When introducing mathematical ideas, this book moves from the concrete to the abstract, rather than the reverse. It is the authors philosophy that learning is increased when students can relate a concept to something in their lives. This approach increases both interest and motivation. Students see the importance of a topic from a practical and intuitive point of view, with models and applications playing a central part in the learning process.
Table of Contents
1. Introduction To Functions and Graphs.
Numbers, Data, and Problem Solving. Visualization of Data. Functions and Their Representations. Types of Functions and Their Rates of Change.
2. Linear Functions and Equations.
Linear Functions and Models. Equations of Lines. Linear Equations and Problem Solving. Linear Inequalities. Piecewise-Defined Linear Functions. Linear Approximation.
3. Quadratic Functions and Equations.
Quadratic Functions and Models. Quadratic Equations and Problem Solving. Quadratic Inequalities. Transformations of Graphs.
4. Nonlinear Functions and Equations.
Nonlinear Functions and Their Graphs. Polynomial Functions and Models. Real Zeros of Polynomial Functions. The Fundamental Theorem of Algebra. Rational Functions and Models. Polynomial and Rational Inequalities. Power Functions and Radical Equations .
5. Exponential and Logarithmic Functions.
Combining Functions. Inverse Functions and Their Representations. Exponential Functions and Models. Logarithmic Functions and Models. Properties of Logarithms. Exponential and Logarithmic Equations. Constructing Nonlinear Models.
6. Systems of Equations and Inequalities.
Functions and Equations of More Than One Variable. Linear Systems of Equations and Inequalities in Two Variables. Solutions of Linear Systems Using Matrices. Properties and Applications of Matrices. Inverses of Matrices. Determinants.
7. Conic Sections.
Parabolas. Ellipses. Hyperbolas.
8. Further Topics in Algebra.
Sequences. Series. Counting. The Binomial Theorem. Probability.