Precalculus
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Specificații
ISBN-13: 9780137141609
ISBN-10: 0137141602
Pagini: 1200
Ilustrații: Illustrations
Dimensiuni: 215 x 274 x 40 mm
Greutate: 2.38 kg
Ediția:Nouă
Editura: Pearson Education (US)
Locul publicării:Upper Saddle River, United States
ISBN-10: 0137141602
Pagini: 1200
Ilustrații: Illustrations
Dimensiuni: 215 x 274 x 40 mm
Greutate: 2.38 kg
Ediția:Nouă
Editura: Pearson Education (US)
Locul publicării:Upper Saddle River, United States
Cuprins
Chapter 1 Graphs
1.1 Rectangular Coordinates; Graphing Utilities; Introduction to Graphing Equations
1.2 Intercepts; Symmetry; Graphing Key Equations
1.3 Solving Equations Using a Graphing Utility
1.4 Lines
1.5 Circles
Chapter 2 Functions and Their Graphs
2.1 Functions
2.2 The Graph of a Function
2.3 Properties of Functions
2.4 Library of Functions; Piecewise-defined Functions
2.5 Graphing Techniques: Transformations
2.6 Mathematical Models: Building Functions
Chapter 3 Linear and Quadratic Functions
3.1 Linear Functions, Their Properties, and Linear Models
3.2 Building Linear Models from Data; Direct Variation
3.3 Quadratic Functions and Their Properties
3.4 Building Quadratic Models from Verbal Descriptions and Data
3.5 Inequalities Involving Quadratic Functions
Chapter 4 Polynomial and Rational Functions
4.1 Polynomial Functions and Models
4.2 Properties of Rational Functions
4.3 The Graph of a Rational Function
4.4 Polynomial and Rational Inequalities
4.5 The Real Zeros of a Polynomial Function
4.6 Complex Zeros; Fundamental Theorem of Algebra
Chapter 5 Exponential and Logarithmic Functions
5.1 Composite Functions
5.2 One-to-One Functions; Inverse Functions
5.3 Exponential Functions
5.4 Logarithmic Functions
5.5 Properties of Logarithms
5.6 Logarithmic and Exponential Equations
5.7 Financial Models
5.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models
5.9 Building Exponential, Logarithmic, and Logistic Models from Data
Chapter 6 Trigonometric Functions
6.1 Angles and Their Measure
6.2 Trigonometric Functions: Unit Circle Approach
6.3 Properties of the Trigonometric Functions
6.4 Graphs of the Sine and Cosine Functions
6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
6.6 Phase Shift; Building Sinusoidal Models
Chapter 7 Analytic Trigonometry
7.1 The Inverse Sine, Cosine, and Tangent Functions
7.2 The Inverse Trigonometric Functions (Continued)
7.3 Trigonometric Identities
7.4 Sum and Difference Formulas
7.5 Double-angle and Half-angle Formulas
7.6 Product-to-Sum and Sum-to-Product Formulas
7.7 Trigonometric Equations (I)
7.8 Trigonometric Equations (II)
Chapter 8 Applications of Trigonometric Functions
8.1 Applications Involving Right Triangles
8.2 The Law of Sines
8.3 The Law of Cosines
8.4 Area of a Triangle
8.5 Simple Harmonic Motion; Damped Motion; Combining Waves
Chapter 9 Polar Coordinates; Vectors
9.1 Polar Coordinates
9.2 Polar Equations and Graphs
9.3 The Complex Plane; DeMoivre’s Theorem
9.4 Vectors
9.5 The Dot Product
9.6 Vectors in Space
9.7 The Cross Product
Chapter 10 Analytic Geometry
10.1 Conics
10.2 The Parabola
10.3 The Ellipse
10.4 The Hyperbola
10.5 Rotation of Axes; General Form of a Conic
10.6 Polar Equations of Conics
10.7 Plane Curves and Parametric Equations
Chapter 11 Systems of Equations and Inequalities
11.1 Systems of Linear Equations: Substitution and Elimination
11.2 Systems of Linear Equations: Matrices
11.3 Systems of Linear Equations: Determinants
11.4 Matrix Algebra
11.5 Partial Fraction Decomposition
11.6 Systems of Nonlinear Equations
11.7 Systems of Inequalities
11.8 Linear Programming
Chapter 12 Sequences; Induction; the Binomial Theorem
12.1 Sequences
12.2 Arithmetic Sequences
12.3 Geometric Sequences; Geometric Series
12.4 Mathematical Induction
12.5 The Binomial Theorem
Chapter 13 Counting and Probability
13.1 Counting
13.2 Permutations and Combinations
