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層級課程資料
媒體類型影音課程
講義課程
標題高等微積分二
授課教師國立清華大學 高淑蓉
授課日期2017-09(起) 2018-01(迄)
關鍵字Advanced Calculus II
Conditions for differentiability
Taylor's theorem and Higher derivatives
Implicit function Theorem
The innor product spaces
Constrained Extrema and Lagrange Multiplier
Completeness and Convergence thm
學習型式課程
分類號與分類名稱310 數學
摘要【課程簡述】
Brief course description
本課程以訓練嚴謹的邏輯推導、撰寫明確的證明、流利的口語表達為手段,追求如何思考、如何有效的學習為目標。
This course is based on teaching you how to think logically, how to prove clearly and
express yourself fluency.Also,how to think and how to learn effectively and the goals of this course.



【課程說明】
Course Description
本課程以訓練嚴謹的邏輯推導、撰寫明確的證明、流利的口語表達為手段,追求如何思考、如何有效的學習為目標。本課程內容探討歐幾里德空間的多變數函數之解析理論。本學期將介紹以下題材:
This course is based on teaching you how to think logically, how to prove clearly and
express yourself fluency.Also,how to think and how to learn effectively and the goals of this course.The content of this course includes the analysis of the multivariable functions in Euclidean space. The following topics are introduced in this semester:


1. Differentiable Mappings
2. The Inverse and Implicit Function Theorems and Related Topics
3. Integration
4. Fubini's Theorem and The Change of Variables Formula
5. Fourier Analysis



【指定用書】
Text Books

J. E. Marsden and M. J. Hoffman, Elementary Classical Analysis, second edition.



【參考書籍】
References
* D. Widder, Advanced Calculus.
* T. Apostal, Advanced Calculus.



【教學方式/教學進度】
Teaching Method/Syllabus
黑板授課/循序漸進
Teaching with Blackboard / Step by step

網址http://ocw.nthu.edu.tw/ocw/index.php?page=course&cid=225&

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