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Full Description
PRECALCULUS, International Edition prepares learners for calculus and the rigors of that course, having been written by teachers who have taught the courses and seen where learners need help-and where other texts have come up short. The text features precise definitions and exposition, carefully crafted pedagogy, and a strong emphasis on algebraic, transcendental, and trigonometric functions. To show readers how important and relevant precalculus topics are to their future coursework, an optional Looking Ahead to Calculus feature appears in each chapter. The varied examples and exercises include many that encourage readers to use and understand graphs, as opposed to simply draw them, providing additional sound preparation for calculus.
Contents
R. BASIC CONCEPTS. Linear Equations and Applications. Complex Numbers. Quadratic Equations and Applications. Other Types of Equations. Inequalities. The Rectangular Coordinate System. Equations of Lines. Chapter Summary. Chapter Test. Looking Ahead to Calculus. 1. GRAPHS AND FUNCTIONS. Graphs of Equations. Functions and Function Notation. Graphs of Functions. Basic Graphs. Transformations of Graphs. Operations on Functions. Inverse Functions. Chapter Summary. Chapter Test. Looking Ahead to Calculus 2. POLYNOMIAL AND RATIONAL FUNCTIONS. Quadratic Functions. Polynomial Functions. Rational Zeros of Polynomial Functions. Roots of Polynomial Equations. Rational Functions. Polynomial and Rational Inequalities. Chapter Summary. Chapter Test. Looking Ahead to Calculus. 3. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions, Graphs, and Applications. Applications of Exponential Functions. Logarithmic Functions and Their Graphs. Applications of Logarithmic Functions. Properties of Logarithms. Exponential and Logarithmic Equations. Chapter Summary. Chapter Test. Looking Ahead to Calculus. 4. TRIGONOMETRIC FUNCTIONS. Angles and Their Measurement. The Unit Circle and Trigonometric Functions. Trigonometric Functions of Any Angle; Fundamental Identities. Graphs of the Sine and Cosine Functions. Graphs of the Tangent, Cotangent, Secant and Cosecant Functions. Regression and Other Graphs Involving Trigonometric Functions. Chapter Summary. Chapter Test. Looking Ahead to Calculus. 5. ANALYTIC TRIGONOMETRY. Inverse Trigonometric Functions. Inverse Cotangent, Secant, and Cosecant Functions (Optional). Verifying Trigonometric Identities. Sum and Difference Formulas. Double-Angle, Power-Reduction, Half-Angle Formulas. Product-to-Sum and Sum-to-Product Formulas. Trigonometric Equations I. Trigonometric Equations II. Chapter Summary. Chapter Test. Looking Ahead to Calculus. 6. APPLICATIONS; OBLIQUE TRIANGLES. Solving Right Triangles. More Right Triangle Applications. Law of Sines. Law of Cosines. Area of Triangles. Angular and Linear Velocity-Circular Motion. Chapter Summary. Chapter Test. Looking Ahead to Calculus. 7. POLAR COORDINATES; VECTORS. Polar Coordinates. Polar Equations and Graphs. Complex Plane; Polar Form of Complex Numbers; DeMoivre's Theorem. Vectors. Dot Product. Chapter Summary. Chapter Test. Looking Ahead to Calculus. 8. LINEAR SYSTEMS AND MATRICES. Systems of Linear Equations. Gaussian Elimination and Matrix Methods. Matrix Algebra. Matrix Inversion. Determinants. Partial Fractions. Graphs of Linear Inequalities. Linear Programming (available on website). Chapter Summary. Chapter Test. Looking Ahead to Calculus. 9. CONIC SECTIONS AND QUADRATIC SYSTEMS. The Circle and the Parabola. The Ellipse. The Hyperbola. Solving Non-linear Systems of Equations. Plane Curves and Parametric Equations. Conic Sections in Polar Coordinates. Chapter Summary. Chapter Test. Looking Ahead to Calculus. 10. NATURAL NUMBER FUNCTIONS AND PROBABILITY. The Binomial Theorem. Sequences, Series, and Summation Notation. Arithmetic Sequences. Geometric Sequences. Mathematical Induction. Permutations and Combinations (available on website). Probability (available on website). Chapter Summary. Chapter Test. Looking Ahead to Calculus. 11. INTRODUCTION TO CALCULUS (available on website). Limits. Properties of Limits. Limits and Continuity. Average Rate of Change. Tangents and Derivatives. Area and Integrals. Chapter Summary. Chapter Test. APPENDIX. Sets of Real Numbers. Integer Exponents and Scientific Notation. Radicals and Rational Exponents. Polynomials. Factoring Polynomials. Rational Expressions.
