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Implicit Differentiation.

The material on derivatives, including their definition as a function and basic differentiation formulas.

It is about two-thirds the size of the author's other calculus books.

The area problem and the distance problem.

Stokes’ Theorem.

Integrals that have infinite limits or integrands that approach infinity.

Four diagnostic tests in Basic Algebra, Analytic Geometry, Functions, and Trigonometry.

It indicates problems that require the full resources of a computer algebra system.

Pre-calculus reviews, homework hints, additional examples, challenge problems, and more.

Vectors, dot and cross products, vector-valued functions, and Kepler's laws.

Providing customized learning solutions.

Using specific formulas that relate polar coordinates to area and length.

Reviewer from Auburn University.

Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

Liz Covello.

Users should visit www.cengage.com/highered to search by ISBN#, author, title, or keyword.

Vector Fields.

A function whose derivative is the given function.

Jim Propp and Steve Ott.

It is essential for success in calculus.

Editorial review has deemed that any suppressed content does not materially affect the overall learning experience.

Some third-party content may be suppressed due to electronic rights.

Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

Check answers against the provided answers and refresh skills if necessary.

The right to remove additional content at any time if subsequent rights restrictions require it.

Functions and Their Representations.

Basic Differentiation Formulas.

Line Integrals.

Completely worked-out solutions to all odd-numbered exercises in the text.

Continuity is essential for the existence of limits and derivatives.

To offer complete worked-out solutions to all exercises in the text and allow instructors to create customized, secure solution printouts.

The ability to create, deliver, and customize tests in print and online formats, including hundreds of multiple-choice, numerical response, and short answer test items.

Cylindrical and spherical coordinates.

Some third-party content may be suppressed due to electronic rights.

Fourier Series, Linear Differential Equations, Complex Numbers, and History of Mathematics.

Three-Dimensional Coordinate Systems, Vectors, The Dot Product, The Cross Product, Equations of Lines and Planes, Cylinders and Quadric Surfaces, Vector Functions and Space Curves, Arc Length and Curvature, Motion in Space: Velocity and Acceleration.

The Chain Rule.

To compute the derivative of a function with respect to one variable while considering the dependence on other variables.

Suggested time to allot, points to stress, text discussion topics, core materials for lecture, work-show/discussion suggestions, group work exercises, and suggested homework assignments.

Parametric Surfaces and Their Areas.

Surface Integrals.

A technique used to integrate products of functions.

Section 7.5 (Area of a Surface of Revolution).

Prior written permission from the publisher.

To find the area of surfaces generated by revolving curves.

Applications to Physics and Engineering.

To guide students toward a solution without giving the answer directly.

Functions and limits, including limits of trigonometric functions and limits involving infinity.

To diagnose weaknesses in algebra, analytic geometry, functions, and trigonometry.

It does not materially affect the overall learning experience.

A self-study tool for students that includes interactive learning, study, and exam preparation tools.

Double Integrals over Rectangles, Double Integrals over General Regions, Double Integrals in Polar Coordinates, Applications of Double Integrals, Triple Integrals, Triple Integrals in Cylindrical Coordinates, Triple Integrals in Spherical Coordinates, Change of Variables in Multiple Integrals.

Green’s Theorem.

Curl and Divergence.

The Mean Value Theorem.

Condensing exposition, eliminating chapter opening spreads and photographs, and reducing examples and exercises.

To serve as a powerful tool for instructors and a tutorial environment for students to explore and review selected topics.

It encourages you to try solving the problem yourself, enhancing understanding.

It applies inverse functions to optimize seating choices in a theater.

978-1-133-11229-7.

Online at www.cengage.com/permissions.

It investigates series and their convergence properties.

Graphics to elucidate concepts like graphs, contour maps, and gradients.

To represent functions as infinite sums of terms calculated from the values of their derivatives.

Algebra, analytic geometry, functions, and trigonometry.

Some third-party content may be suppressed due to electronic rights.

No, it may not be copied, scanned, or duplicated, in whole or in part.

To provide additional practice and enhance problem-solving skills.

