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Summary
This best selling author team explains concepts simply and clearly, without glossing over difficult points. Problem solving and mathematical modeling are introduced early and reinforced throughout, so that when students finish the course, they have a solid foundation in the principles of mathematical thinking. This comprehensive, evenly paced book provides complete coverage of the function concept and integrates substantial graphing calculator materials that help students develop insight into mathematical ideas. The authors' attention to detail and clarity, as in James Stewart's market-leading Calculus text, is what makes this text the market leader.
Table of Contents
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. TRIGONOMETRIC FUNCTIONS OF REAL NUMBERS. 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