Linear Equations in Two Variables 422(11)
Systems of Linear Equations in Three Variables 433(12)
Gauss-Jordan Elimination and Electrical Networks 445(7)
Systems of Nonlinear Equations 452(6)
Systems of Linear Inequalities 458(6)
Linear Programming and Optimal Use of Resources 464(12)
Chapter Project: Linear Programming 471(1)
Highlights 472(1)
Review Exercises 473(2)
Test 475(1)
Matrices 476(59)
Matrices and Group Relationships in Sociology 477(15)
Multiplication of Matrices and Population Movements 492(11)
The Inverse of a Matrix and the Interdependence of Industries 503(9)
Determinants and Cramer's Rule 512(10)
Symmetric Matrices and Archaeology 522(13)
Chapter Project: Influence Within a Group 528(2)
Highlights 530(1)
Review Exercises 531(2)
Test 533(2)
Sequences and Series 535(47)
Sequences, Series, and the Fibonacci Sequence 536(8)
Arithmetic Sequences 544(8)
Geometric Sequences, Count of Bacteria, and the Flaw in the Pentium Chip 552(14)
Mathematical Induction 566(1)
The Binomial Theorem 567(15)
Chapter Project: E-Mail Messages 576(2)
Highlights 578(1)
Review Exercises 579(1)
Test 580(2)
Permutations, Combinations, and Probability 582(32)
Permutations and Combinations 583(9)
Probability and Blood Groups 592(22)
Chapter Project: Traffic Flow 607(1)
Highlights 608(1)
Review Exercises 609(2)
Test 611(1)
Cumulative Test 612(2)
Conic Sections 614(12)
TI-82/TI-83 Calculator Reference 626(7)
Answers to Odd-Numbered Exercises 633(42)
Index 675
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