Precalculus

Bob Blitzer is a native of Manhattan and received a Bachelor of Arts degree with dual majors in mathematics and psychology (minor: English literature) from the City College of New York. His unusual combination of academic interests led him toward a Master of Arts in mathematics from the University of Miami and a doctorate in behavioral sciences fro Nova University. Bob is most energized by teaching mathematics and has taught a variety of mathematics courses at Miami-Dade College for nearly 30 years. He has received numerous teaching awards, including Innovator of the Year from the League for Innovations in the Community College, and was among the first group of recipients at Miami-Dade College for an endowed chair based on excellence in the classroom. Bob has written Intermediate Algebra for College Students, Introductory Algebra for College Students, Essentials of Intermediate Algebra for College Students, Introductory and Intermediate Algebra for College Students, Essentials of Introductory and Intermediate Algebra for College Students, Algebra for College Students, Thinking Mathematically, College Algebra, Algebra and Trigonometry, and Precalculus, all published by Prentice Hall.

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