Essential Calculus: Early Transcendental, Metric Version (Custom Solutions), 2/e (Paperback)

本書序言

• More than 20% of the exercises are new:
   Basic exercises have been added, where appropriate, near the beginning of exercise sets. These exercises are intended to build student confidence and reinforce understanding of the fundamental concepts of a section.
Some new exercises include graphs intended to encourage students to understand how a graph facilitates the solution of a problem; these exercises complement subsequent exercises in which students need to supply their own graph.
   Some exercises have been structured in two stages, where part (a) asks for the setup and part (b) is the evaluation. This allows students to check their answer to part (a) before completing the problem.
   Some challenging and extended exercises have been added toward the end of selected exercise sets.
   Titles have been added to selected exercises when the exercise extends a concept discussed in the section.
• New examples have been added, and additional steps have been added to the solutions of some existing examples.
• Several sections have been restructured and new subheads added to focus the organization around key concepts.
• Many new graphs and illustrations have been added, and existing ones updated, to provide additional graphical insights into key concepts.
• A few new topics have been added and others expanded (within a section or in extended exercises) that were requested by reviewers.
• New projects have been added and some existing projects have been updated.
• Derivatives of logarithmic functions and inverse trigonometric functions are now covered in one section (3.6) that emphasizes the concept of the derivative of an inverse function.
• Alternating series and absolute convergence are now covered in one section (10.5). 

本書特色

• Conceptual Exercises
The most important way to foster conceptual understanding is through the problems that the instructor assigns. To that end we have included various types of problems. Some exercise sets begin with requests to explain the meanings of the basic concepts of the section and most exercise sets contain exercises designed to reinforce basic understanding. Other exercises test conceptual understanding through graphs or tables.
   Many exercises provide a graph to aid in visualization. Another type of exercise uses verbal descriptions to gauge conceptual understanding.
   We particularly value problems that combine and compare graphical, numerical, and algebraic approaches.
• Graded Exercise Sets
Each exercise set is carefully graded, progressing from basic conceptual exercises, to skill-development and graphical exercises, and then to more challenging exercises that often extend the concepts of the section, draw on concepts from previous sections, or involve applications or proofs.
• Real-World Data
Real-world data provide a tangible way to introduce, motivate, or illustrate the concepts of calculus. As a result, many of the examples and exercises deal with functions defined by such numerical data or graphs. These real-world data have been obtained by contacting companies and government agencies as well as researching on the Internet and in libraries.
• Projects
One way of involving students and making them active learners is to have them work (perhaps in groups) on extended projects that give a feeling of substantial accomplishment when completed.
   Applied Projects involve applications that are designed to appeal to the imagination of students.
   Discovery Projects anticipate results to be discussed later or encourage discovery through pattern recognition. Other discovery projects explore aspects of geometry: tetrahedra, hyperspheres, and intersections of three cylinders.

本書序言

- 超過20%的練習題是新的：
- 適當的章節中新增了基礎練習題，旨在建立學生的信心，並加強對該章節基本概念的理解。
- 一些新的練習題包含圖表，旨在鼓勵學生理解圖表如何幫助解決問題；這些練習題與後續需要學生自己繪製圖表的練習題相輔相成。
- 一些練習題分為兩個階段，其中(a)部分要求設定問題，(b)部分則是評估答案。這使得學生可以在完成問題之前檢查(a)部分的答案。
- 在選定的練習題組末尾新增了一些具有挑戰性和延伸性的練習題。
- 在某些練習題中，當練習題延伸了該章節中討論的概念時，為選定的練習題新增了標題。
- 新增了新的例子，並在一些現有例子的解決方案中增加了額外的步驟。
- 重新結構了幾個章節，並新增了新的小標題，以便將組織重點放在關鍵概念上。
- 新增了許多新的圖表和插圖，並更新了現有的圖表和插圖，以提供對關鍵概念的額外圖形洞察。
- 根據審稿人的要求，新增了一些新的主題，並擴展了其他主題（在章節內或在延伸練習中）。
- 新增了新的專案，並更新了一些現有專案。
- 對數函數的導數和反三角函數的導數現在在一個強調反函數導數概念的章節（3.6）中進行了涵蓋。
- 交替級數和絕對收斂現在在一個章節（10.5）中進行了涵蓋。

