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課程名稱 |
微積分3
CALCULUS (3) |
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開課學期 |
114-2 |
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授課對象 |
生化科技學系 |
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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 |
14 |
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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
星期四8,9,10(15:30~18:20)星期五10,A(17:30~19:15) |
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上課地點 |
新102普102 |
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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.實習課五A.
限本系所學生(含輔系、雙修生)
總人數上限：190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 |
Building upon the foundation laid in MATH4006-7, which focused on Calculus of functions with a single real variable, MATH4008 delves into the principles and applications of multivariable calculus, particularly in the context of 2-variable functions. This course serves as a crucial cornerstone for future courses in quantitative sciences.
Key topics include :
1. Introduction to Curves and Surfaces
2. Partial Derivatives
3. Chain Rule and Directional Derivatives
4. Optimizations in Multivariables
5. Multiple Integrations
Applications of multivariable calculus, including, the meaning of partial derivatives in and the concept of a shadow price in economics, the principle of linear regression will also be discussed in the 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. |
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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) Apply the chain rule to compute derivatives of composed functions in multivariables & directional derivatives
(3) Determine local extrema of a given two-variable function
(4) Use Lagrange multiplier to resolve constrained optimization problems
(5) Compute multiple integrations by Fubini's Theorem and/or change of variables
(6) Understand the geometric meanings of multiple integrations |
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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 |
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參考書目 |
Instructor's lecture notes |
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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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