| 課程概述 | |
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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，和變數變換；並以求實體質量、質心等幾何量作為其應用。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. specifically, 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, as well as applications such as computing the mass and center of mass of a solid. 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. |
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| 課程目標 | |
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修完本課程學生能熟悉微積分工具，並應用在各學科。「微積分1, 2, 3, 4」將奠定學生修讀工程數學、分析、微分方程等進階課程的基礎。
students would be familiar with calculus as a tool and be able to apply it in various subjects after finishing this course. "calculus 1, 2, 3, 4" provide the basis for the study of various advanced courses like engineering mathematics, analysis and differential |
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| 課程要求 | |
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修這門課以前，學生要熟練高中數學。學生應積極參與課堂和習題課的活動與討論。
students participating in the course should be already skilled in high school mathematics. they are expected to attend and participate actively in lectures as well as discussion sessions. |
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| 指定閱讀 | |
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| 參考書目 | |
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其他相關資訊
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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