本書特色

- 概念練習題：
- 通過教師分配的問題來培養概念理解是最重要的方法。為此，我們包含了各種類型的問題。一些練習題組以要求解釋該章節基本概念的含義開始，大多數練習題組包含旨在加強基本理解的練習題。其他練習題通過圖表或表格測試概念理解。
- 許多練習題提供圖表以幫助視覺化。另一種類型的練習題使用口述描述來評估概念理解。
- 我們特別重視結合和比較圖形、數值和代數方法的問題。
- 分級練習題組：
- 每個練習題組都經過精心分級，從基礎概念練習題，到技能發展和圖形練習題，再到更具挑戰性的練習題，這些練習題通常擴展了該章節的概念，借鑒了前面章節的概念，或涉及應用或證明。
- 真實世界數據：
- 真實世界數據提供了一種具體的方式來介紹、激發或說明微積分的概念。因此，許多例子和練習題涉及由數值數據或圖表定義的函數。這些真實世界數據是通過聯繫公司和政府機構，以及在互聯網和圖書館進行研究獲得的。
- 專案：
- 讓學生參與並成為積極學習者的一種方式是讓他們（也許是小組）參與延伸專案，完成時給予他們實質成就感。
- 應用專案涉及設計能激發學生想像力的應用。
- 探索專案預測稍後討論的結果，或通過模式識別鼓勵探索。

JAMES STEWART was professor of mathematics at McMaster University and the University of Toronto for many years. James did graduate studies at Stanford University and the University of Toronto, and subsequently did research at the University of London. His research field was Harmonic Analysis and he also studied the connections between mathematics and music.

DANIEL CLEGG is professor of mathematics at Palomar College in Southern California. He did undergraduate studies at California State University, Fullerton and graduate studies at the University of California, Los Angeles (UCLA). Daniel is a consummate teacher; he has been teaching mathematics ever since he was a graduate student at UCLA.

SALEEM WATSON is professor emeritus of mathematics at California State University, Long Beach. He did undergraduate studies at Andrews University in Michigan and graduate studies at Dalhousie University and McMaster University. After completing a research fellowship at the University of Warsaw, he taught for several years at Penn State before joining the mathematics department at California State University, Long Beach.

JAMES STEWART 是麥克馬斯特大學和多倫多大學的數學教授，任教多年。James 在斯坦福大學和多倫多大學進行研究生學習，隨後在倫敦大學進行研究。他的研究領域是和諧分析，並且他也研究數學和音樂之間的聯繫。

DANIEL CLEGG 是加州南部帕洛瑪學院的數學教授。他在加州州立大學富勒頓分校進行本科學習，並在加州大學洛杉磯分校（UCLA）進行研究生學習。Daniel 是一位出色的教師；自從他在UCLA攻讀研究生以來，他一直在教授數學。

SALEEM WATSON 是加州長灘市加州州立大學的數學名譽教授。他在密歇根州安德魯斯大學進行本科學習，並在達爾豪西大學和麥克馬斯特大學進行研究生學習。在華沙大學完成研究研究員職位後，他在賓夕法尼亞州立大學教授了幾年，然後加入了加州長灘市加州州立大學的數學系。

I. Functions and Models 
2. Limits and Derivatives 
3. Differentiation Rules 
4. Applications of Differentiation 
5. Integrals 
6. Applications ofIntegration 
7. Techniques of Integration 
8. Further Applications of Integration 
9. Parametric Equations and Polar Coordinates 
10. Sequences, Series, and Power Series 
11. Vectors and the Geometry of Space 
12. Partial Derivatives 
13. Multiple Integrals

I. 函數與模型
2. 極限與導數
3. 微分規則
4. 微分應用
5. 積分
6. 積分應用
7. 積分技巧
8. 積分的進一步應用
9. 參數方程與極坐標
10. 數列、級數和冪級數
11. 向量與空間幾何
12. 偏導數
13. 多重積分