1188314491|vladimir|Author's Welcome|Welcome to this website, which contains resources of varous types. Calculus is not an easy subject, but with the help of your instructor, the textbook and its ancillaries, and the resources on this site, you are well equipped to master the subject.
You will see a number of resources. If you think your knowledge of precalculus mathematics might be weak, and particularly if you have been away from mathematics for a while, you should click on Algebra Review. There you will find a review, with examples and exercises, of the very basic rules of algebra that are needed for success in calculus. When I grade calculus exams, I find that the mistakes my students make are often algebra mistakes, not calculus mistakes. So the Algebra Review has warnings about common errors in algebra. You will also see Lies My Calculator and Computer Told Me. Most of my students seem to believe that, when they perform a calculation with their calculator, it always provides the right answer. Here I try to correct this impression by showing certain situations in which calculator answers are unreliable. Some of you might be interested in History of Mathematics, which lists some of the better books and web sites devoted to the history of mathematics and, in particular, the history of calculus. Some of my students value such references because they humanize the subject. Also included are a number of ADDITIONAL TOPICS, which your instructor might assign, or which you might like to explore on your own. More topics will be added from time to time.
When you click on WEB LINKS you’ll see the annotated links, for particular topics, to outside resources.
Under OTHER RESOURCES you can access software for two- and three-dimensional graphing, as well as information on careers and organizations.
In addition, INSTRUCTOR AREA gives instructors access to Archived Problems. These are exercises, together with solutions, that appeared in previous editions. They can be used by the instructor as possible test questions or made available to students for additional practice.
James Stewart|||7||
1145210938|dusan|Additional Examples|ADDITIONAL EXAMPLES:
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
2.8 Linear Approximations and Differentials
3.1 Maximum and Minimum Values
3.3 Derivatives and the Shapes of Graphs
3.4 Curve Sketching
3.6 Newton's Method
3.7 Antiderivatives
4.2 The Definite Integral
4.3 Evaluating Definite Integrals
4.5 The Substitution Rule
5.1 Inverse Functions
5.2 The Natural Logarithmic Function
5.3 The Natural Exponential Function
5.5 Exponential Growth and Decay
5.6 Inverse Trigonometric Functions
6.2 Trigonometric Integrals and Substitutions
6.3 Partial Fractions
6.6 Improper Integrals
7.1 Areas Between Curves
7.5 Applications to Physics and Engineering
7.6 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
10.5 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||
1090906573|default|Chapter 17: Second-Order Differential Equations|Web Links
{nl} Chapter 17: Second Order Differential Equations
{nl}
{nl}Second Order Differential Equations
{nl} This website contains introductory notes on second order differential equations and some elementary solution techniques, including some techniques not covered in the text.
{nl} Section 17.3: Applications of Second-Order Differential Equations
{nl}
{nl}Bungee Jumping
{nl} A project incorporating second order linear differential equations.
{nl} Section 17.4: Series Solutions
{nl}
{nl}Series Solutions - Introduction
{nl} This page uses Taylor Series as an introduction to series solutions with several example problems.
{nl} Series Solutions: First Examples
{nl}This page contains worked examples of series solutions with an introduction to recursion relations.|||2||
1090906521|default|Chapter 16: Vector Calculus|Visuals and Modules{nl}{nl}Web Links
{nl} Chapter 16: Vector Calculus
{nl}
{nl}Vector Calculus
{nl} This comprehensive site offers information on almost every aspect of elementary vector calculus.
{nl} Section 16.1: Vector Fields
{nl}
{nl}Vector Field Analyzer
{nl} 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.
{nl} Section 16.2: Line Integrals
{nl}
{nl}Visualizing Circulation of Vector Fields
{nl} 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.
{nl} Section 16.5: Curl and Divergence
{nl}
{nl}Flows of Vector Fields
{nl} A Java applet that plots the vector fields of several functions and shows the effect of curl and divergence.
{nl}From Points to Regions
{nl} A guide showing how the divergence of a vector field combined with integration can be used to determine characteristics of an entire region in one, two, and three dimensions.
{nl}Divergence in Two and Three Dimensions
{nl} A tutorial using population growth and migration to explain divergence in a vector field in two and three dimensions.
{nl} Section 16.6: Parametric Surfaces and Their Areas
{nl}
{nl} Surface Area for Parametric Surfaces
{nl}This online graphing tool allows the user to generate parametric surfaces.|||2||
1090906493|default|Chapter 15: Multiple Integrals|Visuals and Modules{nl}{nl}Web Links
{nl} Chapter 15: Multiple Integrals
{nl}
{nl} Section 15.3: Double Integrals over General Regions
{nl}
{nl}Volumes and Double Integrals
{nl} A tutorial with illustrations on how to calculate the volumes of solids using multiple integrals.
