Precalculus: Algebra and Trigonometry
Edition: 3
Copyright: 2015
Edition: 3
Copyright: 2015
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The new 3rd edition of Precalculus: Algebra and Trigonometry prepares students for further study in mathematics, the sciences, engineering, the social sciences, and other disciplines. It exposes the student to the basic concepts of algebra and trigonometry with an emphasis in practical applications.
Suitable for a combined course in college algebra and trigonometry or a course in college algebra, Precalculus lucidly presents some of the main concepts, language, and methodology of mathematics while encouraging the reader to enjoy the beauty of mathematics and appreciate the usefulness of algebra and trigonometry in solving real-life problems.
Precalculus: Algebra and Trigonometry motivates the reader and provides problem solving and critical thinking skills through:
- Real-life examples that illustrate why the student is asked to study the materials that are presented.
- Clearly worked out examples that progress from motivational, to mechanical, to conceptual, and to mathematics in the real-world.
- What Have You Learned?, Supplementary Exercises, and a Sample Chapter Test vignettes at the end of each chapter to assess comprehension of material presented.
- An online testing and instant assessment system (Maple T.A ). Assignments can be created for each chapter. By doing homework in Maple T.A., students will receive their grades instantly, so they will know immediately how they are doing and what areas they need to work on while the material is still fresh.
CHAPTER P Some Basic Concepts
P.1 The Real Numbers
P.2 The Real Line, Inequality and Absolute Value
P.3 Integer and Rational Exponents
P.4 Polynomials
P.5 Factoring Polynomials
P.6 Rational Expressions
CHAPTER 1 Solving Equations and Inequalities
Preview of Chapter 1
1.1 Linear Equations in One Variable
1.2 Quadratic Equations
1.3 Other Types of Equations in One Variable
1.4 Solving Inequalities
1.5 Equations and Inequalities with Absolute Value
CHAPTER 2 Functions
Preview of Chapter 2
2.1 The Cartesian Plane and Relations
2.2 The Function Concept
2.3 Combinations of Functions
2.4 Linear Functions
2.5 Quadratic Functions
CHAPTER 3 Exponential and Logarithmic Functions
Preview of Chapter 3
3.1 Inverse Functions
3.2 Exponential Functions
3.3 Logarithmic Functions
3.4 Exponential and Logarithmic Equations
CHAPTER 4 Polynomial and Rational Functions
Preview of Chapter 4
4.1 Polynomial Functions
4.2 Factors and Zeros of Polynomials
4.3 Rational Functions
4.4 Partial Fractions
4.5 Modeling with Variation
CHAPTER 5 The Trigonometric Functions
Preview of Chapter 5
5.1 Angles and Their Measure
5.2 The Sine and Cosine Functions
5.3 Graphs of Sine and Cosine Functions
5.4 Other Trigonometric Functions
5.5 Trigonometric Identities
5.6 Inverse Trigonometric Functions
CHAPTER 6 Applications of Trigonometry
Preview of Chapter 6
6.1 Trigonometric Equations
6.2 Solving Right Triangle
6.3 Solving Oblique Triangles: The Sine Formula
6.4 Solving Oblique Triangles: The Cosine Formula
6.5 Trigonometric Form of Complex Numbers
6.6 Vectors in Two Dimensions
6.7 The Polar Coordinate System
CHAPTER 7 Systems of Equations, Inequalities, and Matrices
Preview of Chapter 7
7.1 Systems of Linear Equations
7.2 Nonlinear Systems of Equations
7.3 Systems of Linear Inequalities and Linear Programming
7.4 The Algebra of Matrices
7.5 Matrices and Systems of Equations
7.6 The Inverse of a Matrix
7.7 Determinants and Cramer’s Rule
CHAPTER 8 Sequences, Series, Counting, and Probability
Preview of Chapter 8
8.1 Sequences, Factorial, and Summation Notations
8.2 Arithmetic Sequences
8.3 Geometric Sequences and Series
8.4 Mathematical Induction
8.5 The Binomial Theorem
8.6 Counting Techniques
8.7 Introduction to Probability
CHAPTER 9 The Conic Sections
Preview of Chapter 9
9.1 The Conic Sections
9.2 The Parabola
9.3 The Ellipse
9.4 The Hyperbola
Appendix A The Complex Numbers
Unit 1. Standard Form of a Complex Number
Unit 2. Equality, Sum, and Product of Complex Numbers
Unit 3. Complex Conjugates
Unit 4. Absolute Value
Unit 5. Division of Complex Numbers
Unit 6. Complex Numbers and Electricity
Brief Test on What You Have Learned
Exercises Appendix A
Answer Key
Index
The new 3rd edition of Precalculus: Algebra and Trigonometry prepares students for further study in mathematics, the sciences, engineering, the social sciences, and other disciplines. It exposes the student to the basic concepts of algebra and trigonometry with an emphasis in practical applications.
