Thomas' Calculus: Early Transcendentals - 14th Edition - 突破理解障碍的数学之旅

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"Thomas' Calculus Early Transcendentals - 14th Edition 是一本由Thomas、Hass和Heil合著的微积分教科书，旨在帮助学生掌握数学的熟练度和成熟度，同时为需要额外支持的学生提供帮助。本版在保留Thomas经典内容的同时，对每一句话和每一张图表进行了更新，以适应现代学生的学习需求，促进学生对核心概念的概括理解，而非仅仅停留在记忆公式和程序化的运算上。" 在《Thomas' Calculus Early Transcendentals》第14版中，作者们强调了平衡清晰的解释、当前的应用以及概念的普遍化。这一版的新合著者Christopher Heil（来自佐治亚理工学院）与Joel Hass合作，致力于提供一个超越传统教学模式的教材，帮助学生不仅仅是掌握计算技巧，而是深化对微积分基本概念的理解。书中的"Early Transcendentals"部分通常指的是在大学一年级或二年级初期接触的超越函数，这些函数包括指数函数、对数函数、三角函数等，它们在微积分中起着关键作用。这部分内容会涉及导数、积分等基本概念的引入，是学生从初等数学过渡到高等数学的重要桥梁。 MyMathLab是一个全球领先的在线数学学习平台，它将在线作业、支持资源、评估和教程集成在一个灵活易用的格式中。这个平台可以帮助学生在学习微积分前先巩固基础知识，掌握微积分本身，并可视化概念。通过MyMathLab，教师可以识别学生在先修知识上的不足，并提供个性化的帮助，确保他们在学习新内容时做好准备。此外，MyMathLab提供了数百个视频教程，涵盖了教材中的关键概念，对于翻转课堂或错过课程的学生尤其有帮助。这些视频教程通过直观的教学方式，帮助学生更好地理解和掌握微积分的核心思想。互动图形是教材的另一大亮点，它们生动地展示了关键概念，允许学生进行操作，以作为教学和学习工具。这种互动性促进了主动学习和批判性思维的发展，使学生能够通过实践来探索和理解微积分原理。《Thomas' Calculus Early Transcendentals》第14版是一本结合了传统教学精华和现代技术的微积分教科书，旨在通过全面的支持和创新的教学方法，帮助学生深入理解微积分的本质，而不仅仅停留在表面的计算技能上。MyMathLab等在线资源则提供了丰富的辅助学习工具，帮助学生克服学习难点，提升学习效果。

Preface xiii

Continuing Features

Rigor The level of rigor is consistent with that of earlier editions. We continue to distin-

guish between formal and informal discussions and to point out their differences. Starting

with a more intuitive, less formal approach helps students understand a new or difficult

concept so they can then appreciate its full mathematical precision and outcomes. We pay

attention to defining ideas carefully and to proving theorems appropriate for calculus stu-

dents, while mentioning deeper or subtler issues they would study in a more advanced

course. Our organization and distinctions between informal and formal discussions give

the instructor a degree of flexibility in the amount and depth of coverage of the various

topics. For example, while we do not prove the Intermediate Value Theorem or the Ex-

treme Value Theorem for continuous functions on a closed finite interval, we do state these

theorems precisely, illustrate their meanings in numerous examples, and use them to prove

other important results. Furthermore, for those instructors who desire greater depth of cov-

erage, in Appendix 6 we discuss the reliance of these theorems on the completeness of the

real numbers.

Writing Exercises Writing exercises placed throughout the text ask students to explore

and explain a variety of calculus concepts and applications. In addition, the end of each

chapter contains a list of questions for students to review and summarize what they have

learned. Many of these exercises make good writing assignments.

End-of-Chapter Reviews and Projects In addition to problems appearing after each

section, each chapter culminates with review questions, practice exercises covering the

entire chapter, and a series of Additional and Advanced Exercises with more challenging

or synthesizing problems. Most chapters also include descriptions of several Technology

Application Projects that can be worked by individual students or groups of students over

a longer period of time. These projects require the use of Mathematica or Maple, along

with pre-made files that are available for download within MyMathLab.

Writing and Applications This text continues to be easy to read, conversational, and

mathematically rich. Each new topic is motivated by clear, easy-to-understand examples

and is then reinforced by its application to real-world problems of immediate interest to

students. A hallmark of this book has been the application of calculus to science and engi-

neering. These applied problems have been updated, improved, and extended continually

over the last several editions.

Technology In a course using the text, technology can be incorporated according to the

taste of the instructor. Each section contains exercises requiring the use of technology;

these are marked with a

if suitable for calculator or computer use, or they are labeled

Computer Explorations if a computer algebra system (CAS, such as Maple or Math-

ematica) is required.

Additional Resources

MyMathLab

Online Course (access code required)

Built around Pearson’s best-selling content, MyMathLab is an online homework, tutorial,

and assessment program designed to work with this text to engage students and improve

results. MyMathLab can be successfully implemented in any classroom environment—

lab-based, hybrid, fully online, or traditional.

A01_HASS9020_14_SE_FM_i-xviii.indd 13 17/10/16 2:44 PM

xvi Preface

•

Instructional videos—hundreds of videos are available as learning aids within exer-

cises and for self-study. The Guide to Video-Based Assignments makes it easy to as-

sign videos for homework by showing which MyMathLab exercises correspond to each

video.

