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

• ISBN13: 9780470131596
• ISBN10: 0470131594
• Edition: 5th
• Format: Hardcover
• Copyright: 2008-12-01
• Publisher: Wiley

Summary

Calculus teachers recognize Calculus as the leading resource among the "reform" projects that employ the rule of four and streamline the curriculum in order to deepen conceptual understanding. The fifth edition uses all strands of the "Rule of Four" graphical, numeric, symbolic/algebraic, and verbal/applied presentations to make concepts easier to understand. The book focuses on exploring fundamental ideas rather than comprehensive coverage of multiple similar cases that are not fundamentally unique. Readers will also gain access to WileyPLUS, an online tool that allows for extensive drills and practice. Calculus teachers will build on their understanding in the field and discover new ways to present concepts to their students.

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

Review Problems

Check Your Understanding

Projects: Rule of 70, Newtonâ Ös 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 Öhopitalâ Ös 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 Ös 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 Ös 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 Ös Formula and the Value of pi, Approximation the Derivative

Differential Equations

What Is a Differential Equation?

Slope Fields

Eulerâ Ös 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 Ös Law, Vibrations in a Molecule

Table of Contents provided by Publisher. All Rights Reserved.