Suitable for a combined course in college algebra and trigonometry or a course in college algebra, Precalculus lucidly presents some of the main concepts, language, and methodology of mathematics while encouraging the reader to enjoy the beauty of mathematics and appreciate the usefulness of algebra and trigonometry in solving real-life problems.
Precalculus: Algebra and Trigonometry motivates the reader and provides problem solving and critical thinking skills through:
- Real-life examples that illustrate why the student is asked to study the materials that are presented.
- Clearly worked out examples that progress from motivational, to mechanical, to conceptual, and to mathematics in the real-world.
- What Have You Learned?, Supplementary Exercises, and a Sample Chapter Test vignettes at the end of each chapter to assess comprehension of material presented.
- An online testing and instant assessment system (Maple T.A ). Assignments can be created for each chapter. By doing homework in Maple T.A., students will receive their grades instantly, so they will know immediately how they are doing and what areas they need to work on while the material is still fresh.
CHAPTER P Some Basic Concepts
P.1 The Real Numbers
P.2 The Real Line, Inequality and Absolute Value
P.3 Integer and Rational Exponents
P.4 Polynomials
P.5 Factoring Polynomials
P.6 Rational Expressions
CHAPTER 1 Solving Equations and Inequalities
Preview of Chapter 1
1.1 Linear Equations in One Variable
1.2 Quadratic Equations
1.3 Other Types of Equations in One Variable
1.4 Solving Inequalities
1.5 Equations and Inequalities with Absolute Value
CHAPTER 2 Functions
Preview of Chapter 2
2.1 The Cartesian Plane and Relations
2.2 The Function Concept
2.3 Combinations of Functions
2.4 Linear Functions
2.5 Quadratic Functions
CHAPTER 3 Exponential and Logarithmic Functions
Preview of Chapter 3
3.1 Inverse Functions
3.2 Exponential Functions
3.3 Logarithmic Functions
3.4 Exponential and Logarithmic Equations
CHAPTER 4 Polynomial and Rational Functions
Preview of Chapter 4
4.1 Polynomial Functions
4.2 Factors and Zeros of Polynomials
4.3 Rational Functions
4.4 Partial Fractions
4.5 Modeling with Variation
CHAPTER 5 The Trigonometric Functions
Preview of Chapter 5
5.1 Angles and Their Measure
5.2 The Sine and Cosine Functions
5.3 Graphs of Sine and Cosine Functions
5.4 Other Trigonometric Functions
5.5 Trigonometric Identities
5.6 Inverse Trigonometric Functions
CHAPTER 6 Applications of Trigonometry
Preview of Chapter 6
6.1 Trigonometric Equations
6.2 Solving Right Triangle
6.3 Solving Oblique Triangles: The Sine Formula
6.4 Solving Oblique Triangles: The Cosine Formula
6.5 Trigonometric Form of Complex Numbers
6.6 Vectors in Two Dimensions
6.7 The Polar Coordinate System
CHAPTER 7 Systems of Equations, Inequalities, and Matrices
Preview of Chapter 7
7.1 Systems of Linear Equations
7.2 Nonlinear Systems of Equations
7.3 Systems of Linear Inequalities and Linear Programming
7.4 The Algebra of Matrices
7.5 Matrices and Systems of Equations
7.6 The Inverse of a Matrix
7.7 Determinants and Cramer’s Rule
CHAPTER 8 Sequences, Series, Counting, and Probability
Preview of Chapter 8
8.1 Sequences, Factorial, and Summation Notations
8.2 Arithmetic Sequences
8.3 Geometric Sequences and Series
8.4 Mathematical Induction
8.5 The Binomial Theorem
8.6 Counting Techniques
8.7 Introduction to Probability
CHAPTER 9 The Conic Sections
Preview of Chapter 9
9.1 The Conic Sections
9.2 The Parabola
9.3 The Ellipse
9.4 The Hyperbola
Appendix A The Complex Numbers
Unit 1. Standard Form of a Complex Number
Unit 2. Equality, Sum, and Product of Complex Numbers
Unit 3. Complex Conjugates
Unit 4. Absolute Value
Unit 5. Division of Complex Numbers
Unit 6. Complex Numbers and Electricity
Brief Test on What You Have Learned
Exercises Appendix A
Answer Key
Index