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1.1 Functions and Their Representations
1.2 A Catalog of Essential Functions
1.3 The Limit of a Function
1.4 Calculating Limits
1.6 Limits Involving Infinity
2.1 Derivatives and Rates of Change
2.2 The Derivative as a Function
2.3 Basic Differentiation Formulas
2.4 The Product and Quotient Rules
2.6 Implicit Differentiation
3.1 Exponential Functions
3.3 Derivatives of Logarithmic and Exponential Functions
3.4 Exponential Growth and Decay
3.5 Inverse Trigonometric Functions
4.1 Maximum and Minimum Values
4.2 The Mean Value Theorem
4.3 Derivatives and the Shapes of Graphs
4.4 Curve Sketching
4.6 Newton's Method
4.7 Antiderivatives
5.2 The Definite Integral
5.3 Evaluating Definite Integrals
5.5 The Substitution Rule
6.2 Trigonometric Integrals and Substitutions
6.3 Partial Fractions
6.6 Improper Integrals
7.1 Areas Between Curves
7.5 Area of a Surface of Revolution
7.6 Applications to Physics and Engineering
7.7 Differential Equations
8.1 Sequences
8.3 The Integral and Comparison Tests
8.7 Taylor and Maclaurin Series
9.1 Parametric Curves
9.2 Calculus with Parametric Curves
9.3 Polar Coordinates
10.1 Three-Dimensional Coordinate Systems
10.5 Equations of Lines and Planes
10.6 Cylinders and Quadric Surfaces
10.8 Arc Length and Curvature
11.7 Maximum and Minimum Values
12.1 Double Integrals over Rectangles
12.3 Double Integrals in Polar Coordinates
12.6 Triple Integrals in Cylindrical Coordinates
12.7 Triple Integrals in Spherical Coordinates|||6||
1090822730|default|Chapter 13: Vector Calculus|Web Links
Chapter 13: Vector Calculus
Vector Calculus
This comprehensive site offers information on almost every aspect of elementary vector calculus.
Section 13.1: Vector Fields
Java Microscope
An interactive Java applet that plots the vector fields of sample functions and lets you zoom with a variety of different "lenses."
Vector Field Analyzer
A similar Java applet that plots the vector fields of sample functions and lets you analyze the flow and other properties of the vector field.
Section 13.2: Line Integrals
Visualizing Circulation of Vector Fields
This site shows how line integrals over a closed curve in a plane can be visualized as ordinary integrals with respect to the arc length parameter.
Section 13.5: Curl and Divergence
Flows of Vector Fields
A Java applet that plots the vector fields of several functions and shows the effect of curl and divergence.
Section 13.6: Parametric Surfaces and Their Areas
Surface Area for Parametric Surfaces
This online graphing tool allows the user to generate parametric surfaces.|||2||
1090822719|default|Chapter 12: Multiple Integrals|Web Links
Chapter 12: Multiple Integrals
Section 12.4: Applications of Double Integrals
Centers of Mass and Moments of Inertia
A page containing a couple of practice problems involving triple integration.
Section 12.5: Triple Integrals
Examples of Triple Integration
A page containing a couple of practice problems involving triple integration.
Section 12.6: Triple Integrals in Cylindrical Coordinates
Cylindrical Coordinates
The first portion of this page illustrates cylindrical coordinates with animations.
Triple Integrals
This site provides an introduction to triple integrals in cylindrical and spherical coordinates, with examples and illustrations.
Section 12.8: Change of Variables in Multiple Integrals
Change of Variables in Multiple Integrals
This site presents a discussion on why a change of variables is useful and then works through several examples.|||2||
1090822711|default|Chapter 11: Partial Derivatives|Web Links
Chapter 11: Partial Derivatives
Section 11.3: Partial Derivatives
Partial Derivatives
This site presents visual interpretations of partial derivatives.
A Non-Differentiable Function with Partial Derivatives Everywhere
Describes (and graphs) a function that has partial derivatives everywhere but is not differentiable everywhere.
Partial Differentiation
A tutorial on "partial functions," partial derivatives, and second partial derivatives with example problems.
Section 11.4: Tangent Planes and Linear Approximations
Gradients, Directional Derivatives, and Tangent Planes
A lengthy discussion of gradients, directional derivatives, and tangent planes with practice problems.
Section 11.6: Directional Derivatives and the Gradient Vector
A Non-Differentiable Function with All Directional Derivatives
A description and graph of a function with all directional derivatives at the origin that is not differentiable there. (Note: uses alternate notations.)
Gradients and Contour Curves
A java applet that plots gradient vectors and level curves according to a function that you specify.
