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This text takes the same approach as the regular Blitzer Precalculus version by deleting chapters. The text explores math the way it evolved: by describing real problems and how math explains them. It is interesting, lively (with applications you won't see in any other math book), and exceedingly clear. Blitzer's philosophy: present the full scope of mathematics, while always (1) engaging the student by opening their minds to learning (2) keeping the student engaged on every page (3) explaining ideas directly, simply, and clearly. Students are strongly supported by a consistent pedagogical framework. A "See it, Hear it, Try it?" format consistently walks students through each and every example in just the same way that an instructor would teach this example in class. Blitzer liberally inserts voice balloons and annotations throughout the text helping clarify the more difficult concepts for students.
Chapter Prerequisites: Fundamental Concepts of Algebra
p.1 Algebraic Expressions and Real Numbers
p.2 Exponents and Scientific Notation
p.3 Radicals and Rational Exponents
p.4 Polynomials
p.5 Factoring Polynomials
Mid-chapter Check Point
p.6 Rational Expressions
p.7 Equations
p.8 Modeling with Equations
p.9 Linear Inequalities and Absolute Value Inequalities
Chapter 1. Functions and Graphs
1.1 Graphs and Graphing Utilities
1.2 Basics of Functions and their Graphs
1.3 More on Functions and their Graphs
1.4 Linear Functions and Slope
1.5 More on Slope
Mid-chapter Check Point
1.6 Transformations of Functions
1.7 Combinations of Functions; Composite Functions
1.8 Inverse Functions
1.9 Distance and Midpoint Formulas; Circles
1.10 Modeling with Functions
Chapter 2. Polynomial and Rational Functions
2.1 Complex Numbers
2.2 Quadratic Functions
2.3 Polynomial Functions and their Graphs
2.4 Dividing Polynomials; Remainder and Factor Theorems
2.5 Zeros of Polynomial Functions
Mid-chapter Check Point
2.6 Rational Functions and their Graphs
2.7 Polynomial and Rational Inequalities
2.8 Modeling Using Variation
Chapter 3. Exponential and Logarithmic Functions
3.1 Exponential Functions
3.2 Logarithmic Functions
3.3 Properties of Logarithms
Mid-chapter Check Point
3.4 Exponential and Logarithmic Equations
3.5 Exponential Growth and Decay; Modeling Data
Chapter 4. Trigonometric Functions
4.1 Angles and Radian Measure
4.2 Trigonometric Functions: The Unit Circle
4.3 Right Triangle Trigonometry
4.4 Trigonometric Functions of Any Angle
Mid-chapter Check Point
4.5 Graphs of Sine and Cosine Functions
4.6 Graphs of other Trigonometric Functions
4.7 Inverse Trigonometric Functions
4.8 Applications of Trigonometric Functions
Chapter 5. Analytic Trigonometry
5.1 Verifying Trigonometric Identities
5.2 Sum and Difference Formulas
5.3 Double-Angle, Power-Reducing, and Half-Angle Formulas
Mid-chapter Check Point
5.4 Product-to-Sum and Sum-to-Product Formulas
5.5 Trigonometric Equations
Chapter 6. Additional Topics in Trigonometry
6.1 The Law of Sines
6.2 The Law of Cosines
6.3 Polar Coordinates
6.4 Graphs of Polar Equations
Mid-chapter Check Point
6.5 Complex Numbers in Polar Form; DeMoivre's Theorem
6.6 Vectors
6.7 The Dot Product
Chapter 7. Systems of Equations and Inequalities
7.1 Systems of Linear Equations in Two Variables
7.2 Systems of Linear Equations in Three Variables
7.3 Partial Fractions
7.4 Systems of Nonlinear Equations in Two Variables
Mid-chapter Check Point
7.5 Systems of Inequalities
7.6 Linear Programming
Chapter 8. Matrices and Determinants
8.1 Matrix Solutions to Linear Systems
8.2 Inconsistent and Dependent Systems and Their Applications
8.3 Matrix Operations and Their Applications
Mid-chapter Check Point
8.4 Multiplicative Inverses of Matrices and Matrix Equations
8.5 Determinants and Cramer's Rule
Chapter 9. Conic Sections and Analytic Geometry
9.1 The Ellipse
9.2 The Hyperbola
9.3 The Parabola
Mid-chapter Check Point
9.4 Rotation of Axes
9.5 Parametric Equations
9.6 Conic Sections in Polar Coordinates
Chapter 10. Sequences, Induction, and Probability
10.1 Sequences and Summation Notation
10.2 Arithmetic Sequences
10.3 Geometric Sequences and Series
Mid-chapter Check Point
10.4 Mathematical Induction
10.5 The Binomial Theorem
10.6 Counting Principles, Permutations, and Combinations
10.7 Probability
Chapter 11. Introduction to Calculus
11.1 Finding Limits Using Tables and Graphs
11.2 Finding Limits Using Properties of Limits
11.3 Limits and Continuity
Mid-chapter Check Point
11.4 Introduction to Derivatives
Appendix: Where Did That Come From? Selected Proofs
This text takes the same approach as the regular Blitzer Precalculus version by deleting chapters. The text explores math the way it evolved: by describing real problems and how math explains them. It is interesting, lively (with applications you won't see in any other math book), and exceedingly clear. Blitzer's philosophy: present the full scope of mathematics, while always (1) engaging the student by opening their minds to learning (2) keeping the student engaged on every page (3) explaining ideas directly, simply, and clearly. Students are strongly supported by a consistent pedagogical framework. A "See it, Hear it, Try it?" format consistently walks students through each and every example in just the same way that an instructor would teach this example in class. Blitzer liberally inserts voice balloons and annotations throughout the text helping clarify the more difficult concepts for students.
