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2007 | 15 | 2 | 59-63
Tytuł artykułu

Riemann Indefinite Integral of Functions of Real Variable

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this article we define the Riemann indefinite integral of functions of real variable and prove the linearity of that [1]. And we give some examples of the indefinite integral of some elementary functions. Furthermore, also the theorem about integral operation and uniform convergent sequence of functions is proved.
Słowa kluczowe
Wydawca
Rocznik
Tom
15
Numer
2
Strony
59-63
Opis fizyczny
Daty
wydano
2007-01-01
online
2008-06-09
Twórcy
  • Shinshu University, Nagano, Japan
autor
  • Gifu National College of Technology, Japan
  • Shinshu University, Nagano, Japan
Bibliografia
  • [7] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • [8] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  • [9] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.
  • [10] Czesław Byliński and Piotr Rudnicki. Bounding boxes for compact sets in ε2. Formalized Mathematics, 6(3):427-440, 1997.
  • [11] Noboru Endou and Artur Korniłowicz. The definition of the Riemann definite integral and some related lemmas. Formalized Mathematics, 8(1):93-102, 1999.
  • [12] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definition of integrability for partial functions from R to R and integrability for continuous functions. Formalized Mathematics, 9(2):281-284, 2001.
  • [13] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
  • [14] Jarosław Kotowicz. Convergent real sequences. Upper and lower bound of sets of real numbers. Formalized Mathematics, 1(3):477-481, 1990.
  • [15] Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990.
  • [16] Jarosław Kotowicz. Partial functions from a domain to the set of real numbers. Formalized Mathematics, 1(4):703-709, 1990.
  • [17] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.
  • [18] Beata Perkowska. Functional sequence from a domain to a domain. Formalized Mathematics, 3(1):17-21, 1992.
  • [19] Konrad Raczkowski and Paweł Sadowski. Real function continuity. Formalized Mathematics, 1(4):787-791, 1990.
  • [20] Konrad Raczkowski and Paweł Sadowski. Real function differentiability. Formalized Mathematics, 1(4):797-801, 1990.
  • [21] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.
  • [22] Yasunari Shidama. The Taylor expansions. Formalized Mathematics, 12(2):195-200, 2004.
  • [23] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics.
  • [24] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990.
  • [25] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • [26] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
  • [27] Yuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio. Formalized Mathematics, 7(2):255-263, 1998.
  • [1] Tom M. Apostol. Mathematical Analysis. Addison-Wesley, 1969.
  • [2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
  • [3] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  • [4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
  • [5] Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
  • [6] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_v10037-007-0007-6
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