Essential Calculus: Early Transcendental Functions, 5/e (Metric Version)

Description
Welcome to the International Metric Version of Essential Calculus: Early Transcendental Functions. For this metric version, the units of measurement used in most of the examples and exercises have been changed from U.S. Customary units to metric units. We did not convert problems that are specific to the U.S. Customary units, such as dimensions of a baseball field or U.S. postal rates. We are excited to offer you a new edition with more resources then ever that will help you understand and master calculus. This text includes features and resources that continue to make Essential Calculus: Early Transcendental Functions a valuable learning tool for students and a trustworthy teaching tool for instructors.

Essential Calculus: Early Transcendental Functions provides the clear instruction, precise mathematics, and thorough coverage that you expect for your course.

Features

• NEW Big Ideas of Calculus
  • We have added a new feature to help you discover and understand the Big Ideas of Calculus. This feature has three parts.
  • The Big Ideas of Calculus notes give you an overview of the major concepts of a chapter and how they relate to the earlier concepts you have studied. These notes appear near the beginning of a chapter and in the chapter review.
  • In each section and in the chapter review, make sure you do the Exploring Concepts exercises. These exercises will help you develop a deeper and clearer knowledge of calculus. Work through these exercises to build and strengthen your understanding of the concepts.
  • To continue exploring calculus, do the Building on Concepts exercises at the end of the chapter review. Not only will these exercises help you expand your knowledge and use of calculus, they will prepare you to learn concepts in later chapters.
• UPDATED Exercise Sets
  The exercise sets have been carefully and extensively examined to ensure they are rigorous and relevant and to include topics out users have suggested. The exercises are organized and titled so you can better see the connections better see the connections between examples and exercises. Multi-step, real-life exercises reinforce problem-solving skills and mastery of concepts by giving you the opportunity to apply the concepts in real-life situations.
• Section Objectives
  A bulleted list of learning objectives provides you with the opportunity to preview what will be presented in the upcoming section.
• Theorems
  Theorems provide the conceptual framework for calculus. Theorems are clearly stated and separated from the rest of the text by boxes for quick visual reference. Key proofs often follow the theorem and can be found in appendix A.
• Definitions
  As with theorems, definitions are clearly stated using precise, formal wording and are separated from the text by boxes for quick visual reference.
• Explorations
  Explorations provide unique challenges to study concepts that have not yet been formally covered in the text. They allow you to learn by discovery and introduce topics related to ones presently being studied. Exploring topics in this way encourages you to think outside the box.
• UPDATED Remarks
  These hints and tips reinforce or expand upon concepts, help you learn how to study mathematics, caution you about common errors, address special cases, or show an alternative solution to an example. We have added several new Remarks to help students who need more in-depth algebra support.
• UPDATED Historical Notes and Biographies
  Historical Notes provide you with background information on the foundations of calculus. The Biographies introduce you to the people who created and contributed to calculus. We have added several new biographies.
• Technology
  Throughout the book, technology boxes show you how to use technology to solve problems and explore concepts of calculus. These tips also point out some pitfalls of using technology.
• How Do You See It? Exercise
  The How Do You See It? exercise in each section presents a problem that you will solve by visual inspection using the concepts learned in the lesson.
• UPDATED Applications
  Carefully chosen applied exercises and examples are included throughout to address the question, “When will I use this ?”These applications are pulled from diverse sources, such as current events, world data, industry trends, and more, and relate to a wide range of interests. Understanding where calculus is (or can be) used promotes fuller understanding of the material.
• Putnam Exam Challenges
  Putnam Exam questions appear in selected sections. These actual Putnam Exam questions will challenge you and push the limits of your understanding of calculus.

