● 課程說明(Course Desc<x>ription)
<br>討論函數的連續、可微及積分性質
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<br>● 指定用書(Text Books)
<br>William Wade, 
<br>An Introduction to Analysis (4th Edition).
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<br>● 參考書籍(References)
<br>William Wade, 
<br>An Introduction to Analysis (4th Edition).
<br>
<br>● 教學方式(Teaching Method)
<br>板書
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<br>● 教學進度(Syllabus)
<br>單元主題	內容綱要	上課週數
<br>Sequences in R 
<br>(a) Completeness axiom. 1 weeks
<br>(b) Limits of sequences. 1 weeks.
<br>(c) Limit theorems. 1 week.
<br>(d) Bolzano-Weierstrass Theorem. 1 week.
<br>(e) Cauchy sequences. 1 week.
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<br>Continuity on R 
<br>(a) Two-sided limits. 0.5 week.
<br>(b) One-sided limits. 0.5 week.
<br>(c) Continuity. 1 week.
<br>(d) Uniform continuity	1 week.
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<br>Differentiability on R  
<br>(a) The derivative. 1 week.
<br>(b) Differentiability theorems. 1 week. 
<br>(c) Mean-value theorem and Taylor's formula. 1 week. 
<br>(d) Local extrema and second derivative test.	1 week. 
<br>
<br>Integrability on R 
<br>(a) Riemann integrals. 1 week.
<br>(b) Fundamental theorem of Calculus. 1 week.
<br>(c) Improper integrals.	1 week.
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<br>Infinite series of functions R	
<br>(a) Uniform convergence of series. 1 week.
<br>(b) Power series. 1 week.
<br>(c) Analytic functions.	1 week.
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<br>● 成績考核(Evaluation)
<br>期中考兩次 (25%+25%)
<br>期末考 (25%)
<br>小考 (25%)