Calculus, 3rd Edition, Single Variable, Student Solutions Manual, 3rd Edition

by Deborah Hughes-Hallett (Univ. of Arizona); Andrew M. Gleason (Harvard Univ.); Daniel E. Flath (Univ. of South Alabama); Patti Frazer Lock (St. Lawrence Univ.); Sheldon P. Gordon (SUNY at Framingdale); David O. Lomen (Univ. of Arizona); David Loveloc

• ISBN13: 9780471441892
• ISBN10: 0471441899
• Edition: 3rd
• Format: Paperback
• Copyright: 2002-01-01
• Publisher: Wiley

Summary

The new edition exhibits the same strengths from earlier editions including the Rule of Four, an emphasis on modeling, exposition that students can read and understand and a flexible approach to technology. The conceptual and modeling problems, praised for their creativity and variety, continue to motivate and challenge students.

Table of Contents

A Library of Functions

Functions and Chang

Material from former

And 1.2

Exponential Functions Material from former

And 1.7

New Functions from Old Material from former

And 1.8

Logarithmic Functions Material from former

And 1.7

Trigonometric Functions Former 1.9

Powers, Polynomials, and Rational Functions Material from former

And 1.10

Introduction to Continuity Former

Including Intermediate Value Theorem

The Binomial Theorem is now a section available on the web site

Key Concept: The Derivative

How Do We Measure Speed?

Limits NEW section from former Focus on Theory section

The Derivative at a Point

The Derivative Function

Interpretations of the Derivative

The Second Derivative

Continuity and Differentiability NEW section from former Focus on Theory section

Short-Cuts to Differentiation

Powers and Polynomials

The Exponential Function

The Product and Quotient Rules

The Chain Rule

The Trigonometric Functions

Applications of the Chain Rule

Implicit Functions

Parametric Equations NEW: Material on Motion and Parametric Curves and Differentiation based on Appendix F and G and 16.1

Linear Approximations and the Derivative NEW: Material on Estimating the Error in the Approximation and theory on Differentiability and Local Linearity included

Using Local Linearity to Find Limits Includes L"Hopital"s rule

New

Using the Derivative

Using First and Second Derivatives

Families of Curves

Optimization

Applications to Marginality

More Optimization: Introduction to Modeling

Hyperbolic Functions

Theorems about Continuous and Differentiable Functions NEW

Extreme Value Theorem, Local Extrema and Critical Points, Mean Value Theorem, Increasing Function Theorem, Constant Function Theorem, Racetrack Principle

Key Concept: The Definite Integral

How Do We Measure Distance Traveled?

The Definite Integral Now includes general Riemann sum

Interpretations of the Definite Integral Material about integrating rates of change is now in this section

Theorems About Definite Integrals

Constructing Antiderivatives

Antiderivatives Graphically and Numerically

Constructing Antiderivatives Analytically

Differential Equations

Second Fundamental Theorem of Calculus

The Equations of Motion Former Focus on Modeling Section

Integration

Integration by Substitution

Integration by Parts

Tables of Integrals

Algebraic Identities and Trigonometric Substitutions

NEW section including partial factions and trigonometric substitutions involving completing the square

Approximating Definite Integrals

Approximating Errors and Simpson"s Rule

Improper Integrals

More on Improper Integrals

Using the Definite Integral

Areas and Volumes

More accessible introduction to setting up integrals focusing on basic concepts

Applications to Geometry

Section simplified and made easier to use

Density and Center of Mass Material on Center of Mass expanded

Applications to Physics

Applications to Economics

Distribution Functions

Probability and More on Distributions Note

And 10 replace

In the 2nd edition

The material has been expanded and extensively reorganized and rewritten

All sections have new problems

Material is clearly divided between series and convergence (Chapter 9) and approximations of functions (Chapter 10) for users who wish to emphasize one or the other

Series

Geometric Series Former 9.4

Convergence of Sequences and Series NEW section from former Focus on Theory

New material on integral test added

Tests for Convergence From Focus on Theory section with substantial new material on integral test, ratio test, and alternating series added

Power Series Material from former

With substantial new material on intervals and radius of convergence added

Approximating Functions

Taylor Polynomials First part of former 9.1

Taylor Series Second part of former

And 9.2

Finding and Using Series Former 9.3

The Error in Taylor Polynomial Approximations Former Focus on Theory section, substantially rewritten

Fourier Series

Differential Equations

What Is a Differential Equation?

Slope Fields

Euler"s Method

Separation of Variables

Growth and Decay

Applications and Modeling

Models of Population Growth

Systems of Differential Equations

Analyzing the Phase Plane

Second-Order Differential Equations: Oscillations

Linear Second-Order Differential Equations

Functions of Several Variables

Functions of Two Variable?

Former

And 11.2

Graphs of Functions of Two Variables

Contour Diagrams

Linear Functions

Functions of More than Two Variables

Limits and Continuity

NEW section from former Focus on Theory section

A Fundamental Tool: Vectors

Displacement Vectors

Vectors in General

The Dot Product

The Cross Product

Differentiating Functions of Many Variables

The Partial Derivative

Computing Partial Derivatives Algebraically

Local Linearity and the Differential

Gradients and Directional Derivatives in the Plane

Gradients and Directional Derivatives in Space

The Chain Rule

Second Order Partial Derivatives

Differentiability and Error Bounds

Optimization: Local and Global Extrema

Local Extrema

Global Extrema:Unconstrained Optimization

Constrained Optimization: Lagrange Multipliers

Integrating Functions of Many Variables

The Definite Integral of a Function of Two Variables

Iterated Integrals

Triple Integrals

Double Integrals in Polar Coordinates

Integrals in Cylindrical and Spherical Coordinates

Applications of Integrationto Probability

Change of Variables in a Multiple Integral NEW section from former Focus on Theory section

Parameterized Curves and Vector Fields

Parameterized Curves

Motion, Velocity, and Acceleration

Vector Fields

The Flow of a Vector Field

Line Integrals

The Idea of a Line Integral

Computing Line Integrals Over Parameterized Curves

Gradient Fields and Path-Independent Fields

Path-Independent Vector Fields and Green"s Theorem

Proof of Green"s Theorem

NEW section from former Focus on Theory section

Flux Integrals

The Idea of a Flux Integral

Flux Integrals for Graphs, Cylinders, and Spheres

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