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課程名稱 |
微積分3
CALCULUS (3) |
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開課學期 |
114-2 |
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授課對象 |
地理環境資源學系 |
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授課教師 |
蔡雅如 |
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課號 |
MATH4008 |
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課程識別碼 |
201 49830 |
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班次 |
11 |
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學分 |
2.0 |
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全/半年 |
半年 |
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必/選修 |
必修 |
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上課時間 |
第1,2,3,4,5,6,7,8 週
星期二1,2(8:10~10:00)星期四3,4,10(10:20~18:20) |
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上課地點 |
共201共201 |
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備註 |
本課程中文授課,使用英文教科書。密集課程。統一教學.四10為實習課.
限本系所學生(含輔系、雙修生)
總人數上限：174人 |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
這是一門半學期的課程，主要介紹多變數函數的微積分運算，和其在各領域豐富的應用。
微分主題包含多變數函數的偏微分、切平面、線性逼近、方向導數，和連鎖律；並討論求函數極值，Lagrange乘子法等應用問題。 積分部分涵蓋多重積分與逐次積分的定義，Fubini定理，和變數變換；並探究機率如何使用重積分。課堂上將講解定義並推導重要定理，以培養學生邏輯推理與分析能力；同時會示範微積分在各領域的應用，幫助學生將微積分與其他專業科目結合。本課程還設有習題課，學生將在助教的帶領下熟練計算並探索微積分的應用。
Calculus of multivariable functions together with its profound applications in various subject areas are introduced in this half-semester course. Especially, topics about differentiation include partial derivatives, tangent planes, linear approximations, directional derivatives, and the chain rule. Also, applications such as finding extreme values and methods of Lagrange multipliers are discussed. Topics about integration involve definitions of multiple integrals and iterated integrals, Fubini’s theorem, change of variables, and how multiple integrals are used in probability.
Definitions are discussed and the most important theorems are derived in the lectures with a view to help students to develop their abilities in logical deduction and analysis. Practical applications of Calculus in various fields are illustrated in order to promote a more organic interaction between the theory of Calculus and students' own fields of study. This course also provides discussion sessions in which students are able to improve their skills in handling calculations and explore applications of Calculus under the guidance of teaching assistants. |
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課程目標 |
學生修習本課程後，應具備下列能力：
1. 使用參數方程描述平面或空間中的曲線，並通過微分和積分計算曲線的幾何量
2. 計算偏導數並理解其幾何意義
3. 應用 chain rule 計算多變數組合函數的導數及方向導數
4. 判斷給定的二變數函數的局部極值
5. 使用 Lagrange multipliers解決受限優化問題
6. 通過Fubini定理和/或變數代換計算二重積分，並理解二重積分的幾何意義
Upon completing this course, students are expected to be able to :
1. describe curves in plane or space using parametric equations and compute geometric quantities of curves by using differentiation and integration
2. compute partial derivatives and understand their geometric meaning
3. apply the chain rule to compute derivatives of composed functions in multivariables & directional derivatives
4. determine local extrema of a given two-variable function
5. use Lagrange multiplier to resolve constrained optimization problems
6. compute double integrals by Fubini's Theorem and/or change of variables, understand the geometric meanings of double integrals |
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課程要求 |
學生應熟練微積分1、2的內容。
學生應出席並積極參與課堂與習題課的討論。
Before taking this course, students should be already familiar with concepts and techniques in Calculus 1 and Calculus 2.
Students are expected to attend and participate actively in lectures as well as discussion sessions. |
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預期每週課前或/與課後學習時數 |
為了達到最好的學習效果，鼓勵同學每周花 8 小時課後時間，依序完成以下任務
Step 1. 理解、整理並背下課堂中介紹的定義、定理與公式
Step 2. 複習課堂上的重要例題
Step 3. 寫 WeBWorK作業、紙本作業、學習單
Step 4. 回顧寫作業中遇到的瓶頸，如果有不完全理解的內容，盡快尋求助教和老師的協助。
強烈鼓勵同學參加 office hours 和助教習題課。
To ensure maximum engagement and the highest learning outcomes, students are advised to
allocate a minimum of 8 hours per week to independent study after class to the following tasks :
1. Assimilate and organize the course materials, including the definitions, theorems, and
formulae introduced during lectures.
2. Review and reproduce the examples and problem-solving methodologies demonstrated by
the instructor or teaching assistants.
3. Ensure the timely and thorough completion of all assigned work, including WeBWorK
exercises, written homework, and Worksheets.
4. Reflect critically on any challenging areas or ambiguities encountered. Proactively pinpoint
concepts needing clarification and immediately seek guidance from the instructor or teaching
assistants. Students are strongly encouraged to utilize all designated office hours and support
sessions. |
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Office Hours |
每週二 13:30~15:30 |
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指定閱讀 |
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參考書目 |
Textbook: James Stewart, Daniel Clegg, and Saleem Watson,
Calculus Early Transcendentals, 9th edition.
其他相關資訊
微積分統一教學網站: http://www.math.ntu.edu.tw/~calc/Default.html
台大微積分考古題: http://www.math.ntu.edu.tw/~calc/cl_n_34455.html
數學知識網站: http://episte.math.ntu.edu.tw/cgi/mathfield.pl?fld=cal
免費線上數學繪圖軟體Desmos Calculator: https://www.desmos.com/calculator
免費知識型計算引擎: https://www.wolframalpha.com |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Assessment |
30% |
1. Weekly WeBWorK assignments :http://webwork.math.ntu.edu.tw/webwork2/114_Calculus3_10_13/
2. Weekly written homework
3. 3 worksheets
不接受遲交作業，請留意各個作業的繳交期限。 |
2. |
Quizzes |
20% |
1. Quiz 1: 3/12 (Section 11.9, 11.10, 10.1-10.2, 12.6, 14.1, 14.3)
2. Quiz 2: 4/2 (Section 14.4 - 14.8、15.1 - 15.2) |
3. |
Final Exam |
50% |
4/18 or 4/19 |
- 本校尚無訂定 A+ 比例上限。
- 本校採用等第制評定成績，學生成績評量辦法中的百分制分數區間與單科成績對照表僅供參考，授課教師可依等第定義調整分數區間。詳見學習評量專區 (連結)。
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針對學生困難提供學生調整方式 |
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上課形式 |
以錄影輔助 |
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作業繳交方式 |
延長作業繳交期限 |
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考試形式 |
延後期末考試日期(時間) |
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其他 |
由師生雙方議定 |
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