Description
Book SynopsisWhen John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics, education, or journalism. His ultimate decision was to become a teacher, but after twenty-five years of teaching at the high school and university levels and fifteen years of writing mathematics textbooks, all three of his goals have been realized; his love for teaching and for mathematics is evident in his passion for working with students and fellow teachers as well. His specific professional interests are recreational mathematics, mathematics history, and incorporating graphing calculators into the curriculum. John's personal life is busy as he devotes time to his family (wife Gwen, and sons Chris, Jack, and Josh). He has been a rabid baseball fan all of his life. John's other hobbies include numismatics (the study of coins) and record collecting. He loves the music of the 1960s and has an extensive collection of the recorded work
Table of Contents
Table of Contents
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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
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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
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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
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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
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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
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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
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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
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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
-
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
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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
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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
-
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
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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
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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
Appendix A: Geometry Formulas Appendix B: Vectors in Space Appendix C: Polar Form of Conic Sections Appendix D: Rotation of Axes Instructor’s Answers Answers to Selected Exercises* Index *In the AIE, Instructor’s Answers replaces Answers to Selected Exercises.