Section 11.8: Lagrange Multipliers
Lagrange Multipliers
An in-depth discussion of Lagrange Multipliers with geometric interpretations.|||2||
1090822703|default|Chapter 10: Vectors and the Geometry of Space|Web Links
Chapter 10: Vectors and Geometry of Space
Section 10.2: Vectors
Exploring Vectors with Geometer's Sketchpad
This site illustrates a number of vector concepts for those who have Geometer’s Sketchpad software.
Section 10.3: The Dod Product
What Good Are Dot Products?
A summary of the various reasons that dot products are useful.
Section 10.7: Vector Functions and Space Curves
TI-92 -- Integrating Vector-Valued Functions
A quick guide to integrating a vector-valued function on a TI-92 graphing calculator.
Section 10.9: Motion in Space: Velocity and Acceleration
Johannes Kepler: The Laws of Planetary Motion
Describes the development of Kepler's ideas along with an explanation of each of his three Laws of Planetary Motion.
Kepler's Laws of Planetary Motion
Uses diagrams and animations to illustrate Kepler's Laws of Planetary Motion.|||2||
1090822695|default|Chapter 9: Parametric Equations and Polar Coordinates|Web Links
Chapter 9: Parametric Equations and Polar Coordinates
Parametric and Polar Equations
This page features a comprehensive introduction to parametric equations and polar coordinates. Includes a large number of worked out examples.
Section 9.2: Calculus with Parametric Curves
Visual Calculus / Tangent Lines and Parametric Curves
This page has a tutorial and practice problems on finding the tangent line to a parametric curve.
Visual Calculus / Area Bounded by a Parametric Curve
A tutorial with animations on finding the area bounded by a parametric curve.
Section 9.3: Polar Coordinates
Visual Calculus / Polar Coordinates
A good tutorial on polar coordinates, how to plot them, and using a TI-86 (or TI-85) graphing calculator to graph them.
Polar Plot
This online applet plots the graph of a function given in polar coordinates.
Section 9.4: Areas and Lengths in Polar Coordinates
Visual Calculus / Arc Length
A tutorial on finding the arc length of a curve, including curves given by parametric equations.|||2||
1090822687|default|Chapter 8: Series|Web Links
Chapter 8: Series
Section 8.1: Sequences
Visual Calculus / Sequences
A tutorial on sequences, with examples and diagrams.
Analysis WebNotes: Sequences
A collection of notes on sequences with examples, animations, and practice problems.
Section 8.2: Series
Introduction to Series
An introduction to series, covering partial sums, convergence tests, geometric series, and more.
Visual Calculus / Series
Another good introduction to series, covering partial sums, convergence tests, geometric series, harmonic series, practice problems, and more.
Section 8.3: The Integral and Comparison Tests
Visual Calculus / Integral Test
A tutorial on the Integral Test with examples and solutions.
Visual Calculus / Error Estimates Using the Integral Test
A tutorial on using the Integral Test to estimate errors.
Section 8.4: Other Convergence Tests
Visual Calculus / Alternating Series
A tutorial on alternating series, including the test for alternating series, how to estimate errors, and practice problems with solutions.
Visual Calculus / Absolute Convergence
A tutorial on absolute convergence and the Ratio Test, with practice problems and solutions.
Absolute Convergence
A guide to determining if a series is absolutely convergent, including practice problems and solutions.
Visual Calculus / The Ratio Test
A tutorial on the Ratio Test, with practice problems and solutions.
The Root and Ratio Tests
A tutorial on the Ratio Test, with practice problems and solutions.
Section 8.5: Power Series
Visual Calculus / Power Series
An explanation of power series with many example problems.
Power Series
Another tutorial on power series, with practice problems and solutions.
Section 8.6: Representing Functions as Power Series
Representing a Function as a Power Series
This page demonstrates using a geometric series to represent a function as a power series.
Section 8.7: Taylor and Maclaurin Series
Visual Calculus / Taylor Polynomials
A site on Taylor polynomials, with practice problems and solutions.
Function Plotter
An online Java applet that plots the graphs of functions and their Taylor polynomials.
Taylor Series
A tutorial on Taylor series, with practice problems and solutions.
Section 8.8: Applications of Taylor Polynomials
Taylor Polynomials
This site provides examples applying Taylor series to explain physical behavior, including modeling the behavior of a swinging pendulum, and using radiation to measure wavelengths.|||2||
1090822678|default|Chapter 7: Applications of Integration |Web Links
Chapter 7: Applications of Integration
Applications of Integration
Visual Calculus / Applications of Integration: An excellent site that has tutorials covering applications of integration, including volumes and work. It also has interactive online applets, practice problems with solutions, examples, quizzes, tutorials on using graphing calculators, and more.