{nl} Section 15.5: Applications of Double Integrals
{nl}
{nl}Centers of Mass and Moments of Inertia
{nl} An introduction to calculating centers of mass and moments of inertia with example problems.
{nl} Section 15.6: Triple Integrals
{nl}
{nl}Examples of Triple Integration
{nl} A page containing a couple of practice problems involving triple integration.
{nl}Section 15.7:Triple Integrals in Cylindrical coordinates
{nl}
{nl}Cylindrical Coordinates
{nl} The first portion of this page illustrates cylindrical coordinates with animations.
{nl} Section 15.8: Triple Integrals in Spherical coordinates
{nl}
{nl}Triple Integrals
{nl} This site provides an introduction to triple integrals in cylindrical and spherical coordinates, with examples and illustrations.
{nl} Spherical Coordinates
{nl}The first portion of this page illustrates spherical coordinates with animations.{nl}
{nl} Section 15.9: Change of Variables in Multiple Integrals
{nl}
{nl}Change of Variables in Multiple Integrals
{nl} This site presents a discussion on why a change of variables is useful and then works through several examples.|||2||
1090906461|default|Chapter 14: Partial Derivatives|Visuals and Modules{nl}{nl}Web Links
{nl}Chapter 14: Partial Derivatives
{nl}
{nl}Section 14.3: Partial Derivatives
{nl}Partial Derivatives
{nl} This site presents visual interpretations of partial derivatives.
{nl}A Non-Differentiable Function with Partial Derivatives Everywhere
{nl} Describes (and graphs) a function that has partial derivatives everywhere but is not differentiable everywhere.
{nl}Partial Differentiation
{nl} A tutorial on "partial functions," partial derivatives, and second partial derivatives with example problems.
{nl} Section 14.4: Tangent Planes and Linear Approximations
{nl}Gradients, Directional Derivatives, and Tangent Planes
{nl} A lengthy discussion of gradients, directional derivatives, and tangent planes with practice problems.
{nl} Section 14.6: Directional Derivatives and the Gradient Vector
{nl}A Non-Differentiable Function with All Directional Derivatives
{nl} A description and graph of a function with all directional derivatives at the origin that is not differentiable there. (Note: uses alternate notations.)
{nl}Gradient
{nl} A project exploring the concept of gradient with interactive Java applets.
{nl}The Gradient and the Directional Derivative
{nl} A tutorial on gradients and directional derivatives, with instructions on how to calculate and illustrate them on a TI-92.
{nl}Gradients and Contour Curves
{nl} A java applet that plots gradient vectors and level curves according to a function that you specify.
{nl} Section 14.8: Lagrange Multipliers
{nl} Lagrange Multipliers
{nl}An in-depth discussion of Lagrange Multipliers with geometric interpretations.|||2||
1090906430|default|Chapter 13: Vector Functions|Visuals and Modules{nl}{nl}Web Links
{nl} Chapter 13: Vector Functions
{nl}
{nl} Section 13.2: Derivatives and Integrals of Vector Functions
{nl}
{nl}TI-92 -- Integrating Vector-Valued Functions
{nl} A quick guide to integrating a vector-valued function on a TI-92 graphing calculator.
{nl} Section 13.3: Arc Length and Curvature
{nl}
{nl}Arc Length, Tangents, Normals, and Curvature
{nl} A tutorial on finding the arc length, tangents, normals, and curvature of a curve using vector equations.
{nl} Section 13.4: Motion in Space: Velocity and Acceleration
{nl}
{nl}Johannes Kepler: The Laws of Planetary Motion
{nl} Describes the development of Kepler's ideas along with an explanation of each of his three Laws of Planetary Motion.
{nl} Kepler's Laws of Planetary Motion
{nl}Uses diagrams and animations to illustrate Kepler's Laws of Planetary Motion|||2||
1090822730|default|Chapter 12: Vectors and the Geometry of Space|Visuals and Modules{nl}{nl}Web Links
{nl} Chapter 12: Vectors and Geometry of Space
{nl}
{nl} Section 12.2: Vectors
{nl}
{nl}Exploring Vectors with Geometer's Sketchpad
{nl} This site illustrates a number of vector concepts for those who have Geometer’s Sketchpad software.
