| Title:
|
Maple tools for the Kurzweil integral (English) |
| Author:
|
Adams, Peter |
| Author:
|
Výborný, Rudolf |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
131 |
| Issue:
|
4 |
| Year:
|
2006 |
| Pages:
|
337-346 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Riemann sums based on $\delta $-fine partitions are illustrated with a Maple procedure. (English) |
| Keyword:
|
Kurzweil’s integral |
| Keyword:
|
fine partition |
| Keyword:
|
Riemann sum |
| MSC:
|
26-04 |
| MSC:
|
26A39 |
| MSC:
|
28-01 |
| MSC:
|
28-02 |
| MSC:
|
28-04 |
| MSC:
|
28E99 |
| idZBL:
|
Zbl 1112.28015 |
| idMR:
|
MR2273926 |
| DOI:
|
10.21136/MB.2006.133971 |
| . |
| Date available:
|
2009-09-24T22:27:07Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133971 |
| . |
| Reference:
|
[1] P. Adams, K. Smith, R. Výborný: Introduction to Mathematics with Maple.World Scientific, Singapore, 2004. |
| Reference:
|
[2] Robert G. Bartle: A Modern Theory of Integration.AMS, Graduate Studies in Mathematics, vol. 32, Providence, Rhode Island, 2001. MR 1817647 |
| Reference:
|
[3] Robert G. Bartle, Donald R. Sherbert: Introduction to Real Analysis.John Wiley & Sons, New York, 2000. MR 1135107 |
| Reference:
|
[4] J. D. DePree, C. Swartz: Introduction to Real Analysis.Wiley, New York, 1988. MR 1042294 |
| Reference:
|
[5] Russel A. Gordon: The Integrals of Lebesgue, Denjoy, Perron, and Henstock.AMS, Graduate Studies in Mathematics, vol. 4, Providence, Rhode Island, 1991. |
| Reference:
|
[6] R. Henstock: Definitions of Riemann type of the variational integrals.Proc. London Math. Soc. 11 (1961), 401–418. Zbl 0099.27402, MR 0132147 |
| Reference:
|
[7] R. Henstock: Theory of Integration.Butterworths, London, 1963. Zbl 0154.05001, MR 0158047 |
| Reference:
|
[8] R. Henstock: Linear Analysis.Butterworths, London, 1967. Zbl 0172.39001, MR 0419707 |
| Reference:
|
[9] R. Henstock: A Riemann integral of Lebesgue power.Canad. J. Math. 20 (1968), 79–87. MR 0219675, 10.4153/CJM-1968-010-5 |
| Reference:
|
[10] R. Henstock: Lectures on the Theory of Integration.World Scientific, Singapore, 1988. Zbl 0668.28001, MR 0963249 |
| Reference:
|
[11] J. Kurzweil: Generalized ordinary differential equations.Czechoslovak Math. J. 7 (1957), 418–446. Zbl 0090.30002, MR 0111875 |
| Reference:
|
[12] J. Kurzweil: Nichtabsolut konvergente Integrale.Teubner, Leipzig, 1980. Zbl 0441.28001, MR 0597703 |
| Reference:
|
[13] P. Y. Lee, R. Výborný: The Integral: An easy approach after Kurzweil and Henstock.Cambridge University Press, Cambridge, UK, 2000. MR 1756319 |
| Reference:
|
[14] P. Y. Lee: Lanzhou Lectures on Henstock Integration.W.A. Benjamin, Inc, New York, Amsterdam, 1967. |
| Reference:
|
[15] J. Mawhin: Introduction à l’Analyse.3rd edition, Cabay, Louvain-la-Neuve, 1983. |
| Reference:
|
[16] Robert M. McLeod: The Generalized Riemann Integral, Carus Mathematical Monographs, vol. 20.Mathematical Association of America, Washington D.C., 1980. MR 0588510 |
| Reference:
|
[17] P. Muldowney: A General Theory of Integration in Function Spaces.Longmans, Harlow, 1987. Zbl 0623.28008 |
| . |
