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# Calculus: Single Variable, 5th Edition

**by**Deborah Hughes-Hallett; Andrew M. Gleason (Harvard Univ.); William G. McCallum (Univ. of Arizona); David O. Lomen (Univ. of Arizona); David Lovelock (Univ. of Arizona); Jeff Tecosky-Feldman (Haverford College); Thomas W. Tucker (Colgate Univ.); Danie

5th

### 9780470089156

0470089156

Paperback

12/1/2008

Wiley

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## Summary

Work more effectively and gauge your progress as you go along! This Student Study Guide is designed to accompany Hughes-Hallett's "Calculus: Single Variable, 4th Edition." It contains additional study aids for students that are tied directly to the text. Now in its Fourth Edition, Hughes-Hallett's Calculus: Single Variable reflects the strong consensus within the mathematics community for a balance between contemporary and traditional ideas. Building on previous work, it brings together the best of both new and traditional curricula in an effort to meet the needs of instructors and students alike. The text exhibits the same strengths from earlier editions including the Rule of Four, an emphasis on modeling, exposition that is easy to understand, and a flexible approach to technology.

## Table of Contents

A Library Of Functions | |

Functions and Change | |

Exponential Functions | |

New Functions from Old | |

Logarithmic Functions | |

Trigonometric Functions | |

Powers, Polynomials, and Rational Functions | |

Introduction to Continuity | |

Limits | |

Review Problems | |

Check Your Understanding | |

Projects: Matching Functions to Data, Which Way Is the Wind Blowing? | |

Key Concept: The Derivative | |

How Do We Measure Speed? | |

The Derivative at a Point | |

The Derivative Function | |

Interpretations of the Derivative | |

The Second Derivative | |

Differentiability | |

Review Problems | |

Check Your Understanding | |

Projects: Hours of Daylight as a Function of Latitude, US Population | |

Short-Cuts To Differentiation | |

Powers and Polynomials | |

The Exponential Function | |

The Product and Quotient Rules | |

The Chain Rule | |

The Trigonometric Functions | |

The Chain Rule and Inverse Functions | |

Implicit Functions | |

Hyperbolic Functions | |

Linear Approximation and the Derivative | |

Theorems about Differentiable Functions | |

Review Problems | |

Check Your Understanding | |

Projects: Rule of 70, Newtonâ s Method | |

Using The Derivative | |

Using First and Second Derivatives | |

Optimization | |

Families of Functions | |

Optimization, Geometry, and Modeling | |

Applications to Marginality | |

Rates and Related Rates | |

Lâ hopitalâ s Rule, Growth, and Dominance | |

Parametric Equations | |

Review Problems | |

Check Your Understanding | |

Projects: Building a Greenhouse, Fitting a Line to Data, Firebreaks | |

Key Concept: The Definite Integral | |

How Do We Measure Distance Traveled? | |

The Definite Integral | |

The Fundamental Theorem and Interpretations | |

Theorems about Definite Integrals | |

Review Problems | |

Check Your Understanding | |

Projects: The Car and the Truck, An Orbiting Satellite | |

Constructing Antiderivatives | |

Antiderivatives Graphically and Numerically | |

Constructing Antiderivatives Analytically | |

Differential Equations | |

Second Fundamental Theorem of Calculus | |

The Equations of Motion | |

Review Problems | |

Check Your Understanding | |

Projects: Distribution of Resources, Yield from an Apple Orchard, Slope Fields | |

Integration | |

Integration by Substitution | |

Integration by Parts | |

Tables of Integrals | |

Algebraic Identities and Trigonometric Substitutions | |

Approximating Definite Integrals | |

Approximation Errors and Simpsonâ s Rule | |

Improper Integrals | |

Comparison of Improper Integrals | |

Review Problems | |

Check Your Understanding | |

Projects: Taylor Polynomial Inequalities | |

Using The Definite Integral | |

Areas and Volumes | |

Applications to Geometry | |

Area and Arc Length in Polar Coordinates | |

Density and Center of Mass | |

Applications to Physics | |

Applications to Economics | |

Distribution Functions | |

Probability, Mean, and Median | |

Review Problems | |

Check Your Understanding | |

Projects: Volume Enclosed by Two Cylinders, Length of a Hanging Cable, Surface Area of an Unpaintable Can of Paint, Maxwellâ s Distribution of Molecular Velocities | |

Sequences And Series | |

Sequences | |

Geometric Series | |

Convergence of Series | |

Tests for Convergence | |

Power Series and Interval of Convergence | |

Review Problems | |

Check Your Understanding | |

Projects: A Definition of e, Probability of Winning in Sports, Prednisone | |

Approximating Functions Using Series | |

Taylor Polynomials | |

Taylor Series | |

Finding and Using Taylor Series | |

The Error in Taylor Polynomial Approximations | |

Fourier Series | |

Review Problems | |

Check Your Understanding | |

Projects: Shape of Planets, Machinâ s Formula and the Value of pi, Approximation the Derivative | |

Differential Equations | |

What Is a Differential Equation? | |

Slope Fields | |

Eulerâ s Method | |

Separation of Variables | |

Growth and Decay | |

Applications and Modeling | |

The Logistic Model | |

Systems of Differential Equations | |

Analyzing the Phase Plane | |

Second-Order Differential Equations: Oscillations | |

Linear Second-Order Differential Equations | |

Review Problems | |

Check Your Understanding | |

Projects: SARS Predictions for Hong Kong, A S-I-R Model for SARS, Paretoâ s Law, Vibrations in a Molecule | |

Table of Contents provided by Publisher. All Rights Reserved. |