{nl} Section 12.3: The Dot Product
{nl}
{nl}What Good Are Dot Products?
{nl} A summary of the various reasons that dot products are useful.
|||2||
1090822719|default|Chapter 11: Infinite Sequences and Series|Web Links
{nl} Chapter 11: Infinite Sequences and Series
{nl}
{nl} Section 11.1: Sequences
{nl}
{nl}Visual Calculus / Sequences
{nl} A tutorial on sequences, with examples and diagrams.
{nl}Analysis WebNotes: Sequences
{nl} A collection of notes on sequences with examples, animations, and practice problems.
{nl}Sequences
{nl} An overview of sequences, with many practice problems with solutions.
{nl} Section 11.2: Series
{nl}
{nl}Introduction to Series
{nl} An introduction to series, covering partial sums, convergence tests, geometric series, and more.
{nl}Visual Calculus / Series
{nl} Another good introduction to series, covering partial sums, convergence tests, geometric series, harmonic series, practice problems, and more.
{nl} Section 11.3: The Integral Test and Estimates of Sums
{nl}
{nl}Visual Calculus / Integral Test
{nl} A tutorial on the Integral Test with examples and solutions.
{nl}Visual Calculus / Error Estimates Using the Integral Test
{nl} A tutorial on using the Integral Test to estimate errors.
{nl} Section 11.5: Alternating Series
{nl}
{nl}Visual Calculus / Alternating Series
{nl} A tutorial on alternating series, including the test for alternating series, how to estimate errors, and practice problems with solutions.
{nl} Section 11.6: Absolute Convergence and the Ratio and Root Tests
{nl}
{nl}Visual Calculus / Absolute Convergence
{nl} A tutorial on absolute convergence and the Ratio Test, with practice problems and solutions.
{nl}Absolute Convergence
{nl} A guide to determining if a series is absolutely convergent, including practice problems and solutions.
{nl}Visual Calculus / The Ratio Test
{nl} A tutorial on the Ratio Test, with practice problems and solutions.
{nl}The Root and Ratio Tests
{nl} Another tutorial on the Root and Ratio Tests, with many example problems and solutions.
{nl} Section 11.7: Strategy for Testing Series
{nl}
{nl}Testing Series
{nl} This page presents a summary of all series tests, including the comparison tests.
{nl} Section 11.8: Power Series
{nl}
{nl}Visual Calculus / Power Series
{nl} An explanation of power series with many example problems.
{nl}Power Series
{nl} Another tutorial on power series, with practice problems and solutions.
{nl}Power Series Approximation
{nl} A Java applet that computes the first n terms of the power series expansion of a function.
{nl} Section 11.9: Representations of Functions as Power Series
{nl}
{nl}Representing a Function as a Power Series
{nl} This page demonstrates using a geometric series to represent a function as a power series.
{nl} Section 11.10: Taylor and Maclaurin Series
{nl}
{nl}Visual Calculus / Taylor Polynomials
{nl} A site on Taylor polynomials, with practice problems and solutions.
{nl}Function Plotter
{nl} An online Java applet that plots the graphs of functions and their Taylor polynomials.
{nl}Taylor Series
{nl} A tutorial on Taylor series, with practice problems and solutions.
{nl} Section 11.12: Applications of Taylor Polynomials
{nl}
{nl} Taylor Polynomials
{nl}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||
1090822711|default|Chapter 10: Parametric Equations and Polar Coordinates|Web Links
{nl} Chapter 10: Parametric Equations and Polar Coordinates
{nl}
{nl}Parametric and Polar Equations
{nl} This page features a comprehensive introduction to parametric equations and polar coordinates. Includes a large number of worked out examples.
{nl} Section 10.1: Curves Defined by Parametric Equations
{nl}
{nl}Plotting Parametric Curves
{nl} An online tool that plots a parametrically defined curve based on parametric equations that you specify.
{nl} Section 10.2: Calculus with Parametric Curves
{nl}
{nl}Visual Calculus / Tangent Lines and Parametric Curves This page has a tutorial and practice problems on finding the tangent line to a parametric curve.
{nl}Visual Calculus / Area Bounded by a Parametric Curve
{nl} A tutorial with animations on finding the area bounded by a parametric curve.
{nl} Section 10.3: Polar Coordinates
{nl}
{nl}Visual Calculus / Polar Coordinates
{nl} A good tutorial on polar coordinates, how to plot them, and using a TI-86 (or TI-85) graphing calculator to graph them.
{nl}Polar Plot
{nl} This online applet plots the graph of a function given in polar coordinates.
