托马斯微积分 Thomas' Calculus (15th Edition, Global Edition)英文版2024


Joel Hass, Christopher Heil, Przemyslaw Bogacki, Maurice Weir
Thomas' Calculus
Early Transcendentals, SI Units

15th edition
Publication year: 2023
Print-ISBN: 978-1-292-72590-1
E-ISBN: 978-1-292-45762-8
Pages: 1.224
Language: English




作者: George B·Thomas Jr， Maurice D·Weir ， Joel R·Hass   
出版社: Pearson



50多年来，该书平均每4至5年就有一个新版面世（中文最新第10版，英文最新第15版），每版较之先前版本都有不少改进之处，体现了这是一部锐意革新的教材；与此同时，该书的一些基本特色始终注意保持且有所增强，说明它又是一部重视继承传统的教材。与我国现行通用高等数学教材相比，其基本内容和结构框架有着许多近似之处，但在题材选取和处理上又有更多不同特色，尤其是，突出应用和数学建模，重视数值计算和程序应用。在适时引进现代数学和新学科知识等方面，更有不少精彩之处。

Abstract            
For 3-semester or 4-quarter courses in Calculus for students majoring in mathematics, engineering, or science.Clarity and precisionThomas' Calculus: Early Transcendentals goes beyond memorizing formulas and routine procedures to help students develop deeper understanding. It guides students to a level of mathematical proficiency and maturity needed for the course, with support for those who require it through its balance of clear and intuitive explanations, current applications and generalized concepts. The 15th Edition meets the needs of students with increasingly varied levels of readiness for the calculus sequence. This revision also adds exercises, revises figures and narrative for clarity, and updates many applications with modern topics.Hallmark features of this titleKey topics are presented both informally and formally.Results are carefully stated and proved throughout, and proofs are clearly explained and motivated.Strong exercise sets feature a wide range from skills problems to applied and theoretical problems.Writing exercises ask students to explore and explain various concepts and applications. A list of questions at the end of each chapter asks them to review and summarize what they have learned.Technology exercises in each section ask students to use the calculator or computer when solving the problems. Computer Explorations offer exercises requiring a computer algebra system such as Maple or Mathematica.Annotations within examples guide students through the problem solution and emphasize that each step in a mathematical argument is justified.New and updated features of this title Many narrative clarifications and revisions have been made throughout the text.A new appendix on Determinants and Gradient Descent has been added, covering many topics relevant to students interested in Machine Learning and Neural Networks.Many updated graphics and figures have been enhanced to bring out clear visualization and mathematical correctness.Many exercise instructions have been clarified, such as suggesting where the use of a calculator may be needed.Notation of inverse trig functions has been changed throughout the text to favor arcsin notation over sin^{-1}, etc.


摘要

适用于数学、工程或科学专业学生的三学期或四季度微积分课程。清晰精准

托马斯的《微积分：早期先验函数》超越了死记硬背公式和常规程序，帮助学生加深理解。它引导学生达到课程所需的数学熟练程度和成熟度，并通过清晰直观的解释、当前应用和广义概念之间的平衡，为有需要的学生提供支持。

第15版满足了学生对微积分学习准备程度日益多样化的需求。本次修订还增加了练习，修改了图表和叙述以提高清晰度，并用现代主题更新了许多应用。

本书的标志性特点是：关键主题以非正式和正式两种形式呈现。结果贯穿始终，经过仔细的陈述和论证，证明过程清晰明了，并有清晰的解释和说明。丰富的练习集涵盖了从技能问题到应用和理论问题的广泛内容。写作练习要求学生探索和解释各种概念和应用。每章末尾的问题列表要求学生复习和总结所学知识。每个部分的技术练习都要求学生使用计算器或计算机解决问题。计算机探索提供需要计算机代数系统（如 Maple 或 Mathematica）的练习。示例中的注释指导学生解决问题，并强调数学论证中的每一步都是合理的。本书的新增和更新功能对全文进行了许多叙述澄清和修订。增加了关于行列式和梯度下降的新附录，涵盖了许多与对机器学习和神经网络感兴趣的学生相关的主题。许多更新的图形和数字得到了增强，以实现清晰的可视化和数学正确性。许多练习说明已经澄清，例如建议在何处可能需要使用计算器。反三角函数的符号在全文中进行了更改，现在更倾向于使用反正弦符号而不是 sin^{-1} 等。


内容包括：
0.预备知识；1.极限和连续；2.导数；3.导数的应用；4.积分；5.积分的应用；6.超越函数和微分方程；7.积分方法、洛必达法则和反常积分。