描述

歡迎使用《基礎微積分：早期超越函數》的國際公制版本。在這個公制版本中，大部分範例和練習中使用的測量單位已從美國慣用單位轉換為公制單位。我們沒有轉換與美國慣用單位特定的問題，例如棒球場的尺寸或美國郵政費率。我們很高興為您提供一個比以往更多資源的新版本，這將幫助您理解和掌握微積分。本書包含的功能和資源仍然使《基礎微積分：早期超越函數》成為學生寶貴的學習工具和教師可靠的教學工具。



《基礎微積分：早期超越函數》提供清晰的指導、精確的數學和全面的涵蓋範圍，符合您的課程期望。

特點

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  全新 微積分的重要概念
  
  
  • 我們新增了一個新功能，以幫助您發現和理解微積分的重要概念。此功能分為三個部分。
  
  
  • 
    微積分的重要概念筆記為您提供章節的主要概念概述，以及它們與您之前學習的概念的關聯。這些筆記出現在章節的開頭和章節回顧中。
  
  
  • 在每個章節和章節回顧中，請務必完成探索概念練習。這些練習將幫助您深入和清晰地了解微積分。通過這些練習來建立和加強對概念的理解。
  
  
  • 為了繼續探索微積分，請在章節回顧的末尾完成基於概念的建構練習。這些練習不僅將幫助您擴展對微積分的知識和應用，還將為您學習後面章節的概念做好準備。
  
  
  
  


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  更新 練習集
  
  練習集經過仔細審查，確保其嚴謹性和相關性，並包含用戶建議的主題。練習按組織和標題進行，以便您更好地看到示例和練習之間的聯繫。多步驟的實際練習通過讓您有機會在實際情況中應用概念，加強解決問題的能力和概念的掌握。


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  章節目標
  
  學習目標的項目清單為您提供預覽即將呈現的內容的機會。


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  定理
  
  定理為微積分提供了概念框架。定理以方框清晰陳述，與其他文本分開，以便快速視覺參考。關鍵證明通常跟隨在定理之後，可以在附錄A中找到。


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  定義
  
  與定理一樣，定義使用精確的正式措辭清晰陳述，並以方框分開，以便快速視覺參考。


• 
  探索
  
  探索提供了研究尚未正式涵蓋的概念的獨特挑戰。它們使您能夠通過發現學習，並引入與目前正在學習的主題相關的主題。以這種方式探索主題鼓勵您跳出框架思考。


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  更新的備註
  
  這些提示和技巧強化或擴展概念，幫助您學習如何學習數學，警告您常見的錯誤，處理特殊情況，或展示一個示例的替代解決方案。我們新增了幾個新的備註，以幫助需要更深入的代數支持的學生。

Table of Contents
1. Limits and Their Properties
2. Differentiation
3. Applications of Differentiation
4. Integration
5. Applications of Integration
6. Integration Techniques and Improper Integrals
7. Infinite Series
8. Parametric Equations, and Polar Coordinates
9. Vectores and the Geometry of Space
10. Vector-Valued Functions
11. Functions of Several Variables
12. Multiple Integration
13. Vector Analysis

Appendix A. Proofs of Selected Theorems (Online)*
Appendix B. Integration Tables
Appendix C. Precalculus Reviews (Online)*
Appendix D. Rotation and the General Second-Degree Equation (Online)*
Appendix E. Complex Numberss (Online)*
Appendix F. Business and Economic Applications (Online)*
Answers to Selected Exercises
Index

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目錄

1. 限制與其性質

2. 微分

3. 微分的應用

4. 積分

5. 積分的應用

6. 積分技巧和不定積分

7. 無窮級數

8. 參數方程和極座標

9. 向量和空間幾何

10. 向量值函數

11. 多變數函數

12. 多重積分

13. 向量分析



附錄 A. 選定定理的證明（線上）*

附錄 B. 積分表

附錄 C. 預備知識回顧（線上）*

附錄 D. 旋轉和一般二次方程（線上）*

附錄 E. 複數（線上）*

附錄 F. 商業和經濟應用（線上）*

選定習題的答案

索引
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