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A Preview of Calculus. 1. FUNCTIONS AND MODELS. Four Ways to Represent a Function. Mathematical Models. New Functions from Old Functions. Graphing Calculators and Computers. Exponential Functions. Inverse Functions and Logarithms. Review. Principles of Problem Solving. 2. LIMITS AND DERIVATIVES. The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. The Precise Definition of a Limit. Continuity. Limits at Infinity; Horizontal Asymptotes. Tangents, Velocities, and Other Rates of Change. Derivatives. The Derivative as a Function. Review. Problems Plus. 3. DIFFERENTIATION RULES. Derivatives of Polynomials and Exponential Functions. The Product and Quotient Rules. Rates of Change in the Natural and Social Sciences. Derivatives of Trigonometric Functions. The Chain Rule. Implicit Differentiation. Higher Derivatives. Derivatives of Logarithmic Functions. Hyperbolic Functions. Related Rates. Linear Approximations and Differentials. Review. Problems Plus. 4. APPLICATIONS OF DIFFERENTIATION. Maximum and Minimum Values. The Mean Value Theorem. How Derivatives Affect the Shape of a Graph. Indeterminate Forms and L'Hospital's Rule. Summary of Curve Sketching. Graphing with Calculus and Calculators. Optimization Problems. Applications to Economics. Newton's Method. Antiderivatives. Review. Problems Plus. 5. INTEGRALS. Areas and Distances. The Definite Integral. The Fundamental Theorem of Calculus. Indefinite Integrals and the Total Change Theorem. The Substitution Rule. The Logarithm Defined as an Integral. Review. Problems Plus. 6. APPLICATIONS OF INTEGRATION. Areas between Curves. Volumes. Volumes by Cylindrical Shells. Work. Average Value of a Function. Review. Problems Plus. 7. TECHNIQUES OF INTEGRATION. Integration by Parts. Trigonometric Integrals. Trigonometric Substitution. Integration of Rational Functions by Partial Functions. Strategy for Integration. Integration Using Tables and Computer Algebra Systems. Approximate Integration. Improper Integrals. Review. Problems Plus. 8. FURTHER APPLICATIONS OF INTEGRATION. Arc Length. Area of a Surface of Revolution. Applications to Physics and Engineering. Applications to Economics and Biology. Probability. Review. Problems Plus. 9. DIFFERENTIAL EQUATIONS. Modeling with Differential Equations. Direction Fields and Euler's Method. Separable Equations. Exponential Growth and Decay. The Logistic Equation. Linear Equations. Predator-Prey Systems. Review. Problems Plus. 10. PARAMETRIC EQUATIONS AND POLAR COORDINATES. Curves Defined by Parametric Equations. Tangents and Areas. Arc Length and Surface Area. Polar Coordinates. Areas and Lengths in Polar Coordinates. Conic Sections. Conic Sections in Polar Coordinates. Review. Problems Plus. 11. INFINITE SEQUENCES AND SERIES. Sequences. Series. The Integral Test and Estimates of Sums. The Comparison Tests. Alternating Series. Absolute Convergence and the Ratio and Root Tests. Strategy for Testing Series.