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.
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Höhe: 254 mm
Breite: 202 mm
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ISBN-13
978-0-321-08138-4 (9780321081384)
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Schweitzer Klassifikation
Gary Rockswold Dr. Gary Rockswold has been teaching mathematics for 25 years at all levels from seventh grade to graduate school, including junior high and high school students, talented youth, vocational, undergraduate, and graduate students, and adult education classes. He is currently employed at Minnesota State University, Mankato, where he is a full professor of mathematics and the chair of the mathematics department. He graduated with majors in mathematics and physics from St. Olaf College in Northfield, Minnesota, where he was elected to Phi Beta Kappa. He received his Ph.D. in applied mathematics from Iowa State University. He has an interdisciplinary background and has also taught physical science, astronomy, and computer science.
Dr. Rockswold has been writing for mathematics textbooks for over ten years. Currently he is an author for Addison Wesley, writing textbooks that integrate modeling, visualization, applications, and the graphing calculator into the curriculum.
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.
