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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 | |
Exponential Functions | |
Inverse Functions and Logarithms | |
Review | |
Principles of Problem Solving | |
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 | |
Writing Project: Early Methods for Finding Tangents | |
The Derivative as a Function | |
Review | |
Problems Plus | |
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, Applied Project: Where Should a Pilot Start Descent? , Applied Project: Building a Better Roller Coaster | |
Derivatives of Logarithmic Functions | |
Hyperbolic Functions | |
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 | |
Indeterminate Forms and L?Hospital?s Rule, Writing Project: The Origins of L?Hospital?s Rule | |
Summary of Curve Sketching | |
Graphing with Calculus and Calculators | |
Optimization Problems, Applied Project: The Shape of a Can | |
Applications to Business and Economics | |
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 | |
The Logarithm Defined as an Integral | |
Review | |
Problems Plus | |
Applications Of Integration | |
Areas between Curves | |
Volume | |
Volumes by Cylindrical Shells | |
Work | |
Average Value of a Function | |
Applied Project: Where to Sit at the Movie | |
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 | |
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: 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 | |
The Logistic Equation | |
Linear Equations | |
Predator-Prey Systems | |
Review | |
Problems Plus | |
Curves In Parametric, Vector, And Polar Form | |
Curves Defined by Parametric Equations, Laboratory Project: Running Circles around Circles | |
Calculus with Parametric Curves, Laboratory Project: Bezier Curves | |
Vectors in Two Dimensions | |
Vector Functions and Their Derivatives | |
Curvilinear Motions: Velocity and Acceleration | |
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 Root Tests | |
Strategy for Testing Series | |
Power Series | |
Representation | |
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