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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 |
電機工程學系 |
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授課教師 |
蔡國榮 |
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課號 |
MATH4006 |
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課程識別碼 |
201E49810 |
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班次 |
03 |
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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
星期一10(17:30~18:20)星期三6,7(13:20~15:10)星期五6,7(13:20~15:10) |
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上課地點 |
新203新203新203 |
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備註 |
本課程以英語授課。密集課程。統一教學.一10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：130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 |
This course will be conducted in English.
Calculus was independently founded by Isaac Newton and Gottfried Leibniz to describe and study the change of functions with respect to their variables. This subject has found applications and become fundamental in fields such as physics, chemistry, and engineering. In the first module of this Calculus series (MATH4006-4009), we will introduce differentiation of functions in one real variable.
Specifically, we will define the derivative of a function, derive basic rules and techniques of differentiation, analyze extrema of a function, discuss the statement and applications of the Mean Value Theorem(s), and sketch the graph of a function.
Key definitions are discussed, and important theorems are derived in lectures to help students develop their abilities in logical deduction and analysis. Practical applications of Calculus in various fields are illustrated to promote an organic interaction between the theory of Calculus and students’ own fields of study.
This course also provides TA classes, where students can enhance their proficiency in handling Calculus calculations under the guidance of our teaching assistants.
Provisional Schedule :
Week 1 Functions and Their Limits
Week 2 Continuity
Week 3 Differentiation (I) : Definition and Technique
Week 4 Differentiation (II) : Chain Rule and Implicit
Week 5 Mean Value Theorem and L’Hospital’s Rule
Week 6 Curve Sketching
Week 7 Optimisation Problems
Week 8 Exam Week |
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課程目標 |
Upon completing the course, students are expected to be able to
1. Understand the notion of the limits of a function
2. Use limits to describe properties of a function, including continuity and asymptotic behaviors
3. Define the derivative of a function and determine the differentiability of a function
4. Understand the geometric and physical meanings of differentiation
5. Use chain rule to differentiate composed functions and implicit functions
6. Apply Mean Value Theorem to derive properties of a function from its derivatives
7. Derive and apply the L’Hospital’s rule to compute limits of more sophiscaed functions |
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課程要求 |
Students are expected to be proficient in high school mathematics, including all topics covered in Pre-U/MATH4012 Pre-Calculus.
Before the course begins, students should complete the online Precalculus Self-Diagnostic Test, designed for NTU freshmen.
Students who receive unsatisfactory results on the Diagnostic Test should consider enrolling in MATH4012 Pre-Calculus and consult the instructor for advice as soon as possible. |
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預期每週課前或/與課後學習時數 |
Besides the 4-hour lectures per week, students should expect to spend around 2-3 hours weekly in digesting the lecture materials as well as completing exercises offered by the lecturer or the teaching assistant(s). |
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Office Hours |
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指定閱讀 |
Textbook:
Stewart, Clegg, Watson, CALCULUS: EARLY TRANSCENDENTALS, Metric, 9th Edition.
This course will be supplemented by instructor's lecture notes. |
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參考書目 |
NTUOCW Calculus 1 :
https://ocw.aca.ntu.edu.tw/ntu-ocw/ocw/cou/111S102 |
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評量方式
(僅供參考) |
- 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 |
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考試形式 |
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其他 |
由師生雙方議定 |
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