Precalculus

by Blitzer, Robert F.

• ISBN13: 9780134494890
• ISBN10: 013449489X
• Edition: 6th
• Copyright: 2017-03-21
• Publisher: PEARSO

Summary

For courses in  Precalculus Mathematics.

 

Show students that our world is profoundly mathematical

Bob Blitzer continues to inspire students with his engaging approach to mathematics, making this beloved series the #1 in the market year after year. Blitzer draws on his unique background in mathematics and behavioral science to present a wide range of vivid applications in real-life situations. Students of all majors stay engaged because Blitzer uses pop-culture and up-to-date references to connect math to students’ lives, showing that our world is profoundly mathematical.

 

With the new edition, Blitzer takes student engagement with the mathematical world to a whole new level drawing from applications across all fields as well as topics that are of interest to any college student (e.g., student loan debt, grade inflation, sleep hours of college students). Applications are also brought to life online in a new, assignable video series that explore the entertaining and mathematical Blitzer Bonus boxes. The new edition also aims to help more students to succeed in the course with just-in-time support in the text--such as Brief Review of prerequisite topics, Achieving Success boxes, and Retain the Concepts exercises. 

Author Biography

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 from Nova University. Bob’s love for teaching mathematics was nourished for nearly 30 years at Miami Dade College, where he received numerous teaching awards, including Innovator of the Year from the League for Innovations in the Community College and an endowed chair based on excellence in the classroom. In addition to College Algebra, Bob has written textbooks covering developmental mathematics, introductory algebra, intermediate algebra, trigonometry, algebra and trigonometry, precalculus, and liberal arts mathematics, all published by Pearson. When not secluded in his Northern California writer’s cabin, Bob can be found hiking the beaches and trails of Point Reyes National Seashore and tending to the chores required by his beloved entourage of horses, chickens, and irritable roosters.

Table of Contents

P. Prerequisites: Fundamental Concepts of Algebra

P.1 Algebraic Expressions, Mathematical Models, and Real Numbers

P.2 Exponents and Scientific Notation

P.3 Radicals and Rational Exponents

P.4 Polynomials

P.5 Factoring Polynomials

P.6 Rational Expressions

P.7 Equations

P.8 Modeling with Equations

P.9 Linear Inequalities and Absolute Value Inequalities

Summary, Review, and Test

Review Exercises

Chapter P Test

 

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

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

 

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

2.6 Rational Functions and Their Graphs

2.7 Polynomial and Rational Inequalities

2.8 Modeling Using Variation

 

3. Exponential and Logarithmic Functions

3.1 Exponential Functions

3.2 Logarithmic Functions

3.3 Properties of Logarithms

3.4 Exponential and Logarithmic Equations

3.5 Exponential Growth and Decay; Modeling Data

 

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

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

 

5. Analytic Trigonometry

5.1 Verifying Trigonometric Identities

5.2 Sum and Difference Formulas

5.3 Double-Angle, Power-Reducing, and Half-Angle Formulas

5.4 Product-to-Sum and Sum-to-Product Formulas

5.5 Trigonometric Equations

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

6.5 Complex Numbers in Polar Form; DeMoivre's Theorem

6.6 Vectors

6.7 The Dot Product

 

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

7.5 Systems of Inequalities

7.6 Linear Programming

 

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

8.4 Multiplicative Inverses of Matrices and Matrix Equations

8.5 Determinants and Cramer's Rule

 

9. Conic Sections and Analytic Geometry

9.1 The Ellipse

9.2 The Hyperbola

9.3 The Parabola

9.4 Rotation of Axes

9.5 Parametric Equations

9.6 Conic Sections in Polar Coordinates

 

10. Sequences, Induction, and Probability

10.1 Sequences and Summation Notation

10.2 Arithmetic Sequences

10.3 Geometric Sequences and Series

10.4 Mathematical Induction

10.5 The Binomial Theorem

10.6 Counting Principles, Permutations, and Combinations

10.7 Probability

 

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

11.4 Introduction to Derivatives