Synopsis
Intended to provide a flexible approach to the college algebra and trigonometry curriculum that emphasizes real-world applications, this text integrates technology into the presentation without making it an end in itself, and is suitable for a variety of audiences. Mathematical concepts are presented in an informal manner that stresses meaningful motivation, careful explanations, and numerous examples, with an ongoing focus on real-world problem solving. Pedagogical elements including chapter opening applications, graphing explorations, technology tips, calculator investigations, and discovery projects are some of the tools students will use to master the material and begin applying the mathematics to solve real-world problems. CONTEMPORARY COLLEGE ALGEBRA AND TRIGONOMETRY includes a full review of basic algebra in Chapter 0 and full coverage of trigonometry to prepare students for the standard science/engineering calculus sequence. (The companion volume, CONTEMPORARY COLLEGE ALGEBRA includes all of the non-trigonometry topics, covered in sufficient detail to prepare a student for a business/social science calculus course.) Those who are familiar with the author's CONTEMPORARY PRECALCULUS should note that this book covers topics in a different order, and with a slower, gentle approach. Also, more drill exercises are included.
Review
0. ALGEBRA REVIEW. The Real Number System. Special Topics: Decimal Representation of Real Numbers. Integral Exponents. Roots, Radicals, and Rational Exponents. Polynomials. Factoring. Rational Expressions. Chapter 0 Review. Discovery Project 0. 1. GRAPHS, LINES, AND TECHNOLOGY. The Coordinate Plane. Graphs and Graphing Technology. Lines. Linear Models. Chapter 1 Review. Discovery Project 1. 2. EQUATIONS AND INEQUALITIES. First-Degree Equations and Applications. Special Topics: Variation. Quadratic Equations and Applications. Solving Equations Graphically and Numerically. Polynomial, Radical, and Absolute Value Equations. Linear Inequalities. Polynomial and Rational Inequalities. Chapter 2 Review. Discovery Project 2. 3. FUNCTIONS AND GRAPHS. Functions. Functional Notation. Graphs of Functions. Special Topics: Parametric Graphing. Graphs and Transformations. Special Topics: Symmetry. Operations on Functions. Rates of Change. Special Topics: Instantaneous Rates of Change. Chapter 3 Review. Discovery Project 3. 4. POLYNOMIAL AND RATIONAL FUNCTIONS. Quadratic Functions and Models. Polynomial Functions and Roots. Special Topics: Synthetic Division. Graphs of Polynomial Functions. Special Topics: Optimization Applications. Polynomial Models. Rational Functions. Special Topics: Other Rational Functions. Complex Numbers. The Fundamental Theorem of Algebra. Chapter 4 Review. Discovery Project 4. 5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. Applications of Exponential Functions. Common and Natural Logarithmic Functions. Properties of Logarithms. Special Topics: Logarithms to Other Bases. Solving Exponential and Logarithmic Equations Algebraically. Exponential, Logarithmic, and Other Models. Inverse Functions. Chapter 5 Review. Discovery Project 5. 6. SYSTEMS OF EQUATIONS. Systems of Linear Equations in Two Variables. Special Topics: Systems of Nonlinear Equations. Large Systems of Linear Equations. Matrix Solution Methods. Matrix Methods for Square Systems. Special Topics: Matrix Algebra. Systems of Linear Inequalities. Introduction to Linear Programming. Chapter 6 Review. Discovery Project 6. 7. DISCRETE ALGEBRA. Sequences and Sums. Arithmetic Sequences. Geometric Sequences. Special Topics: Infinite Series. The Binomial Theorem. Permutations and Combinations. Special Topics: Distinguishable Permutations. Introduction to Probability. Mathematical Induction. Chapter 7 Review. Discovery Project 7. 8. ANALYTIC GEOMETRY. Circles and Ellipses. Hyperbolas. Parabolas. Special Topics: Rotations and Second-Degree Equations. Chapter 8 Review. Discovery Project 8. 9. TRIANGLE TRIGONOMETRY. Trigonometric Functions of Acute Angles. Trigonometric Functions of Angles. Applications of Right Triangle Trigonometry. The Law of Cosines. The Law of Sines. Special Topics: The Area of a Triangle. Chapter 9 Review. Discovery Project 9. 10. TRIGONOMETRIC FUNCTIONS. Angles and Radian Measure. Special Topics: Arc Length and Angular Speed. The Sine, Cosine, and Tangent Functions. Algebra and Identities. Basic Graphs. Periodic Graphs and Simple Harmonic Motion. Special Topics: Other Trigonometric Graphs. Other Trigonometric Functions. Chapter 10 Review. Discovery Project 10. 11. TRIGONOMETRIC IDENTITIES AND EQUATIONS. Basic Identities and Proofs. Addition and Subtraction Identities. Other Identities. Inverse Trigonometric Functions. Trigonometric Equations. Special Topics: Other Solution Methods for Trigonometric Equations. Chapter 11 Review. Discovery Project 11. 12. APPLICATIONS OF TRIGONOMETRY. Plane Curves and Parametric Equations. Polar Coordinates. The Complex Plane and Polar Form for Complex Numbers. DeMoivre's Theorem and nth Roots of Complex Numbers. Vectors in the Plane. Chapter 12 Review. Discovery Project 12. Geometry Review Appendix. Program Appendix.
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