Anyone trying to learn algebra and trigonometry may think they understand a concept but then are unable to apply that understanding when they attempt to complete exercises. This innovative book helps them overcome common barriers to learning the concepts and builds confidence in their ability to do mathematics. The second edition presents new sections on modeling at the end of each chapter as well as new material on Limits and Early Functions. Numerous examples are also included that provide more detailed annotations using everyday language. This approach gives them the skills to understand and apply algebra and trigonometry.
Product dimensions: 7.89 (w) x 10.04 (h) x 1.81 (d)
Meet the Author
Cynthia Young received her BA in Math Education from UNC in 1990, has two masters, one in Mathematical Sciences from UCF in 1993 and a second in Electrical Engineering from the University of Washington in 1997. Finally, she received a PhD in Applied Mathematics from the University of Washington in 1996. She is already a tenured professor at UCF and is very actively involved in the supervision of UCF's graduate and undergraduate research assistants. Before becoming an award-winning Associate Professor at UCF, Cynthia taught High School. Cynthia received numerous grants and was named the principal investigator on six military and academic research projects. She has been an administrator/advisor to the Florida Space Institute at the Kennedy Space Center since 1998. Cynthia is a veteran presenter at conferences and conventions and has published over a dozen journal articles. In addition, she has been a contributor to several texts, including a College Algebra workbook for McGraw-Hill. Lastly, she edited the Marcel Decker's Optical Engineering Encyclopedia.
Exponents and Radicals.
Polynomials: Basic Operations.
CHAPTER 1. EQUATIONS AND INEQUALITIES.
Applications Involving Linear Equations.
Radical Equations; Equations in Quadratic Form.
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.
CHAPTER 3. FUNCTIONS AND THEIR GRAPHS.
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.
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.
Verifying Trigonometric Identities.
Sum and Difference Identities.
Double and Half Angle Identities.
Product and Sum Identities.
Inverse Trigonometric Functions.
CHAPTER 8. Applications of Trigonometric Functions and Vectors.
The Law of Sines.
The Law of Cosines.
Polar Equations and Graphs
CHAPTER 9. SYSTEMS OF EQUATIONS AND INEQUALITIES.
Systems of Linear Equations in Two Variables.
Systems of Multivariable Linear Equations.
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.
CHAPTER 11. ANALYTIC GEOMETRY.
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.
Counting, Permutations, and Combinations.