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Calculus: Single Variable, 5th Edition,9780470089156
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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, Newton‚ 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
L‚ hopital‚ 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 Simpson‚ 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, Maxwell‚ 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, Machin‚ s Formula and the Value of pi, Approximation the Derivative
Differential Equations
What Is a Differential Equation?
Slope Fields
Euler‚ 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, Pareto‚ s Law, Vibrations in a Molecule
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