图书简介
Written by David Cohen and co-authors Theodore B. Lee and David Sklar, PRECALCULUS, Seventh Edition, focuses on the use of a graphical perspective to provide a visual understanding of college algebra and trigonometry. Cohen’s texts are known for their clear writing style and outstanding, graded exercises and applications, including many examples and exercises involving applications and real-life data. Combining material from two other Cohen texts, the Seventh Edition accommodates the introduction of trigonometry with either a right-triangle approach or a unit-circle approach. Graphs, visualization of data, and functions are introduced and emphasized early on to aid student understanding. Although the text provides thorough treatment of the graphing calculator, the material is arranged to allow instructors to teach the course with as much or as little graphing utility work as they wish.
1. FUNDAMENTALS.
Sets of Real Numbers. Absolute Value. Solving Equations (Review and Preview). Rectangular Coordinates. Visualizing Data. Graphs and Graphing Utilities. Equations of Lines. Symmetry and Graphs. Circles.
2. EQUATIONS AND INEQUALITIES.
Quadratic Equations: Theory and Examples. Other Types of Equations. Inequalities. More on Inequalities.
3. FUNCTIONS.
The Definition of a Function. The Graph of a Function. Shapes of Graphs. Average Rate of Change. Techniques in Graphing. Methods of Combining Functions. Iteration. Inverse Functions.
4. POLYNOMIAL AND RATIONAL FUNCTIONS: APPLICATIONS TO OPTIMIZATION.
Linear Functions. Quadratic Functions. Using Iteration to Model Populations Growth (Optional Section). Setting Up Equations That Devine Functions. Maximum and Minimum Problems. Polynomial Functions. Rational Functions.
5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions. The Exponential Function y = ex. Logarithmic Functions. Properties of Logarithms. Equations and Inequalities with Logs and Exponents. Compound Interest. Exponential Growth and Decay.
6. AN INTRODUCTION TO TRIGONOMETRY VIA RIGHT TRIANGLES.
Trigonometric Functions of Acute Angles. Right-Triangle Applications. Trigonometric Functions of Angles. Trigonometric Identities.
7. THE TRIGONOMETRIC FUNCTIONS.
Radian Measure. Trigonometric Functions of Angles. Evaluating the Trigonometric Functions. Algebra and the Trigonometric Functions. Right-Triangle Trigonometry.
8. GRAPHS OF TRIGONOMETRIC FUNCTIONS.
Trigonometric Functions of Real Numbers. Graphs of the Sine and Cosine Functions. Graphs of y = A sin(Bx-C) and y = A cos(Bx-C). Simple Harmonic Motion. Graphs of the Tangent and the Reciprocal Functions.
9. ANALYTICAL TRIGONOMETRY.
The Addition Formulas. The Double-Angle Formulas. The Product-to-Sum and Sum-to-Product Formulas. Trigonometric Equations. The Inverse Trigonometric Functions.
10. ADDITIONAL TOPICS IN TRIGONOMETRY.
Right-Triangle Applications. The Law of Sines and the Law of Cosines. Vectors in the Plane: A Geometric Approach. Vectors in the Plane: An Algebraic Approach. Parametric Equations. Introduction to Polar Coordinates. Curves in Polar Coordinates.
DeMoivre’s Theorem.
11. SYSTEMS OF EQUATIONS.
Systems of Two Linear Equations in Two Unknowns. Gaussian Elimination. Matrices. The Inverse of a Square Matrix. Determinants and Cramer’s Rule. Nonlinear Systems of Equations. Systems of Inequalities.
12. THE CONIC SECTIONS.
The Basic Equations. The Parabola. Tangents to Parabolas (Optional Section). The Ellipse. The Hyperbola. The Focus-Directrix Property of Conics. The Conics in Polar Coordinates. Rotation of Axes.
13. ROOTS OF POLYNOMIAL EQUATIONS.
Division of Polynomials. The Remainder Theorem and the Factor Theorem. The Fundamental Theorem of Algebra. Rational and Irrational Roots. Conjugate Roots and Descartes’s Rule of Signs. Introduction to Partial Fractions. More About Partial Fractions.
14. ADDITIONAL TOPICS IN ALGEBRA.
Mathematical Induction. The Binomial Theorem. Introduction to Sequences and Series. Arithmetic Sequences and Series. Geometric Sequences and Series. Introduction to Limits.
Appendix A.1: Significant Digits.
Appendix A.2: √2 is Irrational.
Appendix A.3: The Complex Number System.
Answers.
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