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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 |
生命科學系 |
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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 |
201 49830 |
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班次 |
19 |
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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(8:10~9:00)星期四8,9,10(15:30~18:20) |
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上課地點 |
新303新303 |
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備註 |
本課程英文授課,使用中文教科書。密集課程。統一教學.實習課另外安排.
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,
- Chain rule and directional derivatives,
- Second derivative test for two-variable functions and the method of Lagrange multipliers,
- Geometry of integrations,
- Double 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. 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:
- Compute partial derivatives and understand their geometric meaning
- Apply the chain rule to compute derivatives of composed functions in multivariables & directional derivatives
- Determine local extrema of a given two-variable function
- Use Lagrange multiplier to resolve constrained optimization problems
- Compute multiple integrations by Fubini's Theorem and/or change of variables
- Apply integrations to resolve problems in geometry |
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課程要求 |
Assumed knowledge :
- MATH4006-7,
- Basic trigonometry, vector geometry,
- Determinants of 2x2 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 |
翁秉仁，微積分乙 |
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參考書目 |
- Instructor's lecture notes,
- James Stewart, Daniel Clegg, and Saleem Watson, Calculus Early Transcendentals, 9th edition. |
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評量方式
(僅供參考) |
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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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多變數函數 1 : 偏微分及應用
Partial derivatives and their applications |
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第2週 |
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多變數函數 2 : 連鎖率及方向導數
Chain rule, Directional derivatives |
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第3週 |
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多變數函數 3 : 二階極值測試, Lagrange multipliers
Second derivative tests and method of Lagrange multipliers |
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第4週 |
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積分的幾何應用
Geometries of Integrals |
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第5週 |
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雙重積分 1 : Fubini 定理和極坐標
Fubini's Theorem and polar coordinates |
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第6週 |
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雙重積分 2 : 變數變換法
Change of variables |
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第7週 |
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Reviews |
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第8週 |
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Exam |
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