Designed for the Precalculus course covering Algebra and Trigonometry. This text covers right angle trigonometry first and then develops the unit circle approach. This text requires student use of graphing calculators or a computer based software program. For schools who wish to cover unit circle first, please see "Precalculus: Graphing and Data Analysis".
The goal of this text is to provide a solid mathematical foundation via visualization of real world data. Technology is used as a tool to solve problems, motivate concepts, explore and preview mathematical concepts and to find curves of best fit to the data. Most mathematical concepts are developed and illustrated both algebraically and graphically - with the more intuitive and appropriate method presented first.
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Maße
Höhe: 208 mm
Breite: 260 mm
Dicke: 38 mm
Gewicht
ISBN-13
978-0-13-778481-3 (9780137784813)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Klassifikation
(NOTE: Chapters end with Chapter Review.)
1. Graphs.
Data and its Representation. Rectangular Coordinates; Graphing Utilities; Data in Ordered Pairs. Graphs of Equations. Lines. Parallel and Perpendicular Lines; Circles. Linear Curve Fitting. Variation.
2. Functions and Their Graphs.
Functions. More About Functions. Graphing Techniques. Operations on Functions; Composite Functions. Mathematical Models: Constructing Functions.
3. Equations and Inequalities.
Solving Equations Using A Graphing Utility. Linear and Quadratic Equations. Setting Up Equations: Applications. Other Types of Equations. Inequalities. Equations and Inequalities Involving Absolute Value.
4. Polynomial and Rational Functions.
Quadratic Functions; Curve Fitting. Power Functions; Curve Fitting. Polynomial Functions; Curve Fitting. Rational Functions. The Real Zeros of a Polynomial Function. Complex Numbers; Quadratic Equations with a Negative Discriminant. Complex Zeros; Fundamental Theorem of Algebra. Polynomial and Rational Inequalities.
5. Exponential and Logarithmic Functions.
One-to-One Functions; Inverse Functions. Exponential Functions. Logarithmic Functions. Properties of Logarithms. Logarithmic and Exponential Equations. Compound Interest. Growth and Decay. Exponential, Logarithmic, and Logistic Curve Fitting. Logarithmic Scales.
6. Trigonometric Functions.
Angles and Their Measure. Right Triangle Trigonometry. Computing the Values of Trigonometric Functions of Given Angles. Trigonometric Functions of a General Angle. Properties of the Trigonometric Functions. Graphs of the Trigonometric Functions. The Inverse Trigonometric Functions.
7. Analytic Trigonometry.
Trigonometric Identities. Sum and Difference Formulas. Double-Angle and Half-Angle Formulas. Product-to-Sum and Sum-to-Product Formulas. Trigonometric Equations.
8. Applications of Trigonometric Functions.
Solving Right Triangles. The Law of Sines. The Law of Cosines. The Area of a Triangle. Sinusoidal Graphs: Sinusoidal Curve Fitting. Simple Harmonic Motion: Damped Motion.
9. Polar Coordinates; Vectors.
Polar Coordinates. Polar Equations and Graphs. The Complex Plane; Demoivre's Theorem. Vectors. The Dot Product.
10. Analytic Geometry.
Conics. The Parabola. The Ellipse. The Hyperbola. Rotation of Axes; General Form of a Conic. Polar Equations of Conics. Plane Curves and Parametric Equations.
11. Systems of Equations and Inequalities.
Systems of Linear Equations: Substitution; Elimination. Systems of Linear Equations; Matrices. Systems of Linear Equations: Determinants. Matrix Algebra. Partial Fraction Decomposition. Systems of Nonlinear Equations. Systems of Inequalities. Linear Programming.
12. Sequences; Induction; Counting; Probability.
Sequences. Arithmetic Sequences. Geometric Sequences; Geometric Series. Mathematical Induction. The Binomial Theorem. Sets and Counting Permutations and Combinations. Probability.
Appendix Review:
Topics from Algebra and Geometry. Polynomials and Rational Expressions. Radicals; Rational Exponents. Solving Equations. Completing the Square. Synthetic Division.
Answers.
Index.
