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Precalculus Essentials

Precalculus Essentials Cover


About the Author

Mike Sullivan Professor of Mathematics at Chicago State University received a Ph.D. in mathematics from Illinois Institute of Technology. Mike has taught at Chicago State for over 30 years. He is a native of Chicago’s South Side and currently resides in Oaklawn.  Mike has four children.  The two oldest have degrees in mathematics and assisted in proofing, checking examples and exercises, and writing solutions manuals for this project.  Mike III co-authored the Sullivan Graphing with Data Analysis series as well as this series.  Dan, the youngest, sells for Prentice Hall as a generalist.


Mike has authored or co-authored over ten books.  He owns a travel agency, and splits his time between a condo in Naples, Florida and a home in Oaklawn, where Mike enjoys gardening.  Mike first signed this series with Deleen Publishing (Acquired by Macmillan) in 1985.


Table of Contents

Precalculus Essentials 7e


            The Essentials Edition xiii

            Preface to the Instructor xv

            List of Applications xxi

            Photo Credits xxvChapter 1 Graphs 1

1.1   Rectangular Coordinates 2

1.2   Graph of Equations; Circles 9

1.3   Lines 22

1.4   Scatter Diagrams; Linear Curve Fitting 38

Chapter Review 45

Chapter Projects 48Chapter 2 Functions and Their Graphs 49

            2.1 Functions 50

            2.2 The Graph of a Function 63

            2.3 Properties of Functions 72

            2.4 Library of Functions; Piecewise-defined Functions 83

            2.5 Graphing Techniques: Transformations 94

            2.6 Mathematical Models: Constructing Functions 107

                        Chapter Review 115

                        Chapter Projects 121

                        Cumulative Review 122Chapter 3 Polynomial and Rational Functions 123

            3.1 Quadratic Functions and Models 124

            3.2 Polynomial Functions 144

            3.3 Rational Functions I 162

            3.4 Rational Functions II: Analyzing Graphs 173

            3.5 Polynomial and Rational Inequalities 188

            3.6 The Real Zeros of a Polynomial Function 194

            3.7 Complex Zeros; Fundamental Theorem of Algebra 209

                        Chapter Review 215

                        Chapter Projects 220

                        Cumulative Review 221Chapter 4 Exponential and Logarithmic Functions 223

            4.1 Composite Functions 224

            4.2 Inverse Functions 231

            4.3 Exponential Functions 244

            4.4 Logarithmic Functions 260

            4.5 Properties of Logarithms 273

            4.6 Logarithmic and Exponential Equations 282

            4.7 Compound Interest 287

            4.8 Exponential Growth and Decay; Newton’s Law; Logistic Models 297

            4.9 Fitting Data to Exponential, Logarithmic, and Logistic Functions 306

                        Chapter Review 314

                        Chapter Projects 320

                        Cumulative Review 321

Chapter 5 Trigonometric Functions 323

            5.1 Angles and Their Measure 324

            5.2 Trigonometric Functions: Unit Circle Approach 338

            5.3 Properties of the Trigonometric Functions 355

            5.4 Graphs of the Sine and Cosine Functions 369

            5.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions 386

            5.6 Phase Shift; Sinusoidal Curve Fitting 393

                        Chapter Review 405

                        Chapter Projects 411

                        Cumulative Review 412

Chapter 6 Analytical Trigonometry 413

            6.1 The Inverse Sine, Cosine, and Tangent Functions 414

            6.2 The Inverse Trigonometric Functions (continued) 425

            6.3 Trigonometric Identities 430

            6.4 Sum and Difference Formulas 437

            6.5 Double-angle and Half-angle Formulas 448

            6.6 Product-to-Sum and Sum-to-Product Formulas 457

            6.7 Trigonometric Equations I 461

            6.8 Trigonometric Equations II 467

                        Chapter Review 475

                        Chapter Projects 479

                        Cumulative Review 480

Chapter 7 Applications of Trigonometric Functions 481

            7.1 Right Triangle Trigonometry; Applications 482

            7.2 The Law of Sines 494

            7.3 The Law of Cosines 507

Chapter 8 Polar Coordinates; Vectors 515

            8.1 Polar Coordinates 516

            8.2 Polar Equations and Graphs 525

Chapter 9 Analytical Geometry 543

            9.7 Plane Curves and Parametric Equations 544 

Chapter 10 Systems of Equations and Inequalities 559

            10.1 Systems of Linear Equations: Substitution and Elimination 560

Chapter 11 Sequences; Induction; The Binomial Theorem 577

            11.1 Sequences 578

            11.2 Arithmetic Sequences 587

            11.3 Geometric Sequences; Geometric Series 593           

Appendix A Review 611

         A.1 Algebra Review 611

            A.2 Geometry Review 621

            A.3 Polynomials and Rational Expressions 626

            A.4 Polynomial Division; Synthetic Division 637

            A.5 Solving Equations 644

            A.6 Complex Numbers; Quadratic Equations in the Complex Number System 655

            A.7 Setting Up Equations: Applications 664

            A.8 Interval Notation; Solving Inequalities 676

            A.9 nth Roots; Rational Exponents; Radical Equations 685

Appendix B Graphing Utilities 693

            B.1 The Viewing Rectangle 693

            B.2 Using a Graphing Utility to Graph Equations 695

            B.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry 699

            B.4 Using a Graphing Utility to Solve Equations 701

            B.5 Square Screens 703

            B.8 Using a Graphing Utility to Graph a Polar Equations 705

            B.9 Using a Graphing Utility to Graph Parametric Equations 706


            Answers A1


            Index I1



Product Details

Prentice Hall
Sullivan, Michael
Publication Date:
Grade Level:
College/higher education:
10.3 x 8.16 x 1.205 in 1640 gr

Related Subjects

Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » Calculus » General

Precalculus Essentials
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Product details 832 pages Prentice Hall - English 9780131469839 Reviews:
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