•

The complete eText is available to students through their MyMathLab courses for the

lifetime of the edition, giving students unlimited access to the eText within any course

using that edition of the text.

•

Enhanced Sample Assignments These assignments include just-in-time prerequisite

review, help keep skills fresh with distributed practice of key concepts, and provide oppor-

tunities to work exercises without learning aids so students can check their understanding.

•

PowerPoint Presentations that cover each section of the book are available for down-

load.

•

Mathematica manual and projects, Maple manual and projects, TI Graphing Cal-

culator manual—These manuals cover Maple 17, Mathematica 8, and the TI-84 Plus

and TI-89, respectively. Each provides detailed guidance for integrating the software

package or graphing calculator throughout the course, including syntax and commands.

•

Accessibility and achievement go hand in hand. MyMathLab is compatible with

the JAWS screen reader, and it enables students to read and interact with multiple-

choice and free-response problem types via keyboard controls and math notation input.

MyMathLab also works with screen enlargers, including ZoomText, MAGic, and

SuperNova. And, all MyMathLab videos have closed-captioning. More information is

available at http://mymathlab.com/accessibility.

•

A comprehensive gradebook with enhanced reporting functionality allows you to

efficiently manage your course.

•

The Reporting Dashboard oers insight as you view, analyze, and report learning

outcomes. Student performance data is presented at the class, section, and program

levels in an accessible, visual manner so you’ll have the information you need to

keep your students on track.

•

Item Analysis tracks class-wide understanding of particular exercises so you can

reﬁne your class lectures or adjust the course/department syllabus. Just-in-time

teaching has never been easier!

MyMathLab comes from an experienced partner with educational expertise and an eye

on the future. Whether you are just getting started with MyMathLab, or have a question

along the way, we’re here to help you learn about our technologies and how to incorporate

them into your course. To learn more about how MyMathLab helps students succeed, visit

www.mymathlab.com or contact your Pearson rep.

A01_HASS9020_14_SE_FM_i-xviii.indd 16 17/10/16 2:44 PM

Preface xvii

Instructor’s Solutions Manual (downloadable)

ISBN: 0-13-443932-5 | 978-0-13-443932-7

The Instructor’s Solutions Manual contains complete worked-out solutions to all the ex-

ercises in Thomas’ Calculus: Early Transcendentals. It can be downloaded from within

MyMathLab or the Pearson Instructor Resource Center, www.pearsonhighered.com/irc.

Just-In-Time Algebra and Trigonometry for Early

Transcendentals Calculus, Fourth Edition

ISBN 0-321-67103-1 | 978-0-321-67103-5

Sharp algebra and trigonometry skills are critical to mastering calculus, and Just-in-Time

Algebra and Trigonometry for Early Transcendentals Calculus by Guntram Mueller and

Ronald I. Brent is designed to bolster these skills while students study calculus. As stu-

dents make their way through calculus, this brief supplementary text is with them every

step of the way, showing them the necessary algebra or trigonometry topics and pointing

out potential problem spots. The easy-to-use table of contents has topics arranged in the

order in which students will need them as they study calculus. This supplement is avail-

able in printed form only (note that MyMathLab contains a separate diagnostic and reme-

diation system for gaps in algebra and trigonometry skills).

Technology Manuals and Projects (downloadable)

Maple Manual and Projects by Marie Vanisko, Carroll College

Mathematica Manual and Projects by Marie Vanisko, Carroll College

TI-Graphing Calculator Manual by Elaine McDonald-Newman, Sonoma State University

These manuals and projects cover Maple 17, Mathematica 9, and the TI-84 Plus and TI-

89. Each manual provides detailed guidance for integrating a specific software package or

graphing calculator throughout the course, including syntax and commands. The projects

include instructions and ready-made application files for Maple and Mathematica. These

materials are available to download within MyMathLab.

TestGen

ISBN: 0-13-443936-8 | 978-0-13-443936-5

TestGen

(www.pearsoned.com/testgen) enables instructors to build, edit, print, and ad-

minister tests using a computerized bank of questions developed to cover all the objectives

of the text. TestGen is algorithmically based, allowing instructors to create multiple but

equivalent versions of the same question or test with the click of a button. Instructors can

also modify test bank questions or add new questions. The software and test bank are avail-

able for download from Pearson Education’s online catalog, www.pearsonhighered.com.

PowerPoint

Lecture Slides

ISBN: 0-13-443943-0 | 978-0-13-443943-3

These classroom presentation slides were created for the Thomas’ Calculus series. Key

graphics from the book are included to help bring the concepts alive in the classroom.

These files are available to qualified instructors through the Pearson Instructor Resource

Center, www.pearsonhighered.com/irc, and within MyMathLab.

Student’s Solutions Manual

Single Variable Calculus (Chapters 1–11), ISBN: 0-13-443933-3 | 978-0-13-443933-4

Multivariable Calculus (Chapters 10–16), ISBN: 0-13-443916-3 | 978-0-13-443916-7

The Student’s Solutions Manual contains worked-out solutions to all the odd-numbered

exercises in Thomas’ Calculus: Early Transcendentals. These manuals are available in

print and can be downloaded from within MyMathLab.

A01_HASS9020_14_SE_FM_i-xviii.indd 17 17/10/16 2:44 PM

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