Section 7.1: Areas between Curves
Area Between Two Curves
This page explores the problem of finding the area bounded between two curves, and includes procedures and solved examples.
Section 7.2: Volumes
Volume of a Solid of Revolution
A page containing tutorials about the four principal methods of finding the volume of a solid: the disc method, the washer method, the cross section method, and the shell method.
Section 7.3: Volumes by Cylindrical Shells
The Shell Method
A page containing a tutorial on the shell method for obtaining the volume of a solid. Includes sample problems with solutions.
Section 7.4: Arc Length
Arc Length Approximator
This online tool calculates the arc length of the graph of a function over an interval that you specify. Some example functions with known arc lengths are calculated with various polynomial approximations to the length.
Section 7.6: Applications to Physics and Engineering
Moments of Inertia
A review of moments of inertia, with practice questions.
Section 7.7: Differential Equations
Solving a Separable Ordinary Differential Equation
An online calculator that finds the symbolic solution to separable (and other) ordinary differential equations that you specify.
Tangent Field (Direction Field)
This applet plots the direction field of a first-order ordinary differential equation that you specify.
Java Microscope
A Java applet that draws a slope field of several sample equations.
Raindrops
This portion of an online module solves a differential equation modeling falling raindrops by using Euler's method.
Predator-Prey
This portion of an online module numerically solves the differential equations for predator-prey models by using Euler's method.
Numerical Technique: Euler's Method
A guide to using Euler's method for approximating solutions to differential equations, with the help of diagrams.|||2||
1090822670|default|Chapter 6: Techniques of Integration|Web Links
Chapter 6: Techniques of Integration
Techniques of Integration
An excellent site that has tutorials covering virtually everything about integration techniques. It also has interactive online applets, practice problems with solutions, examples, quizzes, and tutorials on using graphing calculators.
Section 6.1: Integration by Parts
Integration by Parts I
This tutorial on integration by parts that derives the formula, explains each step of integrating by parts, and includes many examples.
Section 6.2: Trigonometric Integrals and Substitutions
Trig Substitutions
This site contains an extensive discussion of trigonometric substitutions for integration.
Sections 6.3: Partial Fractions
Partial Fractions Decomposition
The applet on this page calculates the partial fractions decomposition of any rational function entered by the student.
Sections 6.4: Integration with Tables and Computer Algebra Systems
S.O.S. Math - Mathematical Tables and Formulas
An extensive collection of integration formulas and more.
Sections 6.5: Approximate Integration
Numerical Integrator
An online integrator that will calculate an approximation for the definite integral of a function f over the interval [a, b].
Numerical Integration: Accumulating Rates of Change
This online tutorial explains in depth the application of techniques of numerical integration to models related to nature and everyday life.
Sections 6.6: Improper Integrals
Improper Integrals
This guide to improper integrals covers nearly all aspects, including convergence tests and gamma and beta functions. Scroll 2/3 of the way down the page to access the section on improper integrals.|||2||
1090822660|default|Chapter 5: Integrals|
Web Links
Chapter 5: Integrals
Integrals
The Integrator: An online integrator that uses Mathematica to evaluate integrals. Provided by Wolfram Research.
Visual Calculus / Integration
An excellent site that has tutorials covering virtually everything about integrals. It also has interactive online applets, practice problems with solutions, examples, quizzes, and tutorials on using graphing calculators.
Section 5.2: The Definite Integral
Definite Integral of a Function
This applet computes the definite and indefinite integrals of a function you specify on an interval of your choice.
Computing Riemann Sums
This applet computes and illustrates the Riemann sum of a function you specify, along with the interval and the number of points in the partition.
Section 5.4: The Fundamental Theorem of Calculus
Tutorial for the Indefinite Integral
A tutorial on indefinite integrals, provided by Hofstra University.
Section 5.5: The Substitution Rule
U-Substitution
Practice problems on the method of u-substitution, provided by UC Davis, with solutions.
U-Substitution
Several examples with detailed solutions.|||2||
1090822651|default|Chapter 4: Applications of Differentiation|Web Links
Chapter 4: Applications of Differentiation
Applications of Differentiation
An excellent site that has tutorials covering virtually everything about applications of differentiation. It also has interactive online applets, practice problems with solutions, examples, quizzes, and tutorials on using graphing calculators.
Sections 4.2: The Mean Value Theorem
The Mean Value Theorem
This site offers a proof of the Mean Value Theorem, along with example problems to illustrate the concept.