13.3 Probability
Chapter 14 A Preview of Calculus: The Limit, Derivative, and Integral of a Function
14.1 Finding Limits Using Tables and Graphs
14.2 Algebra Techniques for Finding Limits
14.3 One-side Limits; Continuous Functions
14.4 The Tangent Problem; The Derivative
14.5 The Area Problem; The Integral
Appendix A Review
A.1 Algebra Essentials
A.2 Geometry Essentials
A.3 Polynomials
A.4 Synthetic Division
A.5 Rational Expressions
A.6 Solving Equations
A.7 Complex Numbers; Quadratic Equations in the Complex Number System
A.8 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications
A.9 Interval Notation; Solving Inequalities
A.10 nth Roots; Rational Exponents
Appendix B The Limit of a Sequence; Infinite Series
1.1 Rectangular Coordinates; Graphing Utilities; Introduction to Graphing Equations
1.2 Intercepts; Symmetry; Graphing Key Equations
1.3 Solving Equations Using a Graphing Utility
1.4 Lines
1.5 Circles
Chapter 2 Functions and Their Graphs
2.1 Functions
2.2 The Graph of a Function
2.3 Properties of Functions
2.4 Library of Functions; Piecewise-defined Functions
2.5 Graphing Techniques: Transformations
2.6 Mathematical Models: Building Functions
Chapter 3 Linear and Quadratic Functions
3.1 Linear Functions, Their Properties, and Linear Models
3.2 Building Linear Models from Data; Direct Variation
3.3 Quadratic Functions and Their Properties
3.4 Building Quadratic Models from Verbal Descriptions and Data
3.5 Inequalities Involving Quadratic Functions
Chapter 4 Polynomial and Rational Functions
4.1 Polynomial Functions and Models
4.2 Properties of Rational Functions
4.3 The Graph of a Rational Function
4.4 Polynomial and Rational Inequalities
4.5 The Real Zeros of a Polynomial Function
4.6 Complex Zeros; Fundamental Theorem of Algebra
Chapter 5 Exponential and Logarithmic Functions
5.1 Composite Functions
5.2 One-to-One Functions; Inverse Functions
5.3 Exponential Functions
5.4 Logarithmic Functions
5.5 Properties of Logarithms
5.6 Logarithmic and Exponential Equations
5.7 Financial Models
5.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models
5.9 Building Exponential, Logarithmic, and Logistic Models from Data
Chapter 6 Trigonometric Functions
6.1 Angles and Their Measure
6.2 Trigonometric Functions: Unit Circle Approach
6.3 Properties of the Trigonometric Functions
6.4 Graphs of the Sine and Cosine Functions
6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
6.6 Phase Shift; Building Sinusoidal Models
Chapter 7 Analytic Trigonometry
7.1 The Inverse Sine, Cosine, and Tangent Functions
7.2 The Inverse Trigonometric Functions (Continued)
7.3 Trigonometric Identities
7.4 Sum and Difference Formulas
7.5 Double-angle and Half-angle Formulas
7.6 Product-to-Sum and Sum-to-Product Formulas
7.7 Trigonometric Equations (I)
7.8 Trigonometric Equations (II)
Chapter 8 Applications of Trigonometric Functions
8.1 Applications Involving Right Triangles
8.2 The Law of Sines
8.3 The Law of Cosines
8.4 Area of a Triangle
8.5 Simple Harmonic Motion; Damped Motion; Combining Waves
Chapter 9 Polar Coordinates; Vectors
9.1 Polar Coordinates
9.2 Polar Equations and Graphs
9.3 The Complex Plane; DeMoivre’s Theorem
9.4 Vectors
9.5 The Dot Product
9.6 Vectors in Space
9.7 The Cross Product
Chapter 10 Analytic Geometry
10.1 Conics
10.2 The Parabola
10.3 The Ellipse
10.4 The Hyperbola
10.5 Rotation of Axes; General Form of a Conic
10.6 Polar Equations of Conics
10.7 Plane Curves and Parametric Equations
Chapter 11 Systems of Equations and Inequalities
11.1 Systems of Linear Equations: Substitution and Elimination
11.2 Systems of Linear Equations: Matrices
11.3 Systems of Linear Equations: Determinants
11.4 Matrix Algebra
11.5 Partial Fraction Decomposition
11.6 Systems of Nonlinear Equations
11.7 Systems of Inequalities
11.8 Linear Programming
Chapter 12 Sequences; Induction; the Binomial Theorem
12.1 Sequences