{nl} Section 10.4: Areas and Lengths in Polar Coordinates
{nl}
{nl}Visual Calculus / Arc Length
{nl} A tutorial on finding the arc length of a curve, including curves given by parametric equations.
{nl} Section 10.5: Conic Sections
{nl}
{nl}An Introduction to Conic Sections
{nl} A thorough introduction to conic sections with many examples.
{nl} Conic Section Movie
{nl}An animation that shows how conic sections are generated by the intersection of a plane with a right circular cone.|||2||
1090822703|default|Chapter 9: Differential Equations|Web Links
{nl} Chapter 9: Differential Equations
{nl}
{nl}Intro to Differential Equations
{nl} SOS Math’s site offers a comprehensive overview of all major topics in elementary differential equations.
{nl} Section 9.1: Modeling with Differential Equations
{nl}
{nl}Modeling via Differential Equations
{nl} An introduction to the basic steps of building a model of a system with differential equations.
{nl}Salmon and Steelhead Migration
{nl} A site containing several basic models about salmon and steelhead migration, using differential equations.
{nl}Small Mammal Dispersion
{nl} A page that describes a model of dispersion of a population of beavers using differential equations.
{nl}A Model of a Hydroplane
{nl} A model of the motion a hydroplane racing boat makes, using differential equations and Java applets.
{nl} Section 9.2: Direction Fields and Euler’s Method
{nl}
{nl}Tangent Field (Direction Field)
{nl} This applet plots the direction field of a first-order ordinary differential equation that you specify.
{nl}Raindrops
{nl} This portion of an online module solves a differential equation modeling falling raindrops by using Euler's method.
{nl}Predator-Prey
{nl} This portion of an online module numerically solves the differential equations for predator-prey models by using Euler's method.
{nl}Numerical Technique: Euler's Method
{nl} A guide to using Euler's method for approximating solutions to differential equations, with the help of diagrams.
{nl} Section 9.3: Separable Equations
{nl}
{nl}Solving a Separable Ordinary Differential Equation
{nl} An online calculator that finds the symbolic solution to a separable ordinary differential equation that you specify.
{nl} Section 9.4: Exponential Growth and Decay
{nl}
{nl}Population Dynamics
{nl} A tutorial on building a model of population growth using differential equations, with examples.
{nl}Modeling Population Growth
{nl} A web page that explains how to model population growth through the use of differential equations.
{nl} The Logistic Model
{nl} An online tool that graphs a logistic model based on values that you input.
{nl} Section 9.5: Linear Equations
{nl}
{nl}Linear Equations
{nl} A tutorial on how to solve linear first-order differential equations, with example problems and solutions.
{nl} Section 9.6: Predator-Prey Systems
{nl}
{nl} Predator-Prey Models
{nl}A detailed module on predator-prey models, Euler's method for systems, and more.|||2||
1090822695|default|Chapter 8: Further Applications of Integration|Web Links
{nl} Chapter 8: Further Applications of Integration
{nl}
{nl}Further Applications of Integration
{nl} An excellent site that has tutorials covering applications of integration, including arc length and centers of mass. It also has interactive online applets, practice problems with solutions, examples, quizzes, and tutorials on using graphing calculators.
{nl} Section 8.1: Arc Length
{nl}
{nl}Arc Length of a Curve
{nl} This online tool calculates the arc length of the graph of a function over an interval that you specify.
{nl} Section 8.2: Area of a Surface of Revolution
{nl}
{nl}Area of a Surface of Revolution
{nl} Provides a definition of the area of a surface of revolution, with an animation and an example problem.
{nl} Section 8.3: Applications to Physics and Engineering
{nl}
{nl}Moments of Inertia
{nl} A review of moments of inertia, with practice questions.
{nl} Section 8.4: Applications to Economics and Biology
{nl}
{nl}Use of Calculus in Biology
{nl} This interesting site provides a number of ideas for projects that incorporate calculus and the sciences. Worth a look if only to gain a sense of the way that calculus is interwoven into various academic disciplines.
{nl} Section 8.5: Probability
{nl}
{nl} Calculus and Probability
{nl}A complete text resource on the application of Calculus to Probability and Statistics.|||2||
1090822687|default|Chapter 7: Techniques of Integration|Web Links
{nl}Chapter 7: Techniques of Integration
{nl}
{nl}Techniques of Integration
{nl} 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.
{nl}Section 7.1: Integration by Parts
{nl}Integration by Parts I
{nl} This tutorial on integration by parts that derives the formula, explains each step of integrating by parts, and includes many examples.