Table of Contents
Chapter Prerequisites: Fundamental Concepts of Algebra
p.1 Algebraic Expressions and Real Numbers
p.2 Exponents and Scientific Notation
p.3 Radicals and Rational Exponents
p.4 Polynomials
p.5 Factoring Polynomials
Mid-chapter Check Point
p.6 Rational Expressions
p.7 Equations
p.8 Modeling with Equations
p.9 Linear Inequalities and Absolute Value Inequalities
Chapter 1. Functions and Graphs
1.1 Graphs and Graphing Utilities
1.2 Basics of Functions and their Graphs
1.3 More on Functions and their Graphs
1.4 Linear Functions and Slope
1.5 More on Slope
Mid-chapter Check Point
1.6 Transformations of Functions
1.7 Combinations of Functions; Composite Functions
1.8 Inverse Functions
1.9 Distance and Midpoint Formulas; Circles
1.10 Modeling with Functions
Chapter 2. Polynomial and Rational Functions
2.1 Complex Numbers
2.2 Quadratic Functions
2.3 Polynomial Functions and their Graphs
2.4 Dividing Polynomials; Remainder and Factor Theorems
2.5 Zeros of Polynomial Functions
Mid-chapter Check Point
2.6 Rational Functions and their Graphs
2.7 Polynomial and Rational Inequalities
2.8 Modeling Using Variation
Chapter 3. Exponential and Logarithmic Functions
3.1 Exponential Functions
3.2 Logarithmic Functions
3.3 Properties of Logarithms
Mid-chapter Check Point
3.4 Exponential and Logarithmic Equations
3.5 Exponential Growth and Decay; Modeling Data
Chapter 4. Trigonometric Functions
4.1 Angles and Radian Measure
4.2 Trigonometric Functions: The Unit Circle
4.3 Right Triangle Trigonometry
4.4 Trigonometric Functions of Any Angle
Mid-chapter Check Point
4.5 Graphs of Sine and Cosine Functions
4.6 Graphs of other Trigonometric Functions
4.7 Inverse Trigonometric Functions
4.8 Applications of Trigonometric Functions
Chapter 5. Analytic Trigonometry
5.1 Verifying Trigonometric Identities
5.2 Sum and Difference Formulas
5.3 Double-Angle, Power-Reducing, and Half-Angle Formulas
Mid-chapter Check Point
5.4 Product-to-Sum and Sum-to-Product Formulas
5.5 Trigonometric Equations
Chapter 6. Additional Topics in Trigonometry
6.1 The Law of Sines
6.2 The Law of Cosines
6.3 Polar Coordinates
6.4 Graphs of Polar Equations
Mid-chapter Check Point
6.5 Complex Numbers in Polar Form; DeMoivre's Theorem
6.6 Vectors
6.7 The Dot Product
Chapter 7. Systems of Equations and Inequalities
7.1 Systems of Linear Equations in Two Variables
7.2 Systems of Linear Equations in Three Variables
7.3 Partial Fractions
7.4 Systems of Nonlinear Equations in Two Variables
Mid-chapter Check Point
7.5 Systems of Inequalities
7.6 Linear Programming
Chapter 8. Matrices and Determinants
8.1 Matrix Solutions to Linear Systems
8.2 Inconsistent and Dependent Systems and Their Applications
8.3 Matrix Operations and Their Applications
Mid-chapter Check Point
8.4 Multiplicative Inverses of Matrices and Matrix Equations
8.5 Determinants and Cramer's Rule
Chapter 9. Conic Sections and Analytic Geometry
9.1 The Ellipse
9.2 The Hyperbola
9.3 The Parabola
Mid-chapter Check Point
9.4 Rotation of Axes
9.5 Parametric Equations
9.6 Conic Sections in Polar Coordinates
Chapter 10. Sequences, Induction, and Probability
10.1 Sequences and Summation Notation
10.2 Arithmetic Sequences
10.3 Geometric Sequences and Series
Mid-chapter Check Point
10.4 Mathematical Induction
10.5 The Binomial Theorem
10.6 Counting Principles, Permutations, and Combinations
10.7 Probability
Chapter 11. Introduction to Calculus
11.1 Finding Limits Using Tables and Graphs
11.2 Finding Limits Using Properties of Limits
11.3 Limits and Continuity
Mid-chapter Check Point
11.4 Introduction to Derivatives
Appendix: Where Did That Come From? Selected Proofs