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課程名稱 |
微積分1
CALCULUS (1) |
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開課學期 |
114-1 |
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授課對象 |
機械工程學系 |
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授課教師 |
陳子安 |
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課號 |
MATH4006 |
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課程識別碼 |
201 49810 |
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班次 |
05 |
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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
星期三8,9,10(15:30~18:20)星期五1,2(8:10~10:00) |
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上課地點 |
共301共301 |
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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.三10為實習課.初選將直接帶入此班次的微積分2.加退選階段請自行加選微積分2.
限本系所學生(含輔系、雙修生)
總人數上限：180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 |
微積分1 (Calculus 1)
這是一門半學期的課程，主要介紹單變數函數的微分運算，和微分在各領域豐富的應用。內容涵蓋極限與連續的定義，微分技巧，畫函數圖形，和極值問題等。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微積分的計算並完成學習單。
Differentiation on functions of a single variable together with its profound applications in various subject areas are introduced in this half-semester course. Especially, this course includes the definitions of limits and continuity, techniques of differentiation, curve sketching, strategies in solving extreme-value problem and more.
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 in Calculus and complete small projects under the guidance of our teaching assistants. |
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課程目標 |
學生修習本課程後，應具備以下能力：
1. 理解函數極限 (limit) 的定義，並能計算函數的極限值。
2. 能以極限探討函數性質，包括連續性與漸近行為。
3. 能正確定義函數之導數 (derivative)，說明微分之幾何與物理意涵，並判斷函數的可微性。
4. 能計算函數的微分，熟練運用鏈鎖法則 (chain rule) 處理合成函數、隱函數與反函數之微分。
5. 能利用微分求出函數的局部或全域的極值 (local or global extreme values)。
6. 能應用均值定理 (Mean Value Theorem) 推導出函數的性質，包含遞增、遞減、凹凸性。
7. 能運用羅必達法則 (L’Hôpital’s Rule) 計算較複雜函數之極限。
Upon completing the course, students are expected to be able to
1. Understand the notion of the limits of a function and compute them.
2. Use limits to describe properties of a function, including continuity and asymptotic behaviors.
3. Define the derivative of a function, understand its geometric and physical meanings, and determine the differentiability of a function.
4. Use chain rule to differentiate composed functions, implicit functions and inverse functions.
5. Employ differentiation to determine the local and global extreme values of functions.
6. Apply Mean Value Theorem to derive properties of a function from its derivatives such as monotonicity and concavity.
7. Apply the L’Hôspital’s rule to compute limits of more sophisticated functions.
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課程要求 |
學生應熟練高中數學，並完成為台大新生預備的線上「微積分學前自我檢測」https://cool.ntu.edu.tw/courses/50879。
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 skilled in high school mathematics and finish the online Precalculus Self Diagnostic Test https://cool.ntu.edu.tw/courses/50879 which is designed for NTU freshmen.
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 |
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Office Hours |
每週五 13:00~15:00
每週三 13:00~15:00
每週一 15:20~17:20
每週一 13:00~15:00
每週一 15:20~17:20
每週二 14:00~16:00 備註： 1.陳子安教授，地點：天數459
2.薛鴻立，地點：天數536，在外面敲門即可。
3.何朗軒，地點：天數103
4.魏志宇，地點：天數405
5.許承瀚，地點：天數455(r14246002@ntu.edu.tw)
6.劉孝德，地點：化工一館307(r13524120@ntu.edu.tw)
7.吳孟峰，地點：電二132(b12901066@ntu.edu.tw) |
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指定閱讀 |
待補 |
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參考書目 |
Textbook: James Stewart, Daniel Clegg, and Saleem Watson, Calculus Early Transcendentals, 9th edition, Metric Version.
ISBN: 978-626-7533-06-2
其他相關資訊 Other useful websites
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. |
期考 |
50% |
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2. |
小考 |
20% |
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3. |
學習單 |
12% |
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4. |
WeBWorK |
8% |
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5. |
手寫作業及其他 |
10% |
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- 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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週次 |
日期 |
單元主題 |
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第1週 |
9/03,9/05 |
2.1 The Tangent and Velocity Problems
2.2 The Limit of a Function
2.3 Calculating Limits Using the Limit Laws
[Tutorial: Worksheet 1 (Inverse Trigonometric Functions)] |
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第2週 |
9/10,9/12 |
2.5 Continuity
2.6 Limits at Infinity; Horizontal Asymptotes
2.7 Derivatives and Rates of Change
[Tutorial: Worksheet 2 (The Precise Definition of a Limit)] |
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第3週 |
9/17,9/19 |
2.8 The Derivative as a Function
3.1 Derivatives of Polynomials and Exponential Functions
3.2 The Product and Quotient Rules
3.3 Derivatives of Trigonometric Functions |
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第4週 |
9/24,9/26 |
3.4 The Chain Rule
3.5 Implicit Differentiation
3.6 Derivatives of Logarithmic and Inverse Trigonometric Functions
3.10 Linear Approximations and Differentials
[9/24 (Wed) 17:30-18:20 Quiz 1 (2.1 - 3.2、WS1)] |
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第5週 |
10/01,10/03 |
4.1 Maximum and Minimum Values
4.2 The Mean Value Theorem
4.3 What Derivatives Tell Us about the Shape of a Graph
[Tutorial: Worksheet 3 (Related Rates)] |
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第6週 |
10/08 |
4.4 Indeterminate Forms and l'Hospital's Rule
4.5 Summary of Curve Sketching |
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第7週 |
10/15,10/17 |
4.7 Optimization Problems
4.9 Antiderivatives (*)
[10/15(Wed) 17:30-18:20 Quiz 2 (3.3 - 4.4)] |
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第9週 |
10/29,10/31 |
[11/1(Sat) 09:00-11:30 Exam] |
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