{nl} Section 7.3: Trigonometric Substitution
{nl}Trigonometric Substitution
{nl} A tutorial with examples from Harvey Mudd College on using trigonometric substitutions to evaluate integrals.
{nl} Section 7.4: Integration of Rational Functions by Partial Fractions
{nl}Partial Fraction Expansion of a Rational Function
{nl} This online calculator computes the partial fraction expansion of a rational function that you specify.
{nl} Section 7.5: Strategy for Integration
{nl}Strategies for Integration
{nl} This site provides a broad overview of strategies to employ for a wide array of integrals.
{nl} Section 7.6: Integration Using Tables and Computer Algebra Systems
{nl}S.O.S. Math - Mathematical Tables and Formulas
{nl} An extensive collection of integration formulas and more.
{nl} Section 7.7: Approximate Integration
{nl}Numerical Integration
{nl} An online integrator that will calculate an approximation for the definite integral of a function f over the interval [a, b].
{nl}Simpson's Numerical Integrator
{nl} An online integrator that will use Simpson’s Rule to approximate a definite integral that you specify.
{nl}Numerical Integration: Accumulating Rates of Change
{nl} This online tutorial explains in depth the application of techniques of numerical integration to models related to nature and everyday life.
{nl} Section 7.8: Improper Integrals
{nl} Improper Integrals
{nl}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||
1090822670|default|Chapter 6: Applications of Integration|Web Links
{nl} Chapter 6: Applications of Integration
{nl}Applications of Integration
{nl} 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.
{nl} Section 6.1: Areas Between Curves
{nl}Area Between Two Curves
{nl} This page explores the problem of finding the area bounded between two curves, and includes procedures and solved examples.
{nl} Section 6.2: Volumes
{nl}Volume of a Solid of Revolution
{nl} 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. Each includes sample problems with solutions.
{nl} Section 6.3: Volumes by Cylindrical Shells
{nl}The Shell Method
{nl} A page containing a tutorial on the shell method for obtaining the volume of a solid. Includes sample problems with solutions.
{nl} Section 6.4: Work
{nl}Work and Energy
{nl} A site provided by Montana State University that gives a tutorial on work and energy, along with diagrams and animations. (See "Energy Functions in One Dimension.")
{nl} Section 6.5: Average Value of a Function
{nl} Average Value of a Function
{nl}This site uses Flash and Java animations to illustrate the link between the average value of a function and the Mean Value Theorem.|||2||
1090822660|default|Chapter 5: Integrals|Downloads
{nl}Area and Integrals Alternative Treatment{nl}{nl}Web Links
{nl} Chapter 5: Integrals
{nl}
{nl}Integrals
{nl} The Integrator: An online integrator that uses Mathematica to evaluate integrals. Provided by Wolfram Research.
{nl}Visual Calculus / Integration
{nl} 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.
{nl} Section 5.2: The Definite Integral
{nl}
{nl}Definite Integral of a Function
{nl}This applet computes the definite integral of a function you specify on an interval of your choice.
{nl}
{nl}Computing Riemann Sums
{nl} 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.
{nl} Section 5.4: Indefinite Integrals and the Net Change Theorem
{nl}
{nl}Tutorial for the Indefinite Integral A tutorial on indefinite integrals, provided by Hofstra University.
{nl}
{nl} Section 5.5: The Substitution Rule
{nl}
{nl}U-Substitution
{nl}
{nl}Practice problems on the method of u-substitution, provided by UC Davis, with solutions.
{nl} U-Substitution
{nl}Several examples with detailed solutions.|||2||
1090822651|default|Chapter 4: Applications of Differentiation|Web Links
{nl} {nl} Chapter 4: Applications of Differentiation
{nl} Applications of Differentiation
{nl} 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.
{nl} Section 4.2: The Mean Value Theorem
{nl}
{nl} The Mean Value Theorem
{nl} This site offers a proof of the Mean Value Theorem, along with example problems to illustrate the concept.
{nl} Section 4.3: How Derivatives Affect the Shape of a Graph
{nl}
{nl} Graphing Using First and Second Derivatives
{nl} Practice questions on graphing a variety of functions using first and second derivatives, provided by UC Davis, with solutions.
{nl} Section 4.6: Graphing with Calculus and Calculators
{nl}
{nl} Texas Instruments:
{nl} The official site of the maker of widely-used graphing calculators.
{nl} Ticalc.org
{nl} 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.
{nl} CASIO: Support Classroom With Technology
{nl} Casio's official site for their line of calculators, including product information, a program library, and much more.
