Precalculus: Mathematics for Calculus, Fifth Edition

1. FUNDAMENTALS. Overview. Real Numbers. Exponents and Radicals. Algebraic Expressions. Discovery Project: Visualizing a Formula. Fractional Expressions. Equations. Modeling with Equations. Discovery Project: Equations through the Ages. Inequalities. Coordinate Geometry. Graphing Calculators: Solving Equations and Inequalities Graphically. Lines. Modeling Variation. Review. Test. Focus on Problem Solving: General Principles. 2. FUNCTIONS. Overview. What is a Function? Graphs of Functions. Discovery Project: Relations and Functions. Increasing and Decreasing Functions: Average Rate of Change. Transformations of Functions. Quadratic Functions: Maxima and Minima. Modeling with Functions. Combining Functions.Discovery. Project: Iteration and Chaos. One-to-One Functions and Their Inverses Review. Test. Focus on Modeling: Fitting Lines to Data. 3. POLYNOMIAL AND RATIONAL FUNCTIONS. Overview. Polynomial Functions and Their Graphs. Dividing Polynomials. Real Zeros of Polynomials. Discovery Project: Zeroing in on a Zero. Complex Numbers. Complex Zeros and the Fundamental Theorem of Algebra. Rational Functions. Review. Test. Focus on Modeling: Fitting Polynomials to Data. 4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Overview. Exponential Functions. Discovery Project: Exponential Explosion. Logarithmic Functions. Laws of Logarithms. Exponential and Logarithmic Equations. Modeling with Exponential and Logarithmic Functions. Review. Test. Focus on Modeling: Fitting Exponential and Power Curves to Data. 5. TRIGONOMETIC FUNCTIONS OF ANGLES. Overview. The Unit Circle. Trigonometric Functions of Real Numbers. Trigonometric Graphs. Discovery Project: Predator-Prey Models. More Trigonometric Graphs. Modeling Harmonic Motion. Review. Test. Focus on Modeling: Fitting Sinusoidal Curves to Data. 6. TRIGONOMETRIC FUNCTIONS OF ANGLES. Overview. Angle Measure. Trigonometry of Right Triangles. Discovery Project: Similarity. Trigonometric Functions of Angles. The Law of Sines. The Law of Cosines. Review. Test. Focus on Modeling:Surveying. 7. ANALYTIC TRIGONOMETRY. Overview. Trigonometric Identities. Addition and Subtraction Formulas. Double-Angle, Half-Angle, and Sum-Product Identities. Inverse Trigonometric Functions. Discovery Project: Where to Sit at the Movies. Trigonometric Equations. Review. Test. Focus on Modeling: Traveling and Standing Waves. 8. POLAR COORDINATES AND VECTORS. Overview. Polar Coordinates. Graphs of Polar Equations. Polar Form of Complex Numbers; DeMoivre's Theorem. Discovery Project: Fractals. Vectors. The Dot Product. Discovery Project: Sailing Against the Wind. Review. Test. Focus on Modeling: Mapping the World. 9. SYSTEMS OF EQUATIONS AND INEQUALITIES. Overview. Systems of Equations. Systems of Linear Equations in Two Variables. Systems of Linear Equations in Several Variables. Discovery Project: Best Fit versus Exact Fit. Systems of Linear Equations: Matrices. The Algebra of Matrices. Discovery Project: Will the Species Survive? Inverses of Matrices and Matrix Equations. Discovery Project: Computer Graphics I. Determinants and Cramer's Rule. Partial Fractions. Systems of Inequalities. Review. Test. Focus on Modeling: Linear Programming. 10. ANALYTIC GEOMETRY. Overview. Parabolas. Ellipses. Hyperbolas. Discovery Project: Conics in Architecture Shifted Conics. Rotation of Axes. Discovery Project: Computer Graphics II. Polar Equations of Conics. Plane Curves and Parametric Equations. Review. Test. Focus on Modeling: The Path of a Projectile. 11. SEQUENCES AND SERIES. Overview. Sequences and Summation Notation. Arithmetic Sequences. Geometric Sequences. Discovery Project: Finding Patterns. Mathematical Finance. Mathematical Induction. The Binomial Theorem. Review. Test. Focus on Modeling: Modeling with Recursive Sequences. 12. LIMITS: A PREVIEW OF CALCULUS. Overview. Finding Limits Numerically and Graphically. Finding Limits Algebraically. Tangent Lines and Derivatives. Discovery Project: Designing a Roller Coaster. Limits at Infinity: Limits of Sequences. Areas. Review. Test. Focus on Modeling: Interpretations of Area. Answers to Odd-Numbered Exercises and Chapter Tests. Index.