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 | |
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*. See the Preface.) | |
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 | |
Review | |
Problems Plus | |
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 | |
Review | |
Problems Plus | |
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 | |
Review | |
Problems Plus | |
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 and Baseball | |
Linear Equations | |
Predator-Prey Systems | |
Review | |
Problems Plus | |
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 | |
Review | |
Problems Plus | |
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 | |
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