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Often, algebra & trigonometry students leave class believing that they understand a concept but are unable to apply that understanding when they get home and attempt their homework problems. This mainstream yet innovative text is written by an experienced professor who has identified this gap as one of the biggest challenges that algebra & trigonometry professors face. She uses a clear, voice that speaks directly to students- similar to how instructors communicate to them in class. Students learning from this text will overcome common barriers to learning algebra & trigonometry and will build confidence in their ability to do mathematics.
CHAPTER 0. PREREQUISITES AND REVIEW.
Real Numbers.
Exponents and Radicals.
Polynomials: Basic Operations.
Factoring Polynomials.
Rational Expressions.
Equations.
Complex Numbers.
CHAPTER 1. EQUATIONS AND INEQUALITIES.
Linear Equations.
Applications Involving Linear Equations.
Quadratic Equations.
Radical Equations; Equations in Quadratic Form.
Linear Inequalities.
Polynomial and Rational Inequalities.
Absolute Value Equations and Inequalities.
CHAPTER 2. GRAPHS.
Basic Tools: Cartesian Plane, Distance, and Midpoint.
Graphing Equations: Point Plotting and Symmetry.
Straight Lines.
Circles.
CHAPTER 3. FUNCTIONS AND THEIR GRAPHS.
Functions.
Graphs of Functions: Common Functions and Piecewise-Defined Functions.
Graphing Techniques: Transformations.
Operation on Functions and Composition of Functions.
One-to-One Functions and Inverse Functions
CHAPTER 4. POLYNOMIAL AND RATIONAL FUNCTIONS.
Quadratic Functions.
Polynomial Functions of Higher Degree.
Tests of Zeros of Polynomial Functions.
Rational Dividing Polynomials: Long Division and Synthetic Division.
Properties and Functions.
Modeling with Variation.
CHAPTER 5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions and Their Graphs.
Exponential Functions with Base e.
Logarithmic Functions and Their Graphs.
Properties of Logarithms.
Exponential and Logarithmic Equations.
CHAPTER 6. Trigonometric Functions.
Angles, Degrees and Triangles.
Definition 1 of Trigonometric Functions: Right Triangle Ratios.
Applications of Right Triangle Trigonometry: Solving Right Triangles.
Definition 2 of Trigonometric Functions: Cartesian Plane.
Trigonometric Functions of Non-Acute Angles.
Radian Measure and Applications.
Definition 3 of Trigonometric Functions: Unit Circle Approach.
Graphs of Sine and Cosine Functions.
Graphs of Other Trigonometric Functions.
CHAPTER 7. Analytic Trigonometry.
Fundamental Identities.
Verifying Trigonometric Identities.
Sum and Difference Identities.
Double and Half Angle Identities.
Product and Sum Identities.
Inverse Trigonometric Functions.
Trigonometric Equations.
CHAPTER 8. Applications of Trigonometric Functions and Vectors.
The Law of Sines.
The Law of Cosines.
Vectors.
Dot Product.
Polar Coordinates.
Polar Equations and Graphs
CHAPTER 9. SYSTEMS OF EQUATIONS AND INEQUALITIES.
Systems of Linear Equations in Two Variables.
Systems of Multivariable Linear Equations.
Partial Fractions.
Systems of Nonlinear Equations.
Systems of Inequalities
Linear Programming
CHAPTER 10. MATRICES.
Matrices and Systems of Linear Equations.
Systems of Linear Equations: Augmented Matrices.
Systems of Linear Equations: Determinants.
Matrix Algebra.
CHAPTER 11. ANALYTIC GEOMETRY.
Conic Basics.
Parabola.
Ellipse.
Hyperbola.
Rotation of Axes.
Polar Equations of Conics.
Parametric Equations and Graphs.
CHAPTER 12. SEQUENCES, SERIES, AND PROBABILITY.
Sequences and Series.
Arithmetic Sequences and Series.
Geometric Sequences and Series.
Mathematical Induction.
Binomial Theorem.
Counting, Permutations, and Combinations.
Probability.
