Applications are the hallmark of this series, along with student-friendly pedagogy and engaging examples and exercises. The integration of Connect Hosted by ALEKS, along with new lecture and exercise videos, provides students with the support they need to understand the key concepts of college algebra. Cover 1 Title 2 Copyright 3 Contents 4 Preface 9 Index of Applications 18 CHAPTER R: Review of Basic Concepts and Skills 22 R.1 The Language, Notation, and Numbers of Mathematics 23 R.2 Algebraic Expressions and the Properties of Real Numbers 34 R.3 Exponents, Scientific Notation, and a Review of Polynomials 42 R.4 Radicals and Rational Exponents 56 R.5 Factoring Polynomials 68 R.6 Rational Expressions 79 Overview of Chapter R: Prerequisite Definitions, Properties, Formulas, and Relationships 90 Practice Test 92 CHAPTER 1 Equations and Inequalities 94 1.1 Linear Equations, Formulas, and Problem Solving 95 1.2 Linear Inequalities in One Variable 107 1.3 Absolute Value Equations and Inequalities 117 Mid-Chapter Check 125 1.4 Complex Numbers 125 1.5 Solving Quadratic Equations 135 1.6 Solving Other Types of Equations 149 Making Connections 161 Summary and Concept Review 162 Practice Test 165 Calculator Exploration and Discovery: I. Using a Graphing Calculator as an Investigative Tool 166 II. Absolute Value Equations and Inequalities 167 Strengthening Core Skills: Using Distance to Understand Absolute Value Equations and Inequalities 167 CHAPTER 2 Relations, Functions, and Graphs 168 2.1 Rectangular Coordinates; Graphing Circles and Other Relations 169 2.2 Linear Graphs and Rates of Change 182 2.3 Graphs and Special Forms of Linear Equations 197 Mid-Chapter Check 209 2.4 Functions, Function Notation, and the Graph of a Function 209 2.5 Analyzing the Graph of a Function 223 2.6 Linear Functions and Real Data 245 Making Connections 257 Summary and Concept Review 257 Practice Test 261 Calculator Exploration and Discovery: I. Linear Equations, Window Size, and Friendly Windows 262 II. Locating Zeroes, Maximums, and Minimums 263 Strengthening Core Skills: The Various Forms of a Linear Equation 264 Cumulative Review: Chapters R–2 265 CHAPTER 3 More on Functions 266 3.1 The Toolbox Functions and Transformations 267 3.2 Basic Rational Functions and Power Functions 280 3.3 Variation: The Toolbox Functions in Action 295 Mid-Chapter Check 306 3.4 Piecewise-Defined Functions 306 3.5 The Algebra and Composition of Functions 319 3.6 Another Look at Formulas, Functions, and Problem Solving 335 Making Connections 346 Summary and Concept Review 347 Practice Test 350 Calculator Exploration and Discovery: I. Function Families 352 II. Piecewise-Defined Functions 352 Strengthening Core Skills: Finding the Domain and Range of a Relation from Its Graph 353 Cumulative Review: Chapters R–3 354 CHAPTER 4 Polynomial and Rational Functions 356 4.1 Quadratic Functions and Applications 357 4.2 Synthetic Division; the Remainder and Factor Theorems 369 4.3 The Zeroes of Polynomial Functions 381 Mid-Chapter Check 395 4.4 Graphing Polynomial Functions 396 4.5 Graphing Rational Functions 412 4.6 Polynomial and Rational Inequalities 428 Making Connections 439 Summary and Concept Review 440 Practice Test 443 Calculator Exploration and Discovery: I. Complex Zeroes, Repeated Zeroes, and Inequalities 444 II. Removable Discontinuities 445 Strengthening Core Skills: Solving Inequalities Using the Push Principle 445 Cumulative Review: Chapters R–4 446 CHAPTER 5 Exponential and Logarithmic Functions 448 5.1 One-to-One and Inverse Functions 449 5.2 Exponential Functions 459 5.3 Logarithms and Logarithmic Functions 472 Mid-Chapter Check 484 5.4 Properties of Logarithms 485 5.5 Solving Exponential and Logarithmic Equations 494 5.6 Applications from Business, Finance, and Science 504 Making Connections 517 Summary and Concept Review 518 Practice Test 521 Calculator Exploration and Discovery: I. Solving Exponential Equations Graphically 522 II. Investigating Logistic Equations 522 Strengthening Core Skills: The HerdBurn