NCHU Course Outline

Course Name	(中) 微積分(二)(1232)
	(Eng.) Calculus(II)
Offering Dept	Department of Applied Mathematics
Course Type	Required			Credits	4	Teacher	Jia-Yuan Dai
Department	Department of Applied Mathematics / Undergraduate			Language	Chinese	英文/EMI		Semester	2024-SPRING
Course Description	本課程中文授課，板書英文為主（必要時提供中文翻譯），作業跟考試以英文命題。 我們將學習多變數函數微分與積分的概念與運算，並推廣「微積分基本定理」，亦即 Green 定理、Gauss 定理和 Stokes 定理。微分方面涵蓋極限定義、連續性，微分計算和極值問題。積分方面涵蓋多重積分的定義、計算技巧與應用。此外也探討函數的 Taylor 展開式及其應用。
Prerequisites								self-directed learning in the course	Y

Relevance of Course Objectives and Core Learning Outcomes(%)			Teaching and Assessment Methods for Course Objectives
Course Objectives	Competency Indicators	Ratio(%)	Teaching Methods	Assessment Methods
掌握微積分的重要概念、了解微積分發展的歷史、熟悉微分與積分運算，透過微積分解析各學科的實際問題。另外，本課程將奠定工程數學、微分方程和數學分析等進階課程的基礎。	1.Basic Knowledge in Mathematical Sciences 7.Mathematical and Statistical software skills 8.English Language Ability	80 10 10	Exercises Discussion Practicum Lecturing	Assignment Quiz
Course Content and Homework/Schedule/Tests Schedule
Week Course Content Week 1 Q&A of Calculus; [12.6] Cylinders and Quadric Surfaces Week 2 [14.1] Functions of Several Variables; [14.2] Limits and Continuity; [14.3] Partial Derivatives Week 3 [14.4] Tangent Planes and Linear Approximations; [14.5] The Chain Rule Week 4 [14.6] Directional Derivatives and the Gradient Vector; [14.7] Maximum and Minimum Values Week 5 [14.8] Lagrange Multipliers; [15.1] Double Integrals over Rectangles Week 6 [15.2] Double Integrals over General Regions; [15.3] Double Integrals in Polar Coordinates; [15.5] Surface Area; [15.6] Triple Integrals Week 7 # 4/2, 4/4 Holidays Week 8 [15.7] Triple Integrals in Cylindrical Coordinates; [15.8] Triple Integrals in Spherical Coordinates; [15.9] Change of Variables in Multiple Integrals Week 9 Review; 4/18 Midterm Exam Week 10 [16.1] Vector Fields; [16.2] Line Integrals; [16.3] The Fundamental Theorem for Line Integrals Week 11 [16.4] Green’s Theorem; [16.5] Curl and Divergence; [16.6] Parametric Surfaces and Their Areas Week 12 [16.7] Surface Integrals; [16.9] The Divergence Theorem Week 13 [16.8] Stokes’ Theorem; [16.10] Summary; [11.1] Sequences Week 14 [11.2] Series; [11.3] The Integral Test and Estimates of Sums; [11.4] The Comparison Tests; [11.5] Alternating Series and Absolute Convergence; [11.6] The Ratio and Root Tests; [11.7] Strategy for Testing Series Week 15 [11.8] Power Series; [11.9] Representations of Functions as Power Series Week 16 [11.10] Taylor and Maclaurin Series; [11.11] Applications of Taylor Polynomials Week 17 Review; 6/13 Final Exam Week 18 * Discussion on the Final Exam
Evaluation
作業 30 %、隨堂小考 10 %、期中考 25 %、會考 10 %、期末考 25 %
Textbook & other References
教科書 Calculus, Metric Edition, 9th Edition. (ISBN: 9780357113462) 微積分歷史參考用書 1. 蔡聰明，微積分的歷史步道，三民出版社，2013 2. S. Strogatz，無限的力量，旗標出版社，2020 相關網站 1. 中興大學微積分教學網 http://amath2.nchu.edu.tw/cal/ 2. 線上繪圖 https://www.desmos.com/calculator 3. 線上計算 https://www.wolframalpha.com
Teaching Aids & Teacher's Website
教科書、課程講義（請至 iLearning 3.0 課程網頁下載）
Office Hours
演習課 彭昭融助教 若實體教學　時間：星期四第 2 節　地點：資訊科學大樓 502 若遠距教學　時間：星期四第 2 節　請至 https://meet.google.com/yrd-vmwt-vko _____ Office Hour 戴佳原老師　 若實體教學　時間：星期三 12:10～13:10　地點：資訊科學大樓 302 若遠距教學　時間：星期三 12:10～13:10　請至 https://meet.google.com/iem-ypyf-gwm 許莉敏助教　 若實體教學　時間：星期二 17:10～18:00　地點：資訊科學大樓 406 若遠距教學　時間：星期二 17:10～18:00　請至 https://meet.google.com/tyq-ovsb-tcv 彭昭融助教 若實體教學　時間：星期二 09:10～10:00　地點：資訊科學大樓 406 若遠距教學　時間：星期一 09:10～10:00　請至 https://meet.google.com/yrd-vmwt-vko
Sustainable Development Goals, SDGs(Link URL)
include experience courses：N

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Update Date, year/month/day：2025/02/11 10:46:27	Printed Date, year/month/day：2025 / 5 / 15
The second-hand book website：http://www.myub.com.tw/