Sections 4.3: Derivatives and the Shapes of Graphs
Graphing Using First and Second Derivatives
Practice questions on graphing a variety of functions using first and second derivatives, provided by UC Davis, with solutions.
Sections 4.4: Curve Sketching
Texas Instruments
The official site of the maker of widely-used graphing calculators.
Ticalc.org
This is the self-described "official" unofficial headquarters for TI graphing calculators. A multitude of programs for a wide range of Texas Instruments calculators can be found here for download.
CASIO: Support Classroom With Technology
Casio's official site for their line of calculators, including product information, a program library, and much more.
Hewlett Packard Calculators
Hewlett Packard's official site for their calculators, including product information, technical support, and resources for creating and downloading calculator programs.
Section 4.5: Optimization Problems
Applied Maxima and Minima
Practice maximum/minimum optimization problems, provided by UC Davis, with solutions.
Application to Business and Economics
This page contains a set of interactive maximum/minimum problems related to business and walks the student through the solutions.
Sections 4.6: Newton's Method
Newton's Method
A Java applet that demonstrates Newton's method graphically.
Sections 4.7: Antiderivatives
Visual Calculus / Integration
An excellent site that has tutorials covering virtually everything about integrals. It also has interactive online applets, practice problems with solutions, examples, quizzes, and tutorials on using graphing calculators.|||2||
1090822625|default|Chapter 3: Inverse Functions|
Web Links
Chapter 3: Inverse Functions
Section 3.1-3.3: Exponential Functions; Inverse Functions and Logarithms; Derivatives of Logarithmic and Exponential Functions
Inverses
This page contains a detailed discussion of functional inverses. The graphical meaning of the inverse, the domain and range, and one to one functions all appear in an interactive format.
Derivatives of Exponential and Logarithmic Functions
On this site the student will find rules for differentiating exponential and logarithmic functions as well as practice problems with solutions.
Section 3.4: Exponential Growth and Decay
Ecological Models
A collection of practice problems where the student solves differential equations for exponential growth models. Includes Java applets.
Population Dynamics
A tutorial on building a model of population growth using differential equations, with examples.
Modeling Population Growth
A web page that explains how to model population growth through the use of differential equations.
Section 3.5: Inverse Trigonometric Functions
Differentiation of Inverse Trigonometric Functions
A page on inverse trigonometric functions, and their derivatives, with practice problems and solutions. Provided by UC Davis.|||2||
1090795193|default|Chapter 2: Derivatives|
Web Links
Chapter 2: Derivatives
Section 2.1: Derivatives and Rates of Change
Animated Secant Approaching the Tangent
A Java applet animation that shows a secant approaching the tangent line.
Tangent Line as the Limit of Secant Lines
Construction of the tangent line as the limit of secant lines at a point.
Rate of Change Applied to Import/Export
Discussion of rates of change with an example using export data.
Derivatives Using the Limit Definition
This is a set of practice problems about derivatives provided by the University of California, Davis, with solutions.
Section 2.2: The Derivative as a Function
Differentiation Using the Product Rule
Practice problems relating to the Product Rule, provided by the UC Davis, with solutions.
Differentiation Using the Quotient Rule
Differentiation Using the Quotient Rule
Practice problems relating to the Quotient Rule, provided by UC Davis, with solutions.
Section 2.5: The Chain Rule
Practice Problems on the Chain Rule
Practice questions on the Chain Rule, provided by UC Davis, with solutions.
Section 2.6: Implicit Differentiation
Practice Problems on Implicit Differentiation
Practice questions on implicit differentiation, provided by UC Davis, with solutions.
Section 2.7: Related Rates
Related Rates
A tutorial on solving related rates problems, with step-by-step walkthroughs through examples.|||2||
1090794855|default|Chapter 1: Functions and Limits|Web Links
Chapter 1: Functions and Limits
Visual Calculus / Pre-Calculus
An excellent site that has tutorials covering virtually everything about functions. It also has interactive online applets, practice problems with solutions, examples, quizzes, and tutorials on using graphing calculators.
Section 1.1: Functions and Their Representations
Four ways to represent a function
This site contains flash animated discussions of the meaning of the word function under the four standard representations.
Section 1.2: A Catalog of Essential Functions
Composite Functions
This is a thorough explanation of the concept of composite functions and their domains, along with a couple of worked out examples.
Section 1.5: Continuity
Continuity and Discontinuity
Definitions and examples of continuity and discontinuity both at single points and on intervals.
Section 1.6: Limits Involving Infinity
Limits of Functions as x Approaches Infinity
Practice questions provided by UC Davis, with solutions.|||2||
1090820133|default|Instructor Area|Solution Builder
The Brooks/Cole instructor companion site contains password-protected instructor versions of the following resources:
Lies My Calculator and Computer Told Me
Projects
Archived Problems
Challenge Problems
Additional Topics|||5||
1080255884|default|Book Supplements|Miscellaneous resources for students and teachers.
