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數學
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10602高等微積分二

2017-09-01-2018-01-01

國立清華大學 數學系 高淑蓉

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

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

前往課程 View Course
http://ocw.nthu.edu.tw/ocw/index.php?page=course&cid=225&
https://www.youtube.com/watch?v=q9xlvcqjUN0&list=PLS0SUwlYe8cyEot6ADGGvmdATRhz8iFKC