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| Functions And Models | |
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| Four Ways to Represent a Function | |
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| Mathematical Models: A Catalog of Essential Functions | |
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| New Functions from Old Functions | |
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| Graphing Calculators and Computers | |
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| Exponential Functions | |
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| Inverse Functions and Logarithms | |
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| Review | |
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| Principles of Problem Solving | |
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| Limits And Derivatives | |
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| The Tangent and Velocity Problems | |
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| The Limit of a Function | |
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| Calculating Limits Using the Limit Laws | |
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| The Precise Definition of a Limit | |
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| Continuity | |
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| Limits at Infinity; Horizontal Asymptotes | |
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| Tangents, Velocities, and Other Rates of Change | |
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| Derivatives | |
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| Writing Project: Early Methods for Finding Tangents | |
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| The Derivative as a Function | |
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| Review | |
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| Problems Plus | |
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| Differentiation Rules | |
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| Derivatives of Polynomials and Exponential Functions | |
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| The Product and Quotient Rules | |
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| Rates of Change in the Natural and Social Sciences | |
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| Derivatives of Trigonometric Functions | |
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| The Chain Rule | |
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| Implicit Differentiation | |
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| Higher Derivatives, Applied Project: Where Should a Pilot Start Descent? , Applied Project: Building a Better Roller Coaster | |
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| Derivatives of Logarithmic Functions | |
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| Hyperbolic Functions | |
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| Related Rates | |
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| Linear Approximations and Differentials, Laboratory Project: Taylor Polynomials | |
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| Review | |
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| Problems Plus | |
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| Applications Of Differentiation | |
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| Maximum and Minimum Values, Applied Project: The Calculus of Rainbows | |
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| The Mean Value Theorem | |
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| How Derivatives Affect the Shape of a Graph | |
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| Indeterminate Forms and L''Hospital''s Rule, Writing Project: The Origins of L''Hospital''s Rule | |
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| Summary of Curve Sketching | |
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| Graphing with Calculus and Calculators | |
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| Optimization Problems, Applied Project: The Shape of a Can | |
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| Applications to Business and Economics | |
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| Newton''s Method | |
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| Antiderivatives | |
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| Review | |
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| Problems Plus | |
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| Integrals | |
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| Areas and Distances | |
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| The Definite Integral, Discovery Project: Area Functions | |
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| The Fundamental Theorem of Calculus | |
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| Indefinite Integrals and the Net Change Theorem, Writing Project: Newton, Leibniz and the Invention of Calculus | |
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| The Substitution Rule | |
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| The Logarithm Defined as an Integral | |
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| Review | |
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| Problems Plus | |
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| Applications Of Integration | |
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| Areas between Curves | |
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| Volume | |
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| Volumes by Cylindrical Shells | |
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| Work | |
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| Average Value of a Function, Applied Project: Where to Sit at the Movie | |
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| Review | |
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| Problems Plus | |
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| Techniques Of Integration | |
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| Integration by Parts | |
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| Trigonometric Integrals | |
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| Trigonometric Substitution | |
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| Integration of Rational Functions by Partial Fractions | |
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| Strategy for Integration | |
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| Integration Using Tables and Computer Algebra Systems, Discovery Project: Patterns in Integrals | |
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| Approximate Integration | |
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| Improper Integrals | |
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| Review | |
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| Problems Plus | |
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| Further Applications Of Integration | |
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| Arc Length | |
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| Discovery Project: Arc Length Contest .Area of a Surface of Revolution, Discovery Project: Rotating on a Slant | |
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| Applications to Physics and Engineering | |
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| Applications to Economics and Biology | |
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| Probability | |
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| Review | |
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| Problems Plus | |
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| Differential Equations | |
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| Modeling with Differential Equations | |
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| Direction Fields and Euler''s Method | |
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| Separable Equations, Applied Project: How Fast Does a Tank Drain?, Applied Project: Which is Faster, Going Up or Coming Down? Exponential Growth and Decay, Applied Project: Calculus and Baseball | |
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| The Logistic Equation | |
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| Linear Equations | |
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| Predator-Prey Systems | |
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| Review | |
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| Problems Plus | |
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| Parametric Equations And Polar Coordinates | |
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| Curves Defined by Parametric Equations, Laboratory Project: Families of Hypocycloids | |
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| Calculus with Parametric Curves, Laboratory Project: Bezier Curves | |
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| Polar Coordinates | |
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| Areas and Lengths in Polar Coordinates | |
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| Conic Sections | |
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| Conic Sections in Polar Coordinates | |
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| Review | |
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| Problems Plus | |
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| Infinite Sequences And Series | |
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| Sequences, Laboratory Project: Logistic Sequences | |
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| Series | |
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| The Integral Test and Estimates of Sums | |
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| The Comparison Tests | |
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| Alternating Series | |
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| Absolute Convergence and the Ratio and Root Tests | |
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| Strategy for Testing Series | |
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| Power Series | |
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| Representation of Functions as Power Series | |
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| Taylor and Maclaurin Series | |
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| Laboratory Project: An Ellusive Limit | |
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| The Binomial Series, Writ | |