Please scroll down for instructors' supplements.
For Students and Instructors
Tools for Enriching Calculus On-line
Tools for Enriching Calculus—TEC—functions both as a powerful presentation tool for instructors, and as a tutorial environment in which students can explore and review selected topics. The simulation modules in TEC include audio explanations of the concept, along with exercises, examples, and instructions. TEC also contains Homework Hints for representative exercises from the text (indicated in blue in the text).
Click here for the Web Version of TEC
For Students
The following resources are available to enhance student learning and are available separately for student purchase. Instructors, please contact your sales representative if you would like information on packaging alternatives.
Instant Access 1pass
By purchasing the 1pass Instant Access for this text, students can access Tools for Enriching Calculus, ThomsonNOW Homework and VMentor TM tutorial service with a single password at http://1pass.thomson.com.
ThomsonNOW Homework allows students to solve instructor-assigned homework problems online, and get immediate feedback that helps students focus their study. Assistance is available through worked-out solutions that guide students through the steps of problem solving, or via live online tutoring at vMentor. The tutors at this online service will skillfully guide students through a problem, using unique two-way audio and whiteboard features.
1pass Access Card
ISBN: 0495189855
This card can be bundled with the textbook as an alternate to having students purchase access through the 1pass web site.
Tools for Enriching Calculus CD-ROM
Tools for Enriching Calculus—TEC—functions both as a powerful presentation tool for instructors, and as a tutorial environment in which students can explore and review selected topics. The simulation modules in TEC include audio explanations of the concept, along with exercises, examples, and instructions. TEC also contains Homework Hints for representative exercises from the text (indicated in blue in the text). TEC is accessed through 1pass.
Interactive Video Skillbuilder CD-ROM
ISBN: 0495113719
Student Solutions Manual
ISBN: 049501429X
This Student Solutions Manual, written by James Stewart, contains detailed solutions to the odd-numbered exercises in each chapter section, review section, and True-False Quiz. Also included are solutions to all Concept Check questions. Use of the solutions manual ensures that students learn the correct steps to arrive at an answer.
For Instructors
Complete Solutions Manual
ISBN: 0495014303
The Complete Solutions Manual, written by James Stewart, provides worked-out solutions to all of the problems in the text.
Instructor's Edition
ISBN: 0495019798
This version of the text contains a letter from James Stewart to professors, explaining the rationale for Essential Calculus.
Solution Builder
ISBN: 0495106925
This is an electronic version of the complete solutions manual. It provides instructors with an efficient method for creating solution sets to homework or exams. Instructors can easily view, select, and save solution sets that can then be printed or posted. This material will be available at the password-protected instructor site on the web.
ThomsonNOW™ Instructor Version
Register through ThomsonNOW at www. thomsonedu.com
Providing instructors and students with unsurpassed control, variety, and all-in-one utility, ThomsonNOW is a powerful and fully integrated teaching and learning system. ThomsonNOW TM ties together tutorials (via vMentor), homework, quizzing, and testing. Easy to use, ThomsonNOW offers instructors complete control when creating assessments in which they can draw from the wealth of exercises provided or create their own questions. ThomsonNOW features the greatest variety of problem types – allowing instructors to assess the way they teach! A real time-saver for instructors, ThomsonNOW offers automatic grading of homework, quizzes, and tests with results flowing directly into the gradebook. The auto-enrollment feature also saves time with course setup as students self-enroll into the course gradebook. ThomsonNOW provides seamless integration with Blackboard® and WebCT®.
upd 041006-rls|||4||
1079620895|default|Additional Topics|Adobe® Acrobat® Reader®, a free software for viewing and printing Adobe Portable Document Format (PDF) files, is required to view these documents.
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Principles of Problem Solving
Graphing Calculators and Computers
Strategy for Integration
Strategy for Testing Series
Fourier Series
Linear Differential Equations
Second-Order Linear Differential Equations
Nonhomogeneous Linear Equations
Applications of Second-Order Differential Equations
Using Series to Solve Differential Equations
Complex Numbers
Rotation of Axes |||3||
1079620839|default|News and Announcements|Welcome to the web site for my book [i]Essential Calculus: Early Transcendentals[/i]. The web site has been designed to give you easy access to study materials, book supplements, and challenge problems that will help you with your study of calculus.
Look in this section for information about new material, notices and resources posted to the web site, or features that we would like to draw your attention to. This area will help you identify what has changed since our last update.
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