12.2 Arithmetic Sequences
12.3 Geometric Sequences; Geometric Series
12.4 Mathematical Induction
12.5 The Binomial Theorem
Chapter 13 Counting and Probability
13.1 Counting
13.2 Permutations and Combinations
13.3 Probability
Chapter 14 A Preview of Calculus: The Limit, Derivative, and Integral of a Function
14.1 Finding Limits Using Tables and Graphs
14.2 Algebra Techniques for Finding Limits
14.3 One-side Limits; Continuous Functions
14.4 The Tangent Problem; The Derivative
14.5 The Area Problem; The Integral
Appendix A Review
A.1 Algebra Essentials
A.2 Geometry Essentials
A.3 Polynomials
A.4 Synthetic Division
A.5 Rational Expressions
A.6 Solving Equations
A.7 Complex Numbers; Quadratic Equations in the Complex Number System
A.8 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications
A.9 Interval Notation; Solving Inequalities
A.10 nth Roots; Rational Exponents
Appendix B The Limit of a Sequence; Infinite Series
Notă biografică
Mike Sullivan is a Professor of Mathematics at Chicago State University and received a Ph.D. in mathematics from Illinois Institute of Technology. Mike has taught at Chicago State for over 30 years and has authored or co-authored over fifty books. Mike has four children, all of whom are involved with mathematics or publishing: Kathleen, who teaches college mathematics; Mike III, who co-authors this series and teaches college mathematics; Dan, who is a Pearson Education sales representative; and Colleen, who teaches middle-school mathematics. When he's not writing, Mike enjoys gardening or spending time with his family, including nine grandchildren.
Mike Sullivan III is a professor of mathematics at Joliet Junior College. He holds graduate degrees from DePaul University in both mathematics and economics. Mike is an author or co-author on more than 20 books, including a statistics book and a developmental mathematics series. Mike is the father of three children and an avid golfer who tries to spend as much of his limited free time as possible on the golf course.
Mike Sullivan III is a professor of mathematics at Joliet Junior College. He holds graduate degrees from DePaul University in both mathematics and economics. Mike is an author or co-author on more than 20 books, including a statistics book and a developmental mathematics series. Mike is the father of three children and an avid golfer who tries to spend as much of his limited free time as possible on the golf course.
Caracteristici
Below is a list of just some of the key features for this text. For a more complete list, consult the inside front cover of the text.
Prepare for Class
Prepare for Class
- Preparing for This Section Sections begin with a list of key concepts to review, with page number references. This feature highlights previously learned material to be used in this section. Review it, and you'll always be prepared for quizzes and tests.
- "Now Work" Problems follow most examples, and direct you to a related exercise. Since we learn best by doing, you'll solidify your understanding of examples if you try a similar problem right away, before you forget what you've learned.
- NEW! Showcase Examples provide "how-to" instruction by offering a guided, step-by-step approach to solving a problem. With each step presented on the left and the mathematics displayed on the right, students can immediately see how each of the steps is employed.
- NEW! Model It Problems and Examples require you to build a mathematical model from either a verbal description or data. These problems will allow you to describe the problem mathematically and suggest a solution to the problem.
- 'Are You Prepared?' Problems Special problems that support the Preparing for This Section feature appear at the start of each exercise set. Work the 'Are You Prepared?' Problems and if you get one wrong, you'll know exactly what you need to review and where to review it.
