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 | |
Review | |
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 | |
Review | |
Problems Plus | |
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? Implicit Differentiation | |
Rates of Change in the Natural and Social Sciences | |
Related Rates | |
Linear Approximations and Differentials | |
Laboratory Project: Taylor Polynomials | |
Review | |
Problems Plus | |
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 | |
Review | |
Problems Plus | |
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 | |
Review | |
Problems Plus | |
Applications Of Integration | |
Areas between Curves | |
Volume | |
Volumes by Cylindrical Shells | |
Work | |
Average Value of a Function | |
Review | |
Problems Plus | |
Appendixes | |
Intervals, Inequalities, and Absolute Values | |
Coordinate Geometry and Lines | |
Graphs of Second-Degree Equations | |
Trigonometry | |
Sigma Notation | |
Proofs of Theorems | |
Complex Numbers | |
Answers to Odd-Numbered Exercises | |
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