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課程名稱 |
微積分3
CALCULUS (3) |
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開課學期 |
111-2 |
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授課對象 |
資訊管理學系 |
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授課教師 |
蔡國榮 |
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課號 |
MATH4008 |
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課程識別碼 |
201E49830 |
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班次 |
04 |
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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4.加退選階段請自行加選微積分4.
限本系所學生(含輔系、雙修生)
總人數上限：120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.
Having discussed Calculus on functions of a single (real) variable in MATH4006-7, this course turns to an introduction (and applications) of multivariable (mainly 2- and 3-variable) Calculus, which is the foundation for various disciplines in Science and Engineering.
Topics to be discussed include :
- Partial derivatives,
- Continuous and differentiable functions in multivariables,
- Chain rule and directional derivatives,
- Second derivative test for two-variable functions and the method of Lagrange multipliers,
- Double and triple integrations.
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 sections in which students are able to make their skills in handling calculations in Calculus more proficient under the guidance of our teaching assistants. |
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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 |
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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) |
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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. |
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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) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Final Exam |
50% |
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2. |
Quizzes |
20% |
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3. |
Assessment |
30% |
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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 |
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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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週次 |
日期 |
單元主題 |
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第1週 |
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Scalar Fields I : Limits and continuity
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第2週 |
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Scalar Fields II : Derivatives and chain rule
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第3週 |
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Optimizations in multi-variables
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第4週 |
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Double integrals I : Definitions and Fubini's theorem
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第5週 |
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Double integrals II : Change of coordinates and Jacobians
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第6週 |
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Applications of double integrals, Introduction to triple integrals
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第7週 |
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Triple integrals : Cylindrical and spherical coordinates
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第8週 |
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Reviews and Exam |
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