{nl} Hewlett Packard Calculators
{nl} Hewlett Packard's official site for their calculators, including product information, technical support, and resources for creating and downloading calculator programs.
{nl} Section 4.7: Optimization Problems
{nl}
{nl} Applied Maxima and Minima
{nl} Practice maximum/minimum optimization problems, provided by UC Davis, with solutions.
{nl} Derivatives Applied to Economics
{nl} This page gives three problems with solutions that require the use of the first derivative to solve introductory questions in economics.
{nl} Section 4.8: Newton’s Method
{nl}
{nl} Newton's Method:
{nl} A Java applet that demonstrates Newton's method graphically.
{nl} Section 4.9: Antiderivatives
{nl}
{nl} Visual Calculus / Integration
{nl} 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: Differentiation Rules|Web Links
{nl} {nl} Chapter 3: Differentiation Rules
{nl}
{nl} Section 3.2: The Product and Quotient Rules
{nl}
{nl} Differentiation Using the Product Rule
{nl} Practice problems relating to the Product Rule, provided by the UC Davis, with solutions.
{nl} Differentiation Using the Quotient Rule
{nl} Practice problems relating to the Quotient Rule, provided by UC Davis, with solutions.
{nl} {nl} {nl} Section 3.3: Derivatives of Trigonometric Functions
{nl}
{nl} Practice Problems on Trigonometric Functions
{nl} Practice questions on differentiating trigonometric functions, provided by UC Davis, with solutions.
{nl} Section 3.4: The Chain Rule
{nl}
{nl} Practice Problems on the Chain Rule
{nl} Practice questions on the Chain Rule, provided by UC Davis, with solutions.
{nl} Section 3.5: Implicit Differentiation
{nl}
{nl} Practice Problems on Implicit Differentiation
{nl} Practice questions on implicit differentiation, provided by UC Davis, with solutions.
{nl} {nl} {nl} Section 3.9: Related Rates
{nl}
{nl} Related Rates
{nl} A tutorial on solving related rates problems, with step-by-step walkthroughs through examples.
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1090795193|default|Chapter 2: Limits and Derivatives|Web Links
{nl}{nl} {nl} Chapter 2: Limits and Derivatives
{nl}
{nl} Visual Calculus / Limits and Continuity
{nl} An excellent site that has tutorials covering virtually everything about limits, continuity, and asymptotes. Limits are presented numerically, graphically, and symbolically. It also has interactive online applets, practice problems with solutions, examples, quizzes, and tutorials on using graphing calculators.
{nl} {nl} {nl} Section 2.1: The Tangent and Velocity Problems
{nl}
{nl} Animated Secant Approaching the Tangent
{nl} A Java applet animation that shows a secant approaching the tangent line.
{nl} Section 2.4: The Precise Definition of a Limit
{nl}
{nl} Definition of Limit
{nl} A presentation of the definition of limit, along with a number of solved examples.
{nl} Section 2.5: Continuity
{nl}
{nl} Continuity and Discontinuity
{nl} Definitions and examples of continuity and discontinuity both at single points and on intervals.
{nl} {nl} {nl} Section 2.6: Limits at Infinity; Horizontal Asymptotes
{nl} Limits of Functions as x Approaches Infinity
{nl} Practice questions provided by UC Davis, with solutions.
{nl} {nl} {nl} Section 2.7: Derivatives and Other Rates of Change
{nl}
{nl} Tangent Line as the Limit of Secant Lines
{nl} Construction of the tangent line as the limit of secant lines at a point.
{nl} Rate of Change Applied to Import/Export
{nl} Discussion of rates of change with an example using export data
{nl} {nl} {nl} Visual Calculus / Derivatives
{nl} An excellent site that has tutorials covering virtually everything about derivatives. It also has interactive online applets, practice problems with solutions, examples, quizzes, and tutorials on using graphing calculators.
{nl} Derivatives Using the Limit Definition
{nl} This is a set of practice problems about derivatives provided by the University of California, Davis, with solutions.
{nl} Section 2.8: The Derivative as a Function
{nl}
{nl} Derivative as a Function
{nl}A thorough examination of the concept of the derivative as a function. This site includes a number of worked out examples and is intended to be used with a CAS.
{nl}
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1090794855|default|Chapter 1: Functions and Models|Web Links
{nl} Chapter 1: Functions and Models
{nl} Visual Calculus / Pre-Calculus
{nl}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.
