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Purchase Benefits
What is included with this book?
Preface | |
To the Student | |
Diagnostic Tests | |
A Preview of Calculus | |
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 | |
Parametric Curves | |
Laboratory Project: Running Circles around Circles | |
Review | |
Principles of Problem Solving | |
Limits and Derivatives | |
The Tangent and Velocity Problems | |
The Limit of a Function | |
Calculating Limits Using the Limit Laws | |
Continuity | |
Limits Involving Infinity | |
Derivatives and Rates of Change | |
Writing Project: Early Methods for Finding Tangents | |
The Derivative as a Function | |
What Does f?? Say about f? Review | |
Focus on Problem Solving | |
Differentiation Rules | |
Derivatives of Polynomials and Exponential Functions | |
Applied Project: Building a Better Roller Coaster | |
The Product and Quotient Rules | |
Derivatives of Trigonometric Functions | |
The Chain Rule | |
Laboratory Project: BTzier Curves | |
Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation | |
Inverse Trigonometric Functions and their Derivatives | |
Derivatives of Logarithmic Functions | |
Discovery Project: Hyperbolic Functions | |
Rates of Change in the Natural and Social Sciences | |
Linear Approximations and Differentials | |
Laboratory Project: Taylor Polynomials | |
Review | |
Focus on Problem Solving | |
Applications of Differentiation | |
Related Rates | |
Maximum and Minimum Values | |
Applied Project: The Calculus of Rainbows | |
Derivatives and the Shapes of Curves | |
Graphing with Calculus and Calculators | |
Indeterminate Forms and l'Hospital's Rule | |
Writing Project: The Origins of l'Hospital's Rule | |
Optimization Problems | |
Applied Project: The Shape of a Can | |
Newton's Method | |
Antiderivatives | |
Review | |
Focus on Problem Solving | |
Integrals | |
Areas and Distances | |
The Definite Integral | |
Evaluating Definite Integrals | |
Discovery Project: Area Functions | |
The Fundamental Theorem of Calculus | |
Writing Project: Newton, Leibniz, and the Invention of Calculus | |
The Substitution Rule | |
Integration by Parts | |
Additional Techniques of Integration | |
Integration Using Tables and Computer Algebra Systems | |
Discovery Project: Patterns in Integrals | |
Approximate Integration | |
Improper Integrals | |
Review | |
Focus on Problem Solving | |
Applications of Integration | |
More about Areas | |
Volumes | |
Discovery Project: Rotating on a Slant | |
Volumes by Cylindrical Shells | |
Arc Length | |
Discovery Project: Arc Length Contest | |
Average Value of a Function | |
Applied Project: Where To Sit at the Movies | |
Applications to Physics and Engineering | |
Discovery Project: Complementary Coffee Cups | |
Applications to Economics and Biology | |
Probability | |
Review | |
Focus on Problem Solving | |
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 | |
Predator-Prey Systems | |
Review | |
Focus on Problem Solving | |
Infinte Sequences and Series | |
Sequences | |
Laboratory Project: Logistic Sequences | |
Series | |
The Integral and Comparison Tests | |
Estimating Sums | |
Other Convergence Tests | |
Power Series | |
Representations of Functions as Power Series | |
Taylor and Maclaurin Series | |
Laboratory Project: An Elusive Limit | |
Writing Project: How Newton Discovered the Binomial Series | |
Applications of Taylor Polynomials | |
Applied Project: Radiation from the Stars | |
Review | |
Focus on Problem Solving | |
Vectors and the Geometry of Space | |
Three-Dimensional Coordinate Systems | |
Vectors | |
The Dot Product | |
The Cross Product | |
Discovery Project: The Geometry of a Tetrahedron | |
Equations of Lines and Planes | |
Laboratory Project: Putting 3D in Perspective | |
Functions and Surfaces | |
Cylindrical and Spherical Coordinates | |
Laboratory Project: Families of Surfaces | |
Review | |
Focus on Problem Solving | |
Vector Functions | |
Vector Func | |
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