Description
Book SynopsisTable of Contents1. 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 6.1 - 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. Trigonometric Functions and Applications
- 9.1 Angles, Arcs, and Their Measures
- 9.2 Trigonometric Functions and Fundamental Identities
- 9.3 Right Triangles and Evaluating Trigonometric Functions
- 9.4 Applications of Right Triangles
- 9.5 The Circular Functions
- 9.6 Graphs of the Sine and Cosine Functions
- 9.7 Graphs of the Other Circular Functions
- 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 12.1 - 12.3)
- 12.4 Counting Theory
- 12.5 The Binomial Theorem
- Reviewing Basic Concepts (Sections 12.4 -12.5)
- 12.6 Mathematical Induction
- 12.7 Probability
- Reviewing Basic Concepts (Sections 12.6 - 12.7)
- Summary
- Review Exercises
- Test
R. Review: Basic Algebraic Concepts
- R.1 Review of Sets
- R.2 Review of Exponents and Polynomials
- R.3 Review of Factoring
- R.4 Review of Rational Expressions
- R.5 Review of Negative and Rational Exponents
- R.6 Review of Radicals
- Test
Appendices
- A: Geometry Formulas
- B: Vectors in Space
- C: Polar Form of Conic Sections
- D: Rotation of Axes
Instructor's Answers Answers to Selected Exercises (Note: In the AIE, Instructor's Answers replaces Answers to Selected Exercises.) Index
