This book, intended for a graphing required college algebra and trigonometry or precalculus course, offers an innovative approach by demonstrating the importance of mathematics to students and presenting the material 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 reinforced throughout.
When introducing mathematical ideas, the text 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. Hence, mathematical concepts are often introduced through applications that help make the mathematics "real" to students. 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.
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Gewicht
ISBN-13
978-0-321-04334-4 (9780321043344)
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Schweitzer Klassifikation
1. Introduction to Functions and Graphs.
Data, Numbers, and Algorithms.
Visualization of Data.
Functions and Their Representations.
Types of Functions and Their Rates of Change.
Modeling Data with Functions.
Transformations of Graphs.
2. Linear Functions and Equations.
Linear Equations.
Linear Inequalities.
Equations of Lines.
Piecewise-Defined Functions.
Linear Approximation.
3. Nonlinear Functions and Equations.
Quadratic Equations and Inequalities.
Nonlinear Functions and Their Graphs.
Polynomial Functions and Their Graphs.
Real Zeros of Polynomial Functions.
The Fundamental Theorem of Algebra.
Rational Functions.
4. Inverse Functions.
Combining Functions.
Inverse Functions and Their Representations.
Exponential Functions.
Logarithmic Functions.
Exponential and Logarithmic Equations.
5. Trigonometric Functions.
Angles and Their Measure.
Right Triangle Trigonometry.
The Sine and Cosine Functions and Their Graphs.
Other Trigonometric Functions and Their Graphs.
Modeling Trigonometric Functions.
Inverse Trigonometric Functions.
6. Trigonometric Identities and Equations.
Fundamental Identities.
Verifying Identities.
Trigonometric Equations.
Sum and Difference Identities.
Multiple-Angle Identities.
7. Further Topics in Trigonometry.
Law of Sines.
Law of Cosines.
Vectors.
Parametric Equations.
Polar Equations.
Trigonometric Form and Roots of Complex Numbers.
8. 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.
9. Further Topics in Algebra.
Sequences.
Series.
Conic Sections.
Counting.
Probability.
