課程名稱 |
微積分3 CALCULUS (3) |
開課學期 |
110-2 |
授課對象 |
生命科學系 |
授課教師 |
傅斯緯 |
課號 |
MATH4008 |
課程識別碼 |
201 49830 |
班次 |
19 |
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 星期二1(8:10~9:00)星期四8,9,10(15:30~18:20) |
上課地點 |
新203新203 |
備註 |
本課程英文授課,使用中文教科書。密集課程。英文授課.統一教學.實習課另安排. 限本系所學生(含輔系、雙修生) 總人數上限:140人 |
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1102MATH4008_19 |
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 |
這是一門半學期的課程,主要介紹多變數函數的微積分運算,和其豐富的應用。微分主題包含多變數函數的極限,偏微分,方向導數,切平面,線性逼近,和微分連鎖律;並討論求函數極值,Lagrange乘子法等應用問題。積分部分涵蓋多重積分與逐次積分的定義,Fubini定理,和多重積分的變數變換等等。除此之外,我們將簡介指數成長/遞減模型,牛頓冷卻律,與 logistic 模型,示範各領域如何利用「數學模型」掌握關鍵規律,並解釋這些微分方程式的求解技巧。
課堂上將講解定義並推導重要定理,以培養學生邏輯推理與分析能力;同時會示範微積分在各領域的應用,幫助學生將微積分與其他專業科目結合。本課程還設有習題課,學生將在助教的帶領下熟練微積分的計算。
Calculus of multivariable functions together with its profound applications are introduced in this half-semester course. Especially, topics about differentiation include limits, partial derivatives, directional derivatives, tangent planes, linear approximations, and the chain rule. Also, applications such as finding extreme values and methods of Lagrange multipliers are discussed. Topics about integration involve definitions of multiple integrals and iterated integrals, Fubini’s theorem, change of variables and more. In addition to these, exponential growth/ decay models, Newton’s law of cooling, and Logistic models are introduced as examples of how mathematical models describe various types of phenomena. Then techniques of solving separable differential equations and first order linear differential equations are presented.
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 sessions in which students are able to make their skills in handling calculations in Calculus more proficient under the guidance of our teaching assistants. |
課程目標 |
修完本課程學生能熟悉微積分工具,並應用在各學科。
Students would be familiar with Calculus as a tool and be able to apply it in various subjects after finishing this course.
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課程要求 |
學生應熟練高中數學,並完成為台大新生預備的線上「微積分學前自我檢測」。
學生應出席並積極參與課堂與習題課的討論。
Before taking this course, students should be already skilled in high school mathematics and finish the online Precalculus Self Diagnostic Test which is designed for NTU freshmen.
Students are expected to attend and participate actively in lectures as well as discussion sessions.
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
翁秉仁,微積分乙
Paul's Online Notes: https://tutorial.math.lamar.edu |
參考書目 |
微積分統一教學網站: http://www.math.ntu.edu.tw/~calc/Default.html
台大微積分考古題: http://www.math.ntu.edu.tw/~calc/cl_n_34455.html
數學知識網站: http://episte.math.ntu.edu.tw/cgi/mathfield.pl?fld=cal
免費線上數學繪圖軟體Desmos Calculator: https://www.desmos.com/calculator
免費知識型計算引擎: https://www.wolframalpha.com
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評量方式 (僅供參考) |
No. |
項目 |
百分比 |
說明 |
1. |
期考 |
40% |
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2. |
小考 |
35% |
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3. |
作業 |
25% |
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週次 |
日期 |
單元主題 |
第1週 |
2/15,2/17 |
5.1多變數函數 Functions of Several Variables
5.2多變數函數的微分 Partial Derivatives |
第2週 |
2/22,2/24 |
5.3多變數函數之連鎖法則 Chain Rule for Multivariable Functions
5.4方向導數與梯度 Directional Derivatives and Gradient Vectors |
第3週 |
3/01,3/03 |
5.5.1高階偏導數 Partial Derivatives of Higher Orders
5.6極值測試與應用 Tests for Extrema and Applications
3/1(二) Quiz 1 (範圍:5.1 ~ 5.3) |
第4週 |
3/08,3/10 |
5.7 Lagrange乘子法 Lagrange Multipliers
6.1二重積分 Double Integrals |
第5週 |
3/15,3/17 |
6.2 Fubini定理 Fubini's Theorem
6.3二重積分的極坐標形式Double Integrals in Polar Coordinates
3/15(二) Quiz 2 (範圍:5.4 ~ 5.7) |
第6週 |
3/22,3/24 |
6.4二重積分之變數變換 Change of Variables for Double Integrals
7.1使用指數函數的模型 Modeling with Exponential Functions |
第7週 |
3/29,3/31 |
7.2一階微分方程 First Order Differential Equations
3/29(二) Quiz 3 (範圍:6.1 ~ 6.4) |
第8週 |
4/05,4/07 |
4/7(四) 期考 範圍:5.1 ~7.2 |
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