{nl}
{nl} Section 1.1: Four Ways to Represent a Function
{nl} Quickmath
{nl} This site uses Mathematica to solve, simplify, expand, or factor equations, systems of equations, and inequalities. It also performs operations with matrices and plots graphs.
{nl} {nl} {nl} Section 1.2: Mathematical Models
{nl}
{nl} A Context for Calculus
{nl} An excellent site that walks you through the process of generating a mathematical model for the spread of disease. Includes exercises and sample models of several diseases.
{nl} Section 1.3: New Functions from Old Functions
{nl}
{nl} Composite functions
{nl} This is a thorough explanation of the concept of composite functions and their domains, along with a couple of worked out examples.
{nl} Section 1.4: Graphing Calculators and Computers
{nl}
{nl} Texas Instruments
{nl} The official site of the maker of widely used graphing calculators.
{nl} Ticalc.org
{nl} 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.
{nl} CASIO: Support Classroom With Technology
{nl} Casio's official site for their line of calculators, including product information, a program library, and much more.
{nl} Hewlett Packard Calculators
{nl} Hewlett Packard's official site for their calculators, including product information, technical support, and resources for creating and downloading calculator programs.
{nl} Section 1.6: Inverse Functions and Logarithms
{nl}
{nl} Inverses of Functions
{nl} A thorough and easy-to-understand explanation of inverse functions. This page also uses Flash and Java animations to illustrate the material.
{nl} Problems About Exponential and Logarithmic Functions
{nl} Practice problems with solutions, organized by level of difficulty.
|||2||
1090820133|default|Instructor Area|Some of the links below will take you to a password-protected area of the Brooks/Cole Stewart Calculus Instructor Resources web site. If you are an instructor and need a login, please fill out our online request form and an access code will be e-mailed to you.
Solution Builder
Build and save your own customized solution sets for textbook exercises.
Archive Problems
Problems from past editions of this textbook organized by chapter. Includes complete answers and solutions.
Challenge Problems
Extra challenging problems from author James Stewart organized by chapter. Includs complete answers and solutions.
Lies My Calculator and Computer Told Me
Extra section by James Stewart that discusses the limitations of using calculators and computers for calculus. Includes exercises with solutions.
Additional Topics:
Fourier Series (Instructor Version w/ Solutions)
Optional extra topic for instructors wishing to introduce Fourier Series in their classes. Includes exercises with solutions.
Rotation of Axes (Instructor Version w/ Solutions)
Optional extra topic for instructors wishing to introduce Rotation of Axes in their classes. Includes exercises with solutions.
Formulas for the Remainder Term in Taylor Series
An extension of Section 11.10 of the textbook for instructors wishing to expand this topic in their class coverage.|||5||
1080255884|default|Book Supplements|Miscellaneous resources for students and teachers.
Please scroll down for instructors' supplements.
Studious Video Solutions Manual
NEW! Cengage is proud to announce the latest addition to our online product line for Stewart's Calculus: Early Transcendentals. Studious includes more than 4000 video solutions to exercises from the Stewart textbook, plus hundreds of hours of lecture videos on key concepts in calculus, quizzes, interactive and printable flashcards, and more. Visit www.cengage.com/studious to find out more and to purchase access at a special introductory price.
For Students and Instructors
Enhanced WebAssign - Mathematics and Science Printed Access Card
ISBN: 0538738073
Instant feedback, grading precision, and ease of use are just three reasons why WebAssign is the most widely used homework system in higher education. WebAssign’s homework delivery system lets instructors deliver, collect, grade and record assignments via the web. And now, this proven system has been enhanced to include end-of-section problems from Stewart’s Calculus—incorporating exercises, examples, video skillbuilders and quizzes to promote active learning and provide immediate, relevant feedback students want.
Maple CD-ROM
ISBN: 0495012378 (Maple 10)
ISBN: 0495390526 (Maple 11)
Maple provides an advanced, high performance mathematical computation engine with fully integrated numerics and symbolics, all accessible from a WYSIWYG technical document environment. Available for bundling with your Stewart Calculus text at a special discount.
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). Please contact your Brooks/Cole representative for information on optionally bundling the TEC CD with your text.
Click here for the Web Version of TEC
For Students
The following resources are available to enhance student learning and most are available separately for student purchase via our online catalog. Please note that some items are automatically packaged with the text and are not sold separately. Instructors, please contact your sales representative if you would like information on other packaging alternatives.
Student Solutions Manual
ISBN: 0495012408 (Single variable) | ISBN: 0495012289 (Multivariable)
Provides completely worked out solutions to all odd-numbered exercises within the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer.
