Description
Table of Contents
1. Linear Functions, Equations, and Inequalities
1.1 Real Numbers and the Rectangular Coordinate System
1.2 Introduction to Relations and Functions
Reviewing Basic Concepts (Sections 1.1–1.2)
1.3 Linear Functions
1.4 Equations of Lines and Linear Models
Reviewing Basic Concepts (Sections 1.3–1.4)
1.5 Linear Equations and Inequalities
Unifying Linear Functions
1.6 Applications of Linear Functions
Reviewing Basic Concepts (Sections 1.5–1.6)
Summary
Review Exercises
Test
2. Analysis of Graphs of Functions
2.1 Graphs of Basic Functions and Relations; Symmetry
2.2 Vertical and Horizontal Shifts of Graphs
2.3 Stretching, Shrinking, and Reflecting Graphs
Reviewing Basic Concepts (Sections 2.1–2.3)
2.4 Absolute Value Functions
Unifying Absolute Value Functions
2.5 Piecewise-Defined Functions
2.6 Operations and Composition
Reviewing Basic Concepts (Sections 2.4–2.6)
Summary
Review Exercises
Test
3. Quadratic Functions
3.1 Complex Numbers
3.2 Quadratic Functions and Graphs
Reviewing Basic Concepts (Sections 3.1–3.2)
3.3 Quadratic Equations and Inequalities
Unifying Quadratic Functions
3.4 Applications of Quadratic Functions and Models
Reviewing Basic Concepts (Sections 3.3–3.4)
Summary
Review Exercises
Test
4. Polynomial Functions of Higher Degree
4.1 Graphs of Polynomial Functions
4.2 Topics in the Theory of Polynomial Functions (I)
Reviewing Basic Concepts (Sections 4.1–4.2)
4.3 Topics in the Theory of Polynomial Functions (II)
4.4 Polynomial Equations, Inequalities, Applications, and Models
Reviewing Basic Concepts (Sections 4.3–4.4)
Unifying Polynomial Functions
Summary
Review Exercises
Test
5. Rational, Power, and Root Functions
5.1 Rational Functions and Graphs (I)
5.2 Rational Functions and Graphs (II)
5.3 Rational Equations, Inequalities, Models, and Applications
Reviewing Basic Concepts (Sections 5.1–5.3)
5.4 Functions Defined by Powers and Roots
5.5 Equations, Inequalities, and Applications Involving Root Functions
Reviewing Basic Concepts (Sections 5.4–5.5)
Unifying Root Functions
Summary
Review Exercises
Test
6. Inverse, Exponential, and Logarithmic Functions
6.1 Inverse Functions
6.2 Exponential Functions
Unifying Exponential Functions
6.3 Logarithms and Their Properties
Reviewing Basic Concepts (Sections 6.1ndash;6.3)
6.4 Logarithmic Functions
6.5 Exponential and Logarithmic Equations and Inequalities
Unifying Logarithmic Functions
6.6 Further Applications and Modeling with Exponential and Logarithmic Functions
Reviewing Basic Concepts (Sections 6.4–6.6)
Summary Exercises on Functions: Domains, Defining Equations, and Composition
Summary
Review Exercises
Test
7. Systems and Matrices
7.1 Systems of Equations
7.2 Solution of Linear Systems in Three Variables
7.3 Solution of Linear Systems by Row Transformations
Reviewing Basic Concepts (Sections 7.1–7.3)
7.4 Matrix Properties and Operations
7.5 Determinants and Cramer’s Rule
7.6 Solution of Linear Systems by Matrix Inverses
Reviewing Basic Concepts (Sections 7.4–7.6)
7.7 Systems of Inequalities and Linear Programming
7.8 Partial Fractions
Reviewing Basic Concepts (Sections 7.7–7.8)
Summary
Review Exercises
Test
8. Conic Sections, Nonlinear Systems, and Parametric Equations
8.1 Circles Revisited and Parabolas
8.2 Ellipses and Hyperbolas
Reviewing Basic Concepts (Sections 8.1–8.2)
8.3 The Conic Sections and Nonlinear Systems
8.4 Introduction to Parametric Equations
Reviewing Basic Concepts (Sections 8.3–8.4)
Summary
Review Exercises
Test
9. The Unit Circle and the Functions of Trigonometry
9.1 Angles, Arcs, and Their Measures
9.2 The Unit Circle and Its Functions
9.3 Graphs of the Sine and Cosine Functions
9.4 Graphs of the Other Circular Functions
9.5 Functions of Angles and Fundamental Angles
9.6 Evaluating Trigonometric Functions
9.7 Applications of Right Triangles
9.8 Harmonic Motion
Summary
Review Exercises
Test
10. Trigonometric Identities and Equations
10.1 Trigonometric Identities
10.2 Sum and Difference Identities
10.3 Further Identities
10.4 The Inverse Circular Functions
10.5 Trigonometric Equations and Inequalities (I)
10.6 Trigonometric Equations and Inequalities (II)
Unifying Trigonometric Functions
Summary
Review Exercises
Test
11. Applications of Trigonometry and Vectors
11.1 The Law of Sines
11.2 The Law of Cosines and Area Formulas
11.3 Vectors and Their Applications
11.4 Trigonometric (Polar) Form of Complex Numbers
11.5 Powers and Roots of Complex Numbers
11.6 Polar Equations and Graphs
11.7 More Parametric Equations
Summary
Review Exercises
Test
12. Further Topics in Algebra
12.1 Sequences and Series
12.2 Arithmetic Sequences and Series
12.3 Geometric Sequences and Series
Reviewing Basic Concepts (Sections 9.1–9.3)
12.4 Counting Theory
12.5 The Binomial Theorem
Reviewing Basic Concepts (Sections 9.4–9.5)
12.6 Mathematical Induction
12.7 Probability
Reviewing Basic Concepts (Sections 9.6–9.7)
Summary
Review Exercises
Test
13. Limits, Derivatives, and Definite Integrals
13.1 An Introduction to Limits
13.2 Techniques for Calculating Limits
13.3 One-Sided Limits and Limits Involving Infinity
13.4 Tangent Lines and Derivatives
13.5 Area and the Definite Integral
