NCHU Course Outline

Course Name	(中) 微積分(二)(1219)
	(Eng.) Calculus(II)
Offering Dept	Department of Applied Mathematics
Course Type	Required	Credits	3	Teacher	Jia-Yuan Dai
Department	Bachelor Program in Electrical Engineering and Computer Science/Undergraduate	Language	Chinese	Semester	2023-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。此外也提供課程影片探討函數的 Taylor 展開式及其應用。
Prerequisites				self-directed learning in the course	N

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.	100	Exercises Discussion Practicum Lecturing	Assignment Quiz
Course Content and Homework/Schedule/Tests Schedule
Week Course Content Week 1 Q&A of Calculus; [10.1] Curves Defined by Parametric Equations [10.2] Calculus with Parametric Curves Week 2 [10.3] Polar Coordinates; [10.4] Calculus in Polar Coordinates; [13.1] Vector Functions and Space Curves Week 3 [13.2] Derivatives and Integrals of Vector Functions; [12.6] Cylinders and Quadric Surfaces Supplementary [11.1] Sequences; [11.2] Series Week 4 [14.1] Functions of Several Variables; [14.2] Limits and Continuity; [14.3] Partial Derivatives Week 5 [14.4] Tangent Planes and Linear Approximations; [14.5] The Chain Rule Week 6 [14.6] Directional Derivatives and the Gradient Vector; [14.7] Maximum and Minimum Values Supplementary [11.3] The Integral Test and Estimates of Sums; [11.4] The Comparison Test; [11.5] Alternating Series and Absolute Convergence Week 7 [14.8] Lagrange Multipliers Week 8 Holiday Week 9 Midterm Exam (in English): 09:10～12:00 Week 10 [15.1] Double Integrals over Rectangles; [15.2] Double Integrals over General Regions; [15.3] Double Integrals in Polar Coordinates Week 11 [15.5] Surface Area; [15.6] Triple Integrals Supplementary [11.6] The Ratio and Root Tests; [11.7] Strategy for Testing Series; [11.8] Power Series Week 12 [15.7] Triple Integrals in Cylindrical Coordinates; [15.8] Triple Integrals in Spherical Coordinates; [15.9] Change of Variables in Multiple Integrals Week 13 [16.1] Vector Fields; [16.2] Line Integrals; [16.3] The Fundamental Theorem for Line Integrals Week 14 [16.4] Green’s Theorem; [16.5] Curl and Divergence; [16.6] Parametric Surfaces and Their Areas Supplementary [11.9] Representations of Functions as Power Series; [11.10] Taylor and Maclaurin Series; [11.11] Applications of Taylor Polynomials Week 15 [16.7] Surface Integrals; [16.9] The Divergence Theorem Week 16 [16.8] Stokes’ Theorem; [16.10] Summary Week 17 Final Exam (in English): 09:10～12:00 Week 18 Discussion on the final exam
Evaluation
作業 30 %、期中考 30 %、會考 10 %、期末考 30 %
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 莊立勝助教　 若實體教學　時間：星期三第 1 節　地點：綜合教學大樓 211 教室 若遠距教學　時間：星期三第 1 節　請至 https://meet.google.com/qkw-yrey-xht Office Hour 戴佳原老師　 若實體教學　時間：星期二 1210～1310　地點：資訊科學大樓 512 若遠距教學　時間：星期二 1210～1310　請至 https://meet.google.com/iem-ypyf-gwm 莊立勝助教　 若實體教學　時間：星期五 16:00~17:00　地點：資訊科學大樓 406 若遠距教學　時間：星期五 16:00~17:00　請至 https://meet.google.com/qkw-yrey-xht
Sustainable Development Goals, SDGs
include experience courses：N

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Update Date, year/month/day：2023/04/05 20:14:36	Printed Date, year/month/day：2024 / 9 / 07
The second-hand book website：http://www.myub.com.tw/