About DML-CZ | FAQ | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

Adams, Peter ; Výborný, Rudolf
Maple tools for the Kurzweil integral. (English). Mathematica Bohemica, vol. 131 (2006), issue 4, pp. 337-346
MSC: 26-04, 26A39, 28-01, 28-02, 28-04, 28E99 | MR 2273926 | Zbl 1112.28015 | DOI: 10.21136/MB.2006.133971
Keywords:
Kurzweil’s integral; fine partition; Riemann sum
Summary:
Riemann sums based on $\delta $-fine partitions are illustrated with a Maple procedure.
References:
[1] P. Adams, K. Smith, R. Výborný: Introduction to Mathematics with Maple. World Scientific, Singapore, 2004.
[2] Robert G. Bartle: A Modern Theory of Integration. AMS, Graduate Studies in Mathematics, vol. 32, Providence, Rhode Island, 2001. MR 1817647
[3] Robert G. Bartle, Donald R. Sherbert: Introduction to Real Analysis. John Wiley & Sons, New York, 2000. MR 1135107
[4] J. D. DePree, C. Swartz: Introduction to Real Analysis. Wiley, New York, 1988. MR 1042294
[5] Russel A. Gordon: The Integrals of Lebesgue, Denjoy, Perron, and Henstock. AMS, Graduate Studies in Mathematics, vol. 4, Providence, Rhode Island, 1991.
[6] R. Henstock: Definitions of Riemann type of the variational integrals. Proc. London Math. Soc. 11 (1961), 401–418. MR 0132147 | Zbl 0099.27402
[7] R. Henstock: Theory of Integration. Butterworths, London, 1963. MR 0158047 | Zbl 0154.05001
[8] R. Henstock: Linear Analysis. Butterworths, London, 1967. MR 0419707 | Zbl 0172.39001
[9] R. Henstock: A Riemann integral of Lebesgue power. Canad. J. Math. 20 (1968), 79–87. DOI 10.4153/CJM-1968-010-5 | MR 0219675
[10] R. Henstock: Lectures on the Theory of Integration. World Scientific, Singapore, 1988. MR 0963249 | Zbl 0668.28001
[11] J. Kurzweil: Generalized ordinary differential equations. Czechoslovak Math. J. 7 (1957), 418–446. MR 0111875 | Zbl 0090.30002
[12] J. Kurzweil: Nichtabsolut konvergente Integrale. Teubner, Leipzig, 1980. MR 0597703 | Zbl 0441.28001
[13] P. Y. Lee, R. Výborný: The Integral: An easy approach after Kurzweil and Henstock. Cambridge University Press, Cambridge, UK, 2000. MR 1756319
[14] P. Y. Lee: Lanzhou Lectures on Henstock Integration. W.A. Benjamin, Inc, New York, Amsterdam, 1967.
[15] J. Mawhin: Introduction à l’Analyse. 3rd edition, Cabay, Louvain-la-Neuve, 1983.
[16] Robert M. McLeod: The Generalized Riemann Integral, Carus Mathematical Monographs, vol. 20. Mathematical Association of America, Washington D.C., 1980. MR 0588510
[17] P. Muldowney: A General Theory of Integration in Function Spaces. Longmans, Harlow, 1987. Zbl 0623.28008
Partner of
EuDML logo