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| Functions and Models | |
| Four Ways to Represent a Function | |
| Mathematical Models: A Catalog of Essential Functions | |
| New Functions from Old Functions | |
| Graphing Calculators and Computers | |
| Principles of Problem Solving | |
| Limits | |
| The Tangent and Velocity Problems | |
| The Limit of a Function | |
| Calculating Limits Using the Limit Laws | |
| The Precise Definition of a Limit | |
| Continuity | |
| Derivatives | |
| Derivatives and Rates of Change | |
| Writing Project: Early Methods for Finding Tangents | |
| The Derivative as a Function | |
| Differentiation Formulas | |
| Applied Project: Building a Better Roller Coaster | |
| Derivatives of Trigonometric Functions | |
| The Chain Rule | |
| Applied Project: Where Should a Pilot Start Descent? | |
| Imlicit Differentiation | |
| Rates of Change in the Natural and Social Sciences | |
| Related Rates | |
| Linear Approximations and Differentials | |
| Laboratory Project: Taylor Polynomials | |
| Applications of Differentiation | |
| Maximum and Minimum Values | |
| Applied Project: The Calculus of Rainbows | |
| The Mean Value Theorem | |
| How Derivatives Affect the Shape of a Graph | |
| Limits at Infinity | |
| Horizontal Asymptotes | |
| Summary of Curve Sketching | |
| Graphing with Calculus and Calculators | |
| Optimization Problems | |
| Applied Project: The Shape of a Can | |
| Newton's Method | |
| Antiderivatives | |
| Integrals | |
| Areas and Distances | |
| The Definite Integral | |
| Discovery Project: Area Functions | |
| The Fundamental Theorem of Calculus | |
| Indefinite Integrals and the Net Change | |
| Theorem | |
| Writing Project: Newton, Leibniz, and the Invention of Calculus | |
| The Substitution Rule | |
| Applications of Integration | |
| Areas between Curves | |
| Volume | |
| Volumes by Cylindrical Shells | |
| Work | |
| Average Value of a Function | |
| Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions | |
| Inverse Functions | |
| (Instructors may cover either Sections 7.2? 7.4 or Sections 7.2*?7.4*) | |
| Exponential Functions and Their Derivatives | |
| Logarithmic Functions | |
| Derivatives of Logarithmic Functions | |
| The Natural Logarithmic Function | |
| The Natural Exponential Function | |
| General Logarithmic and Exponential Functions | |
| Exponential Growth and Decay | |
| Inverse Trigonometric Functions | |
| Applied Project: Where to Sit at the Movies | |
| Hyperbolic Functions | |
| Indeterminate Forms and L'Hospital's Rule | |
| Writing Project: The Origins of L'Hospital's Rule | |
| Techniques of Integration | |
| Integration by Parts | |
| Trigonometric Integrals | |
| Trigonometric Substitution | |
| Integration of Rational Functions by Partial Fractions | |
| Strategy for Integration | |
| Integration Using Tables and Computer Algebra Systems | |
| Discovery Project: Patterns in Integrals | |
| Approximate Integration | |
| Improper Integrals | |
| Further Applications of Integration | |
| Arc Length | |
| Discovery Project: Arc Length Contest | |
| Area of a Surface of Revolution | |
| Discovery Project: Rotating on a Slant | |
| Applications to Physics and Engineering | |
| Discovery Project: Complementary Coffee Cups | |
| Applications to Economics and Biology | |
| Probability | |
| Differential Equations | |
| Modeling with Differential Equations | |
| Direction Fields and Euler's Method | |
| Separable Equations | |
| Applied Project: Which is Faster, Going Up or Coming Down? Models for Population Growth | |
| Applied Project: Calculus | |
| Parametric Equations and Polar Coordinates | |
| Curves Defined by Parametric Equations | |
| Laboratory Project: Families of Hypocycloids | |
| Calculus with Parametric Curves | |
| Laboratory Project: Bezier Curves | |
| Polar Coordinates | |
| Areas and Lengths in Polar Coordinates | |
| Conic Sections | |
| Conic Sections in Polar Coordinates | |
| Infinite Sequences and Series | |
| Sequences | |
| Laboratory Project: Logistic 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 | |
| Power Series | |
| Representation of Functions as Power Series | |
| Taylor and Maclaurin Series | |
| Writing Project: How Newton Discovered the Binomial Series | |
| Applications of Taylor Polynomials | |
| Applied Pro | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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