Functions of Several Variables, Limits and Continuity, Partial Derivatives, Tangent Planes and Linear Approximations, The Chain Rule, Directional Derivatives and the Gradient Vector, Maximum and Minimum Values, Lagrange Multipliers.

Maximum and Minimum Values.

To simplify the process of finding integrals by changing variables.

Emphasizes conceptual understanding.

Woven throughout the book instead of being treated in separate chapters.

Areas Between Curves.

On the website www.stewartcalculus.com.

It relates to the flow of a vector field through a surface.

A process where the quantity increases at a rate proportional to its current value.

About 40%.

Data in examples and exercises have been updated to be more timely.

Sequences are ordered lists of numbers, and series are the sums of sequences.

That it is not only useful but also intrinsically beautiful.

Melvin Lax.

It may not be copied, scanned, or duplicated, in whole or in part.

It came from the desire expressed by numerous instructors.

Review of Algebra, Trigonometry, Analytic Geometry, Homework Hints, Additional Examples, and more.

The Limit of a Function.

To establish a relationship between derivatives and the behavior of functions.

An essential tool for exploring, visualizing, and solving complex mathematical problems.

All art from the text in jpeg and PowerPoint formats, pre-built PowerPoint lectures, an electronic version of the Instructor’s Guide, Solution Builder, ExamView algorithmic testing software, Tools for Enriching Calculus, and video instruction.

To provide a concise resource for a three-semester calculus course for scientists and engineers.

It applies concepts of derivatives to improve roller coaster design.

All content is © Cengage Learning.

As an integral, with the exponential function as its inverse.

A homework system that allows instructors to deliver, collect, and record assignments via the Web, along with opportunities for students to review prerequisite skills.

Write in a connected, step-by-step fashion with explanatory sentences.

To discover and analyze patterns in various integral functions.

It applies integration techniques to analyze economic inequality.

Animations in Tools for Enriching Calculus (TEC) accessible in Enhanced WebAssign, CourseMate, and PowerLecture.

The Integral and Comparison Tests.

Curves defined by a set of equations that express the coordinates as functions of a variable.

Central New Mexico Community College.

It has deemed that any suppressed content does not materially affect the overall learning experience.

Fundamental Theorem for line integrals, Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem.

Remove additional content if subsequent rights restrictions require it.

This is an electronic version of the print textbook.

An interactive eBook, Tools for Enriching Calculus, videos, quizzes, flashcards, and more.

The relationship between differentiation and integration.

To find the maximum and minimum values of a function subject to constraints.

Algebra and problem-solving skills of students taking a calculus course.

The logarithm to the base e, where e is approximately 2.71828.

Read and understand a section before attempting exercises, and have pencil, paper, and a calculator ready.

Liz Covello.

Projects, principles of problem solving, and a collection of challenging problems for each chapter.

To enable students to divide a quantity into small pieces and recognize the limit as an integral.

Convergence tests, Taylor series, and their applications to physics.

To explore the relationship between functions and their derivatives.

It explores geometric properties using vectors.

Infinite series of the form Σa_n(x-c)^n.

Finding successively better approximations to the roots (or zeroes) of a real-valued function.

It relates to the evaluation of line integrals.

To help students learn to use technology tools available to them through exercises and labs.

Functions that reverse the effect of the original function.

To provide an introduction to and review of the basic ideas of linear algebra.

It explores applications of differentiation in understanding rainbows.

Volumes by Cylindrical Shells.

Standard methods, computer algebra systems, numerical methods, and improper integrals.

It is an interactive and customizable eBook that allows instructors to modify the textbook narrative, reorder sections, and add media assets.

To evaluate limits of indeterminate forms.

Parametric and polar curves, along with their calculus applications.

Derive.

It applies partial derivatives to optimize rocket design.

Students taking Engineering and Physics courses concurrently with calculus.

Isaac Newton and Gottfried Wilhelm Leibniz.

Arc Length.

They offer different coverage and organization of topics, such as earlier coverage of exponential and logarithmic functions.

Maintaining conceptual understanding and technology integration.

2011942870.

It serves as a useful reference for future courses and applications in science or engineering.

To explore the concept of volume in higher dimensions using multiple integrals.