Precalculus: Graphical, Numerical, Algebraic, Global Edition

Prerequisites

P.1 Real Numbers

P.2 Cartesian Coordinate System

P.3 Linear Equations and Inequalities

P.4 Lines in the Plane

P.5  Solving Equations Graphically, Numerically, and Algebraically

P.6 Complex Numbers

P.7 Solving Inequalities Algebraically and Graphically

 

1. Functions and Graphs

1.1 Modeling and Equation Solving

1.2 Functions and Their Properties

1.3 Twelve Basic Functions

1.4 Building Functions from Functions

1.5 Parametric Relations and Inverses

1.6 Graphical Transformations

1.7 Modeling with Functions

 

2.  Polynomial, Power, and Rational Functions

2.1 Linear and Quadratic Functions and Modeling

2.2 Power Functions with Modeling

2.3  Polynomial Functions of Higher Degree with Modeling

2.4 Real Zeros of Polynomial Functions

2.5  Complex Zeros and the Fundamental Theorem of Algebra

2.6 Graphs of Rational Functions

2.7 Solving Equations in One Variable

2.8 Solving Inequalities in One Variable

 

3.  Exponential, Logistic, and Logarithmic Functions

3.1 Exponential and Logistic Functions

3.2 Exponential and Logistic Modeling

3.3 Logarithmic Functions and Their Graphs

3.4 Properties of Logarithmic Functions

3.5 Equation Solving and Modeling

3.6 Mathematics of Finance

 

4. Trigonometric Functions

4.1 Angles and Their Measures

4.2 Trigonometric Functions of Acute Angles

4.3 Trigonometry Extended: The Circular Functions

4.4 Graphs of Sine and Cosine: Sinusoids

4.5 Graphs of Tangent, Cotangent, Secant, and Cosecant  Graphs of Tangent, Cotangent, Secant, and Cosecant  Graphs of Tangent, Cotangent, Secant, and Cosecant

4.6 Graphs of Composite Trigonometric Functions

4.7 Inverse Trigonometric Functions

4.8 Solving Problems with Trigonometry

 

5.  Analytic Trigonometry

5.1 Fundamental Identities

5.2 Proving Trigonometric Identities

5.3 Sum and Difference Identities

5.4 Multiple-Angle Identities

5.5 The Law of Sines

5.6 The Law of Cosines

 

6.  Applications of Trigonometry

6.1 Vectors in the Plane

6.2 Dot Product of Vectors

6.3 Parametric Equations and Motion

6.4 Polar Coordinates

6.5 Graphs of Polar Equations

6.6 De Moivre’s Theorem and nth Roots

 

7.  Systems and Matrices

7.1 Solving Systems of Two Equations

7.2 Matrix Algebra

7.3 Multivariate Linear Systems and Row Operations

7.4 Systems of Inequalities in Two Variables

 

8.  Analytic Geometry in Two and Three Dimensions

8.1 Conic Sections and a New Look at Parabolas

8.2 Circles and Ellipses

8.3 Hyperbolas

8.4 Quadratic Equations with xy Termsxy Termsxy [space after terms?]

8.5 Polar Equations of Conics

8.6 Three-Dimensional Cartesian Coordinate System

 

9.  Discrete Mathematics

9.1 Basic Combinatorics

9.2 Binomial Theorem

9.3 Sequences

9.4 Series

9.5 Mathematical Induction

 

10.  Statistics and Probability

10.1 Probability  

10.2 Statistics (Graphical)

10.3 Statistics (Numerical)

10.4 Random Variables and Probability Models

10.5 Statistical Literacy

 

11. An Introduction to Calculus: Limits, Derivatives, and Integrals

11.1 Limits and Motion: The Tangent Problem

11.2 Limits and Motion: The Area Problem

11.3 More on Limits

11.4 Numerical Derivatives and Integrals

 

Algebra Review

A.1 Radicals and Rational Exponents

A.2 Polynomials and Factoring

A.3 Fractional