[미적분]미적분학(calculus)의 theorem(정리)와 axiom들 정리자료.
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- 2008.06.21
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- 2007.05
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소개글
미적분학(calculus)의 theorem(정리)와 axiom들 정리자료.
목차
● Field Axiom.
● Order Axiom.
● Least-upper-bound Axiom.
● Irrational Number.
● Integral of a step function.
● Upper and lower integrals.
● Monotonic functions.
● Calculation of integral.
● Continuous function
● Composite functions.
본문내용
● Field Axiom.
Theorem I.1 Cancellation law for addition. If a+b = a+c, then b=c (In particular, this shows that the number 0 of Axiom 4 is unique)
Theorem I.2 Possibility of Subtraction. Given a and b, there is exactly one x such that a+x = b. This x is denoted by b-a. In particular, 0-a is written simply -a and is called the negative of a
Theorem I.3 b-a = b+(-a)
Theorem I.4 -(-a) = a.
Theorem I.5 a(b-c) = ab - ac
Theorem I.6 0 a = a 0 = 0.
Theorem I.7 Cancellation law for multiplication. If ab = ac and a≠0, then b=c. (In particular, this shows that the number 1 of Axiom 4 is unique).
Theorem I.8 Possibility of division. Given a and b with a≠0, there is exactly one x such that ax = b. This x is denoted by b/a or and is called the quotient of b and a. In particular, 1/a is also written a-1 and is called the reciprocal of a.
Theorem I.9 If a ≠ 0 then b/a = b a-1 .
Theorem I.10 If a ≠ 0, then (a-1)-1 = a
Theorem I.11 If ab = 0 then, a=0 or b=0
Theorem I.12 (-a)b = -(ab) and (-a)(-b) = ab.
Theorem I.13 (a/b) + (c/d) = (ad+bc)/(bd) if b≠0 and d≠0
Theorem I.14 (a/b)(c/d) = (ac)/(bd) if b≠0 and d≠0.
Theorem I.15 (a/b)/(c/d) = (ad)/(bc) if b≠0, c≠0, and d≠0.
참고 자료
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