Applied Calculus (Paperback)

<內容簡介>

Description
Applied Calculus is designed as an introduction to calculus for students in business, economics, and the social sciences. To address the trend of information-based economy and decision making, representation of table-property data in functional form is addressed. We take an informal, intuitive approach to the subject, without sacrificing mathematical integrity. And we aim to balance conceptual understanding with technical skills.

There is a wide range of students’ abilities in the applied calculus course and we have taken steps to address this phenomenon: On the one hand, we know that there are many students with weak algebraic skills and so we provide careful, patient explanations in the exposition and plenty of algebraic steps in the solutions of the examples. And before some of the exercise sets we include warm-up problems called “Prepare Yourself” to practice the skills needed for the exercises that follow. On the other hand, in such a course there are usually some students who are quite mathematically talented and accordingly, not wanting to neglect them, we have placed a collection of problems labeled “Challenge Yourself” at the end of most exercise sets.

Features
The writing style speaks clearly and directly to students, guiding them through key ideas, theorems, and problem-solving steps, and encouraging them to think as they read and learn calculus.
Prepare Yourself exercises are designed to check students' prerequisite skills before they attempt the core exercise set. These exercises acknowledge the variety of math abilities, and show students what they need to work on before they move forward.
Challenge Yourself exercises are more difficult problems intended to elicit students' deeper understanding of key concepts. These exercises are designed to be assigned by instructors who wish to aim at a higher level and keep their more advanced students interested.
Projects are included throughout to motivate students and help them see the relation of calculus to real life and their intended fields of study. They can be worked in class, assigned as group projects, or given as extra credit.
At the beginning of each chapter review section is what we call Concept Check, which is a collection of questions designed to make sure that students know the main concepts of the chapter. The answers to these Concept Check questions are all collected on the back endpapers, thus constituting a review of the entire course.
Table of Contents
0 Precalculus Review
1 Functions and Models
2 The Derivative
3 Techniques of Differentiation
4 Applications of Differentiation
5 Integrals
6 Applications of Integration
7 Functions of Several Variables
8 Trigonometric model
9 Power Series Approximation and Taylor Series
Answers to Odd-Numbered Exercises
Index

<章節目錄>

0 Precalculus Review
1 Functions and Models
2 The Derivative
3 Techniques of Differentiation
4 Applications of Differentiation
5 Integrals
6 Applications of Integration
7 Functions of Several Variables
8 Trigonometric model
9 Power Series Approximation and Taylor Series
Answers to Odd-Numbered Exercises
Index

《應用微積分》是為商業、經濟和社會科學專業的學生設計的微積分入門教材。為了應對信息經濟和決策的趨勢，本書介紹了將表格數據以函數形式表示的方法。我們以非正式、直觀的方式來介紹這個主題，同時保持數學的嚴謹性，並力求平衡概念理解和技術技能。

應用微積分課程中的學生能力差異很大，我們已經采取措施應對這一現象：一方面，我們知道有很多代數能力較弱的學生，因此在教學中提供了仔細、耐心的解釋，並在例題的解答中提供了大量的代數步驟。在一些練習題之前，我們還包括了名為“準備自己”的熱身問題，以練習完成後續練習所需的技能。另一方面，在這樣的課程中通常會有一些數學能力較強的學生，為了不忽視他們，我們在大多數練習題組的末尾放置了一系列標有“挑戰自己”的問題。

本書的特點包括：
- 寫作風格清晰直接，引導學生理解關鍵思想、定理和解題步驟，鼓勵他們在閱讀和學習微積分時思考。
- “準備自己”練習旨在檢查學生在進行核心練習之前的先備技能。這些練習承認了數學能力的多樣性，並向學生展示他們在進一步學習之前需要努力提高的方面。
- “挑戰自己”練習是更難的問題，旨在引發學生對關鍵概念的更深入理解。這些練習適合希望達到更高水平並保持對進階學生的興趣的教師分配。
- 整本書中都包含了一些項目，以激勵學生並幫助他們看到微積分與現實生活和他們的預期學習領域的關聯。這些項目可以在課堂上進行，分配為小組項目，或作為額外學分。
- 每章復習部分的開頭是我們稱之為“概念檢查”的問題集，旨在確保學生掌握了該章節的主要概念。這些概念檢查問題的答案都收錄在封底，從而構成了整個課程的復習。
- 目錄：
0 預備微積分回顧
1 函數與模型
2 導數
3 微分技巧
4 微分應用
5 積分
6 積分應用
7 多變量函數
8 三角模型
9 幂級數近似和泰勒級數
奇數練習題答案
索引

請注意，本書的內容簡介和特點是根據原文進行翻譯，並可能有所刪減或修改以符合翻譯需求。