Study Guide
ISBN: 0495012394 (Single Variable) | ISBN: 0495012270 (Multivariable)
This helpful guide contains a short list of key concepts; a short list of skills to master; a brief introduction to the ideas of the section; an elaboration of the concepts and skills, including extra worked-out examples; and links in the margin to earlier and later material in the text and Study Guide.
Interactive Video Skillbuilder CD-ROM
ISBN: 0495012378
Think of it as portable office hours! The Interactive Video Skillbuilder CD-ROM contains more than eight hours of video instruction with detailed explanations and strategies for approaching key examples from the textbook.
CalcLabs for Maple
ISBN: 0495012351 (Single Variable) | ISBN: 0495012319 (Multivariable)
This comprehensive lab manual will help students learn to effectively use the technology tools available to them. Written specifically to correlate with the popular Maple software, each lab contains clearly explained exercises and a variety of labs and projects to accompany the text.
CalcLabs for Mathematica
ISBN: 0495382450 (Single Variable) | ISBN: 0495118907 (Multivariable)
This comprehensive lab manual will help students learn to effectively use the technology tools available to them. Written specifically to correlate with the popular Mathematica software, each lab contains clearly explained exercises and a variety of labs and projects to accompany the text.
For Instructors
The following resources are available to instructors only upon adoption of the text. (Some restrictions may apply). To request a review copy or for details on policies, please contact your sales representative or Thomson Higher Education Academic Support at 800-423-0563.
Multimedia Manager Instructor's Resource CD-ROM
ISBN: 0495012416
Contains PowerPoint lecture outline, database of all the art in the text, animated versions of key figures from the text, and an electronic copy of the Instructor's Guide and Test Bank.
Instructor's Guide
ISBN: 0495012548
Each section of the main text is discussed from several viewpoints and contains suggested time to allot, points to stress, text discussion topics, core materials for lecture, and workshop/discussion suggestions. The guide includes single variable and multivariable content.
Instructor's Guide for AP® Calculus
ISBN: 0495012238
Taking the perspective of optimizing preparation for the AP exam, each section of the main text is discussed from several viewpoints and contains suggested time to allot, points to stress, text discussion topics, core materials for lecture, workshop/discussion suggestions, group work exercises in a form suitable for handout, tips for the AP exam, and suggested homework problems.
Solution Builder
The online Solution Builder lets instructors easily build and save customized solution sets either for printing or posting on password-protected class websites. Visit www.thomsonedu.com/solutionbuilder to request an account.
Printed Solutions Manual
ISBN: 0495012556 (Single Variable) | ISBN: 0495012297 (Multivariable)
Includes worked-out solutions to all exercises in the text.
Printed Test Bank
ISBN: 0495012211
This printed Test Bank includes multiple-choice and short-answer test items that key directly to the text. (Includes single variable and multivariable content).
ExamView® (Windows/Macintosh CD-ROM)
ISBN: 0495012424
Create, deliver, and customize tests and study guides (both print and online) in minutes with this easy-to-use assessment and tutorial software on CD. Includes complete questions from the Calculus: Early Transcendentals Test Bank.
JoinIn™ (with Installation CD-ROM)
ISBN: 049511894X
Enhance how your students interact with you, your lecture, and each other. Thomson Brooks/Cole is now pleased to offer you book-specific content for Response Systems tailored to Stewart's CALCULUS, allowing you to transform your classroom and assess your students' progress with instant in-class quizzes and polls. Pose book-specific questions and display students' answers seamlessly within the Microsoft® PowerPoint® slides of your own lecture, in conjunction with the "clicker" hardware of your choice. Contact your local Thomson representative to learn more.
Text-Specific Instructor DVDs
ISBN: 0495012432
Text-specific DVD set, available at no charge to adopters. Each DVD features a 10- to 20-minute problem solving lesson for each section of the chapter. Covers both single- and multivariable calculus.|||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.
Click here to Download Adobe Acrobat Reader.
Fourier Series
Formulas for the Remainder Term in Taylor Series
Rotation of Axes |||3||
1079620839|default|News and Announcements|Welcome to the website for my new edition of [i]Calculus: Early Transcendentals[/i]. The website 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 website, or features that we would like to draw your attention to. This area will help you identify what has changed since our last update.
Note: Some of the links - such as "Algebra Review" and "Lies My Calculator and Computer Told Me" - point to Acrobat PDF files. For ease of navigation, these links open in a new browser window. If you can't open these links, please disable your popup blocker for this site.|||1||