- Concepts and Vocabulary These Fill-in the-Blank and True/False items assess your understanding of key definitions and concepts. These problems help you understand the 'big ideas' before diving into skill building.
- Skill Development Correlated to section examples, these problems provide straightforward practice, organized by difficulty. These problems provide you with ample practice to develop your problem-solving skills.
- Mixed Practice These problems offer comprehensive assessment of the skills learned in the section by asking questions that relate to more than one concept or objective. These problems may also require you to utilize skills learned in previous sections, helping you to see how concepts are tied together.
- Applications and Extensions Math is everywhere, and these problems demonstrate that. You'll learn to approach real problems, and how to break them down into manageable parts. These can be challenging, but are worth the effort.
- Discussion and Writing These problems, marked by a special icon and red numbers, support class discussion, verbalization of mathematical ideas, and writing projects.
- "You Should be Able To..." Contains a complete list of objectives by section, with corresponding practice exercises. Do the recommended exercises and you'll have mastery over the key material. If you get something wrong, go review the suggested page numbers and try again.
- Chapter Test These are about 15-20 problems that can be taken as a Chapter Test. Take the sample practice test and it will get you ready for your instructor's tests. If the student gets a problem wrong, they can watch the Chapter Test Prep Video CD found in the back of the book.
Caracteristici noi
New Content:
• Section A.2, Geometry Essentials, now contains a discussion of congruent and similar triangles.
• Chapter 3 Linear and Quadratic Functions New to this edition, this chapter gives more emphasis to linear and quadratic functions. The discussions allows for a fuller
explanation of linear and quadratic functions, their properties, models involving the functions, and building models from verbal descriptions and data. A full section on quadratic inequalities is also provided with both graphical and algebraic analysis of the inequality.
• Examples and exercises that involve a more in-depth analysis of graphing and exponential and logarithmic functions are provided.
• Examples and exercises that involve graphing a wider variety of inverse trigonometric functions are provided.
New Features:
• Showcase Examples are used to present examples in a guided, step-by-step format. Students can immediately see how each of the steps in a problem is employed. The “How To” examples have a two-column format in which the left column describes the step in solving the problem and the right column displays the algebra complete with annotations.
• Model It examples and exercises are clearly marked with an icon. These examples and exercises develop the student’s ability to build models from both verbal descriptions and data. Many of the problems involving data require the students to first determine the appropriate model (linear, quadratic, and so on) then fit it to the data and justify their choice.
• Exercise Sets at the end of each section have been classified according to purpose. Where appropriate, more problems to challenge the better student have been added. In addition, Mixed Practice exercises have been added where appropriate so that students may synthesize skills from a variety of sections.
• Applied Problems have been updated and many new problems involving sourced information as well as data sets have been added to bring relevance and timeliness to these exercises.
• Section A.2, Geometry Essentials, now contains a discussion of congruent and similar triangles.
• Chapter 3 Linear and Quadratic Functions New to this edition, this chapter gives more emphasis to linear and quadratic functions. The discussions allows for a fuller
explanation of linear and quadratic functions, their properties, models involving the functions, and building models from verbal descriptions and data. A full section on quadratic inequalities is also provided with both graphical and algebraic analysis of the inequality.
• Examples and exercises that involve a more in-depth analysis of graphing and exponential and logarithmic functions are provided.
• Examples and exercises that involve graphing a wider variety of inverse trigonometric functions are provided.
New Features:
• Showcase Examples are used to present examples in a guided, step-by-step format. Students can immediately see how each of the steps in a problem is employed. The “How To” examples have a two-column format in which the left column describes the step in solving the problem and the right column displays the algebra complete with annotations.
• Model It examples and exercises are clearly marked with an icon. These examples and exercises develop the student’s ability to build models from both verbal descriptions and data. Many of the problems involving data require the students to first determine the appropriate model (linear, quadratic, and so on) then fit it to the data and justify their choice.
• Exercise Sets at the end of each section have been classified according to purpose. Where appropriate, more problems to challenge the better student have been added. In addition, Mixed Practice exercises have been added where appropriate so that students may synthesize skills from a variety of sections.
• Applied Problems have been updated and many new problems involving sourced information as well as data sets have been added to bring relevance and timeliness to these exercises.