9780321081384

This book offers an innovative approach by focusing on learning through modeling and visualization with an integrated use of the graphing calculator. When introducing mathematical ideas, this text moves from the concrete to the abstract. The importance of mathematics is thus demonstrated to students and the material is presented in an accessible manner. The text consistently integrates mathematical concepts with real applications in order to enhance student intuition and understanding. Symbolic (algebraic), graphical, numerical, and verbal skills are continually demonstrated and reinforced throughout.

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.
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. Trigonometric Functions.
Angles and Their Measure.
Right Triangle Trigonometry.
The Sine and Cosine Functions and Their Graphs.
Other Trigonometric Functions and Their Graphs.
Modeling with Trigonometric Functions.
Inverse Trigonometric Functions.

7. Trigonometric Identities and Equations.
Fundamental Identities.
Verifying Trigonometric Identities.
Trigonometric Equations.
Sum and Difference Identities.
Multiple-Angle Identities.

8. Further Topics in Trigonometry.
Law of Sines.
Law of Cosines.
Vectors.
Parametric Equations.
Polar Equations.
Trigonometric Form and Roots of Complex Numbers.

9. Systems of Equations and Inequalities.
Functions and Equations of Two Variables.
Linear Systems of Equations and Inequalities in Two Variables.
Solutions of Linear Systems Using Matrices.
Properties and Applications of Matrices.
Inverses of Matrices.
Determinants.

10. Conic Sections.
Parabolas.
Ellipses.
Hyperbolas.

11. Further Topics in Algebra.
Sequences.
Series.
Counting.
The Binomial Theorem.
Probability.

Reference: Basic Concepts from Algebra and Geometry.
Formulas from Geometry.
Circles.
Integer Exponents.
Polynomial Expressions.
Factoring Polynomials.
Rational Expressions.

Appendix A: A Library of Functions.
Appendix B: Ti-83/83 Plus Graphing Calculators.

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College Algebra and Trigonometry Through Modeling and Visualization

College Algebra and Trigonometry Through Modeling and Visualization

0321081382

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