Calculus: A Complete Course, 10/e (Hardocver)

本書序言

Besides numerous improvements and clarifications throughout the book and tweakings of existing material, this edition introduces, in Chapter 11, the concept of a metric space and its application to spherical trigonometry (and, of course, navigation on the surface of our spherical planet), and Einstein’s theory of special relativity, the conclusions of which follow from the selection of a particular metric for measuring distance in four-dimensional space-time.

Also new in this edition is the introduction to the methods of the Calculus of Variations in Section 20.4, and an introduction, in Appendix VI, to the opensource programming language, Python, which can replace Maple or Mathematica as a free computer algebra system.

本書特色

MyLabMath is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practise what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts. MyLab can be successfully implemented in any classroom environment - lab-based, hybrid, fully online, or traditional. By addressing instructor and student needs, MyLab improves student learning. 
●Student Engagement and Achievement Students are motivated to succeed when they’re engaged in the learning experience and understand the relevance and power of mathematics. MyLab Math’s online homework offers students immediate feedback and tutorial assistance that motivates them to do more, which means they retain more knowledge and improve their test scores.
●Exercises with immediate feedback are based on the textbook exercises, and regenerate algorithmically to give students unlimited opportunity for practice and mastery. MyLab provides helpful feedback when students enter incorrect answers and includes optional learning aids including Help Me Solve This, View an Example, and the eText.
●Learning Catalytics is a student response tool that uses students’ smartphones, tablets, or laptops to engage them in more interactive tasks and thinking. Learning Catalytics fosters student engagement and peer-to-peer learning with real-time analytics.

本書序言

除了在整本書中進行了許多改進和澄清，以及對現有材料進行了微調，本版還在第11章引入了度量空間的概念，並將其應用於球面三角學（當然還有在球面上的導航），以及愛因斯坦的特殊相對論理論，其結論來自於選擇在四維時空中測量距離的特定度量。

本版還在第20.4節中引入了變分計算方法的介紹，以及在附錄VI中對開源編程語言Python的介紹，它可以作為免費的計算機代數系統替代Maple或Mathematica。

本書特色

MyLabMath是一個在線作業、教程和評估計劃，旨在與本教材配合使用，以吸引學生並提高成績。在結構化的環境中，學生可以練習所學知識，測試他們的理解能力，並追求個性化的學習計劃，幫助他們吸收課程材料並理解困難的概念。MyLab可以成功應用於任何教室環境 - 實驗室、混合式、完全在線或傳統式。通過滿足教師和學生的需求，MyLab提高了學生的學習效果。

● 學生參與和成就：當學生參與學習體驗並理解數學的相關性和力量時，他們會被激勵取得成功。MyLab Math的在線作業提供即時反饋和教學協助，激勵學生進一步學習，這意味著他們能夠保留更多知識並提高考試成績。

● 帶有即時反饋的練習：這些練習基於教科書上的練習，並以算法方式重新生成，為學生提供無限的練習和掌握機會。MyLab在學生輸入錯誤答案時提供有用的反饋，並包括可選的學習輔助工具，包括幫助我解決這個問題、查看示例和電子教材。

● Learning Catalytics：這是一個學生反應工具，使用學生的智能手機、平板電腦或筆記型電腦，讓他們參與更多互動任務和思考。Learning Catalytics通過實時分析促進學生參與和同儕學習。

Chapter P: Preliminaries
Chapter 1: Limits and Continuity
Chapter 2: Differentiation
Chapter 3: Transcendental Functions
Chapter 4: More Applications of Differentiation
Chapter 5: Integration
Chapter 6: Techniques of Integration
Chapter 7: Applications of Integration
Chapter 8: Conics, Parametric Curves, and Polar Curves
Chapter 9: Sequence, Series, and Power Series
Chapter 10: Vectors and Coordinate Geometry in 3-Space
Chapter 11: Arc length, Metric Spaces, and Applications
Chapter 12: Vector Functions and Curves
Chapter 13: Partial Differentiation
Chapter 14: Applications of Partial Derivatives
Chapter 15: Multiple Integration
Chapter 16: Vector Fields
Chapter 17: Vector Calculus
Chapter 18: Differential Forms and Exterior Calculus
Chapter 19: Ordinary Differential Equations
Chapter 20: More Topics in Differential Equations
Appendix 1 Complex Numbers
Appendix 2 Complex Functions
Appendix 3 Continuous Functions
Appendix 4 The Riemann Integral
Appendix 5 Doing Calculus with Maple
Appendix 6 Doing Calculus with Python
Answers to Odd-Numbered Exercises

第 P 章：初步知識
第 1 章：極限與連續性
第 2 章：微分
第 3 章：超越函數
第 4 章：微分的更多應用
第 5 章：積分
第 6 章：積分的技巧
第 7 章：積分的應用
第 8 章：圓錐曲線、參數曲線和極坐標曲線
第 9 章：數列、級數和冪級數
第 10 章：三維空間中的向量和座標幾何
第 11 章：弧長、度量空間和應用
第 12 章：向量函數和曲線
第 13 章：偏微分
第 14 章：偏導數的應用
第 15 章：多重積分
第 16 章：向量場
第 17 章：向量微積分
第 18 章：微分形式和外微積分
第 19 章：常微分方程
第 20 章：微分方程的更多主題
附錄 1：複數
附錄 2：複函數
附錄 3：連續函數
附錄 4：黎曼積分
附錄 5：使用 Maple 進行微積分
附錄 6：使用 Python 進行微積分
奇數編號習題的答案