Scale—What's Hot and What's Not 524 Cumulative Review: Chapters R–5 525 CHAPTER 6 Systems of Equations and Inequalities 526 6.1 Linear Systems in Two Variables with Applications 527 6.2 Linear Systems in Three Variables with Applications 542 Mid-Chapter Check 553 6.3 Nonlinear Systems of Equations and Inequalities 553 6.4 Systems of Linear Inequalities and Linear Programming 563 Making Connections 577 Summary and Concept Review 578 Practice Test 580 Calculator Exploration and Discovery: I. Solving Systems Graphically 581 II. Systems of Linear Inequalities 581 Strengthening Core Skills: Solving Linear Systems Using Substitution 582 Cumulative Review: Chapters R–6 583 CHAPTER 7 Matrices and Matrix Applications 584 7.1 Solving Linear Systems Using Matrices and Row Operations 585 7.2 The Algebra of Matrices 597 Mid- Chapter Check 610 7.3 Solving Linear Systems Using Matrix Equations 611 7.4 Applications of Matrices and Determinants: Cramer's Rule, Partial Fractions, and More 626 Making Connections 640 Summary and Concept Review 640 Practice Test 642 Calculator Exploration and Discovery: I. Solving Systems with Technology and Cramer's Rule 644 II. Solving Systems with Matrices, Row Operations, and Technology 644 Strengthening Core Skills: Augmented Matrices and Matrix Inverses 645 Cumulative Review: Chapters R–7 646 CHAPTER 8 Analytic Geometry and the Conic Sections 648 8.1 A Brief Introduction to Analytic Geometry 649 8.2 The Circle and the Ellipse 656 Mid- Chapter Check 668 8.3 The Hyperbola 668 8.4 The Analytic Parabola; More on Nonlinear Systems 680 Making Connections 688 Summary and Concept Review 688 Practice Test 690 Calculator Exploration and Discovery: I. The Graph of a Circle 691 II. Elongation and Eccentricity 691 Strengthening Core Skills: More on Completing the Square 692 Cumulative Review: Chapters R–8 693 CHAPTER 9 Sequences and Series; Counting and Probability 694 9.1 Sequences and Series 695 9.2 Arithmetic Sequences 703 9.3 Geometric Sequences 711 Mid-Chapter Check 721 9.4 Counting Techniques 722 9.5 Introduction to Probability 733 9.6 The Binomial Theorem 745 Making Connections 752 Summary and Concept Review 753 Practice Test 756 Calculator Exploration and Discovery: I. Infinite Series, Finite Results 757 II. Calculating Permutations and Combinations 758 Strengthening Core Skills: Applications of Summation 758 Cumulative Review: Chapters R–9 759 Appendix I: Geometry Review 761 Appendix II: Proof Positive—A Selection of Proofs from College Algebra 772 Appendix III: Deriving the Equation of a Conic 773 Appendix IV: Proof Positive—A Selection of Proofs from College Algebra 775 Student Answer Appendix (SE only) 778 Index 818 A 818 B 818 C 818 D 819 E 819 F 820 G 821 H 821 I 821 J 822 K 822 L 822 M 822 N 822 O 823 P 823 Q 823 R 823 S 824 T 825 U 825 V 825 W 825 X 825 Y 825 Z 825
Three components contribute to a theme sustained throughout the Coburn Series: that of laying a firm foundation, building a solid framework, and providing strong connections. Not only does Coburn present a sound problem-solving process to teach students to recognize a problem, organize a procedure, and formulate a solution, the text encourages students to see beyond procedures in an effort to gain a greater understanding of the big ideas behind mathematical concepts.
Written in a readable, yet mathematically mature manner appropriate for college algebra level students, Coburn’s College Algebra uses narrative, extensive examples, and a range of exercises to connect seemingly disparate mathematical topics into a cohesive whole. Coburn’s hallmark applications are born out of the author’s extensive experiences in and outside the classroom, and appeal to the vast diversity of students and teaching methods in this course area.
Benefiting from the feedback of hundreds of instructors and students across the country, College Algebra second edition, continues to emphasize connections in order to improve the level of student engagement in mathematics and increase their chances of success in college algebra.