Often, algebra & trigonometry students leave class believing that they understand a concept but are unable to apply that understanding when they get home and attempt their homework problems. This mainstream yet innovative text is written by an experienced professor who has identified this gap as one of the biggest challenges that algebra & trigonometry professors face. She uses a clear, voice that speaks directly to students- similar to how instructors communicate to them in class. Students learning from this text will overcome common barriers to learning algebra & trigonometry and will build confidence in their ability to do mathematics.
Table of Contents
CHAPTER 0. PREREQUISITES AND REVIEW.
Real Numbers.
Exponents and Radicals.
Polynomials: Basic Operations.
Factoring Polynomials.
Rational Expressions.
Equations.
Complex Numbers.
CHAPTER 1. EQUATIONS AND INEQUALITIES.
Linear Equations.
Applications Involving Linear Equations.
Quadratic Equations.
Radical Equations; Equations in Quadratic Form.
Linear Inequalities.
Polynomial and Rational Inequalities.
Absolute Value Equations and Inequalities.
CHAPTER 2. GRAPHS.
Basic Tools: Cartesian Plane, Distance, and Midpoint.
Graphing Equations: Point Plotting and Symmetry.
Straight Lines.
Circles.
CHAPTER 3. FUNCTIONS AND THEIR GRAPHS.
Functions.
Graphs of Functions: Common Functions and Piecewise-Defined Functions.
Graphing Techniques: Transformations.
Operation on Functions and Composition of Functions.
One-to-One Functions and Inverse Functions
CHAPTER 4. POLYNOMIAL AND RATIONAL FUNCTIONS.
Quadratic Functions.
Polynomial Functions of Higher Degree.
Tests of Zeros of Polynomial Functions.
Rational Dividing Polynomials: Long Division and Synthetic Division.
Properties and Functions.
Modeling with Variation.
CHAPTER 5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions and Their Graphs.
Exponential Functions with Base e.
Logarithmic Functions and Their Graphs.
Properties of Logarithms.
Exponential and Logarithmic Equations.
CHAPTER 6. Trigonometric Functions.
Angles, Degrees and Triangles.
Definition 1 of Trigonometric Functions: Right Triangle Ratios.
Applications of Right Triangle Trigonometry: Solving Right Triangles.
Definition 2 of Trigonometric Functions: Cartesian Plane.
Trigonometric Functions of Non-Acute Angles.
Radian Measure and Applications.
Definition 3 of Trigonometric Functions: Unit Circle Approach.
Graphs of Sine and Cosine Functions.
Graphs of Other Trigonometric Functions.
CHAPTER 7. Analytic Trigonometry.
Fundamental Identities.
Verifying Trigonometric Identities.
Sum and Difference Identities.
Double and Half Angle Identities.
Product and Sum Identities.
Inverse Trigonometric Functions.
Trigonometric Equations.
CHAPTER 8. Applications of Trigonometric Functions and Vectors.
The Law of Sines.
The Law of Cosines.
Vectors.
Dot Product.
Polar Coordinates.
Polar Equations and Graphs
CHAPTER 9. SYSTEMS OF EQUATIONS AND INEQUALITIES.
Systems of Linear Equations in Two Variables.
Systems of Multivariable Linear Equations.
Partial Fractions.
Systems of Nonlinear Equations.
Systems of Inequalities
Linear Programming
CHAPTER 10. MATRICES.
Matrices and Systems of Linear Equations.
Systems of Linear Equations: Augmented Matrices.
Systems of Linear Equations: Determinants.
Matrix Algebra.
CHAPTER 11. ANALYTIC GEOMETRY.
Conic Basics.
Parabola.
Ellipse.
Hyperbola.
Rotation of Axes.
Polar Equations of Conics.
Parametric Equations and Graphs.
CHAPTER 12. SEQUENCES, SERIES, AND PROBABILITY.
Sequences and Series.
Arithmetic Sequences and Series.
Geometric Sequences and Series.
Mathematical Induction.
Binomial Theorem.
Counting, Permutations, and Combinations.
Probability.