課程名稱 |
微積分3 CALCULUS (3) |
開課學期 |
112-2 |
授課對象 |
電機工程學系 |
授課教師 |
蔡國榮 |
課號 |
MATH4008 |
課程識別碼 |
201E49830 |
班次 |
03 |
學分 |
2.0 |
全/半年 |
半年 |
必/選修 |
必修 |
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) |
上課地點 |
普101普101普101 |
備註 |
本課程以英語授課。密集課程。統一教學.一10為實習課.週末考試. 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 |
課程大綱
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課程概述 |
Building upon the foundation laid in MATH4006-7, which focused on Calculus of functions with a single real variable, Multivariable Calculus (MATH4008-9) delves into the principles and applications of multivariable calculus, particularly in the context of 2- and 3-variable functions. This course serves as a crucial cornerstone for various disciplines in Science and Engineering.
Key topics include
1. Partial Derivatives
2. Continuous and Differentiable Functions in Multivariables
3. Chain Rule and Directional Derivatives:
4. Second Derivative Test and Lagrange Multipliers
5. Double and Triple Integrations
6. Curvilinear Coordinates
In this course, definitions are thoroughly discussed, and key theorems are derived during lectures to foster logical deduction and analytical skills among students. Practical applications of calculus are highlighted to establish a meaningful connection between theoretical concepts and their relevance to various scientific and engineering fields. To enhance students' proficiency in calculus, TA classes are incorporated into the course. Here, students have the opportunity to refine their calculation skills under the guidance of experienced teaching assistants. These sessions aim to reinforce theoretical concepts and provide practical insights into problem-solving techniques. |
課程目標 |
On successful completion of this module students should be able to:
(1) Compute partial derivatives and understand their geometric meaning
(2) Determine whether a multivariable function is continuous and/or differentiable
(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 multiple integrations by Fubini's Theorem and/or change of variables
(7) Understand the geometric and physical meanings of multiple integrations |
課程要求 |
Assumed knowledge :
- MATH4006-7,
- Basic trigonometry, vector geometry,
- Determinants of 2x2 and 3x3 matrices (knowledge in linear algebra will be useful but not necessary) |
預期每週課後學習時數 |
After each week of lectures, you are expected to
- revise examples from the lectures,
- complete relevant sections on WeBWorK,
- complete weekly assessed/non-assessed assignment. |
Office Hours |
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指定閱讀 |
Stewart, Clegg, Watson, CALCULUS: EARLY TRANSCENDENTALS, Metric, 9th Edition
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參考書目 |
Instructor's lecture notes
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評量方式 (僅供參考) |
No. |
項目 |
百分比 |
說明 |
1. |
Exam |
50% |
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2. |
Quizzes |
20% |
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3. |
Assessment |
30% |
WeBWorK, Homework, Worksheet and others |
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針對學生困難提供學生調整方式 |
上課形式 |
提供學生彈性出席課程方式 |
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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