國立中興大學教學大綱
課程名稱 (中) 微積分(二)(1250)
(Eng.) Calculus(II)
開課單位 應數系
課程類別 必修 學分 3 授課教師 簡郁紘
選課單位 電機系 / 學士班 授課使用語言 中文 英文/EMI 開課學期 1132
課程簡述 Calculus is a science that studies the phenomena of change. Its primary content includes differentiation, integration, and computations and applications. Calculus is a branch of mathematics that explores the concept of limits, with two specific definitions: differentiation and integration. The course will cover the concepts of limits, differentiation, and integration, along with their applications. For students outside of science departments, learning calculus is not about becoming a mathematician but rather about utilizing it to support their studies in other professional fields, such as engineering or business management. For business majors, mastering calculus paves the way for further studies in probability theory, statistics, economics, managerial mathematics, compound interest mathematics, and investment and financial management. For engineering or agricultural majors, mastering calculus is essential for further studying in engineering mathematics, statistics, operational research, algorithms, and programming. This highlights the importance of learning calculus. In summary, calculus is a crucial computational science that can enhance your abilities in analytical reasoning and precise calculation—skills fundamental for building a solid foundation for pursuing more advanced knowledge.
Mathematics is the foundation of all sciences, and calculus is a cornerstone of analytical mathematics. Whether undergraduate or graduate students are majoring in science, engineering, business, agriculture, or medicine, mastering calculus is essential for advancing to higher-level courses. Moreover, in today's world, where every industry is globalized, in addition to having foreign language skills and information technology, individuals can train their logical reasoning skills by learning calculus.
先修課程名稱
課程含自主學習 Y
課程與核心能力關聯配比(%) 課程目標之教學方法與評量方法
課程目標 核心能力 配比(%) 教學方法 評量方法
本課程以極限的觀念為基礎,建立微分與積分的運算並以之探討實函數之局部性質與整體行徑。本課程教學目標是引導學生由淺入深地瞭解微積分的基本概念,課程中將討論各種函數及其性質,並介紹極限 (limit) 的概念,進而引導出連續( continuity)、微分 (differentiation) 等觀念,同時經由微積分的基本概念及應用方法的介紹,使同學熟悉經濟學、管理學或工程等相關學科中常使用之數學工具,並經由數學之演算過程,培養學生邏輯分析之能力,進而使在微積分所學的技能可以有效的應用在日後相關課程的學習上。
討論
講授
出席狀況
作業
測驗
授課內容(單元名稱與內容、習作/每週授課、考試進度-共18週)
週次 授課內容
第1週 7.1 Integration by Parts; 7.2 Trigonometric Integrals; 7.3 Trigonometric Substitution
第2週 7.4 Integration of Rational Functions by Partial Fractions; 7.5 Strategy for Integration
第3週 7.6 Integration Using Tables and Technology; 7.7 Approximate Integration; 7.8 Improper Integrals
第4週 8.1 Arc Length; 8.2 Area of a Surface of Revolution
第5週 11.1 Sequences; 11.2 Series
第6週 11.3 The Integral Test and Estimates of Sums; 11.4 The Comparison Tests
第7週 11.5 Alternating Series and Absolute Convergence; 11.6 The Ratio and Root Tests
第8週 11.7 Strategy for Testing Series; 11.8 Power Series
第9週 11.9 Representations of Functions as Power Series; 11.10 Taylor and Maclaurin Series
第10週 11.10 Taylor and Maclaurin Series; 11.11 Applications of Taylor Polynomials
第11週 14.1 Functions of Several Variables; 14.2 Limits and Continuity
第12週 14.3 Partial Derivatives; 14.4 Tangent Planes and Linear Approximates
第13週 14.5 The Chain Rule; 14.6 Directional Derivatives and the Gradient Vector
第14週 14.7 Maximum and Minimum Values; 14.8 Lagrange Multipliers
第15週 15.1 Double Integrals over Rectangles; 15.2 Double Integrals over General Regions
第16週 15.3 Double Integrals in Polar Coordinates; 15.4 Applications of Double Integrals
第17週 15.5 Surface Area; 15.6 Triple Integrals
第18週 15.7 Triple Integrals in Cylindrical Coordinates; 15.8 Triple Integrals in Spherical Coordinates; 15.9 Change of Variables in Multiple Integrals
學習評量方式
各章節單元考試 (60%) + 6/12(星期四18:10)期末微積分A組統一考試 (40%)
教科書&參考書目(書名、作者、書局、代理商、說明)
CALCULUS Metric Version (9E) James Stewart, Daniel Clegg, Saleem Watson 2021年 9版 (滄海書局代理)
課程教材(教師個人網址請列在本校內之網址)

課程輔導時間

聯合國全球永續發展目標(連結網址)
提供體驗課程:N
請尊重智慧財產權及性別平等意識,不得非法影印他人著作。
更新日期 西元年/月/日:2025/01/24 12:37:07 列印日期 西元年/月/日:2025 / 3 / 12
MyTB教科書訂購平台:http://www.mytb.com.tw/