Continuity and Compactness & Continuity and Connectedness

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Continuity and Compactness & Continuity and Connectedness

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週次	課程內容	課程影音
	第一章 The Real and Complex Number Systems Fields Axioms, Order Axioms(1/2)	線上觀看
	Fields Axioms, Order Axioms(2/2)	線上觀看
	Completeness Axioms	線上觀看
	第二章 Basic Topology Cardinality of Sets	線上觀看
	Metric Spaces(1/2)	線上觀看
	Metric Spaces(2/2)	線上觀看
	Compact Sets	線上觀看
	Connected Sets(1/2)	線上觀看
	Connected Sets(2/2)	線上觀看
	第三章 Numerical Sequences and Series Convergent Sequences	線上觀看
	Cauchy Sequences	線上觀看
	Upper and Lower Limits	線上觀看
	Series of Nonnegative Terms	線上觀看
	The Root and Ratio Test	線上觀看
	Absolute Convergence, Rearrangements(1/2)	線上觀看
	Absolute Convergence, Rearrangements(2/2)	線上觀看
	第四章 Continuity Limits of Functions and Continuous Functions	線上觀看
	Continuity and Compactness & Continuity and Connectedness	線上觀看
	Discontinuities, Infinite Limits and Limits at Infinity	線上觀看
	第五章 Differentiation　 The Derivative of a Real Function, Mean Value Theorem(1/2)	線上觀看
	The Derivative of a Real Function, Mean Value Theorem(2/2)	線上觀看
	L’Hopital’s Rule & Taylor’s Theorem	線上觀看
	第六章 The Riemann-Stieltjes Integral　 Differentiation of Vector-valued Functions & Definition and Existence of the Integral	線上觀看
	Definition and Existence of the Integral	線上觀看
	Properties of the Integral(1/2)	線上觀看
	Properties of the Integral(2/2)	線上觀看
	Integration and Differentiation(1/2)	線上觀看
	Integration and Differentiation(2/2)	線上觀看

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