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자연과학 >수학ㆍ물리ㆍ천문ㆍ지리 >수학
강의학기

2016년 1학기

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8,393
평점

0/5.0 (2)

강의계획서

Real and complex number system, basic topology, sequence, series, continuity, differentiation, and Riemann-Stieltjes integral.

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The real number system

차시별 강의

1.	The real number system	We introduce the concept of least upper bound property and identify the least upper bound for various subsets of the set real numbers.
2.	The real number system	mathematical induction
3.	Equivalents of the least upper bound property	We study important properties of the real number system deduced from the least upper bound property such as Archimedian property.
4.	Equivalents of the least upper bound property	Least upper bound property of Real number
5.	Countable and uncountable sets	We introduce the concept of countability and uncountability of various sets.
6.	Sequences of real numbers	We study the metric structure of the real number system and define convergence of sequences. Further, we compute the limits of various sequences.
7.	Convergent sequences	We study the metric structure of the real number system and define convergence of sequences. Further, we compute the limits of various sequences.
8.	Convergent sequences	We study the metric structure of the real number system and define convergence of sequences. Further, we compute the limits of various sequences.
9.	Monotone sequences	We prove the monotone convergence theorem and derive the nested interval property from it.
10.	Sequences and Bolzano-Weierstrass theorem	We introduce the concept of limit points and prove Bolzano-Weierstrass theorem.
11.	Limit points	We introduce the concept of limit points and prove Bolzano-Weierstrass theorem.
12.	Limit points	We introduce the concept of limit points and prove Bolzano-Weierstrass theorem.
13.	Sequences limits	We introduce the concept of limit points and prove Bolzano-Weierstrass theorem.
14.	Sequences limits	We introduce the concept of limit points and prove Bolzano-Weierstrass theorem.
15.	Cauchy sequences	We define Cauchy sequences and learn how Cauchy sequences are related to the least upper bound property.
	Cauchy sequences	Series of real number
	Open and closed sets	We introduce the concept of open sets and closed sets, and use this to define the connectedness of subsets of the real line.
	Open and closed sets Compact sets	We introduce the concept of open sets and closed sets, and use this to define the connectedness of subsets of the real line. We define compactness
	Compact sets	We define compactness and derive some of the basic facts regarding compact sets.
	Compact sets	We define compactness and derive some of the basic facts regarding compact sets.
	Limits of functions	We describe what are the limits of functions and provide sequential criterion for limits of functions.
	Continuity	We define continuity of functions and derive the intermediate value theorem and min-max theorem.
	Continuity	We define continuity of functions and derive the intermediate value theorem and min-max theorem.
	Continuity & Compact sets	Intermediate value theorem and min-max theorem.
	Uniform continuity	We study uniform continuity of functions
	monotone functions	go over some of the basic facts on monotone functions.