Using Maple to Study the Double Integral Problems

Chii-Huei Yu

doi:doi:10.11648/j.acm.20130202.12

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Using Maple to Study the Double Integral Problems

Chii-Huei Yu

Published in Applied and Computational Mathematics (Volume 2, Issue 2)

Received: 22 March 2013 Accepted: Published: 2 April 2013

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Abstract

This paper uses the mathematical software Maple as the auxiliary tool to study the evaluation of two types of double integrals. We can find the closed forms of these two types of double integrals by using Euler's formula and finite geometric series. On the other hand, we propose four examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions by using Maple. This type of research method not only allows the discovery of calculation errors, but also helps modify the original directions of thinking from manual and Maple calculations. For this reason, Maple provides insights and guidance regarding prob-lem-solving methods.

Published in	Applied and Computational Mathematics (Volume 2, Issue 2)
DOI	10.11648/j.acm.20130202.12
Page(s)	28-31
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Double Integrals, Euler's Formula, Finite Geometric Series, Closed Forms, Maple

References

[1]	M. L. Abell and J. P. Braselton, Maple by Example, 3rd ed., Elsevier Academic Press, 2005.
[2]	J. S. Robertson, Engineering Mathematics with Maple, McGraw-Hill, 1996.
[3]	F. Garvan, The Maple Book, Chapman & Hall/CRC, 2001.
[4]	D. Richards, Advanced Mathematical Methods with Maple, Cambridge University Press, 2002.
[5]	C. Tocci and S. G. Adams, Applied Maple for Engineers and Scientists, Artech House Publishers, 1996.
[6]	C. T. J. Dodson and E. A. Gonzalez, Experiments in Mathematics Using Maple, Springer-Verlag, 1995.
[7]	R. J. Stroeker and J. F. Kaashoek, Discovering Mathematics with Maple: An Interactive Exploration for Mathematicians, Engineers and Econometricians, Birkhauser Verlag, 1999.
[8]	D. V. Widder, Advanced Calculus, Prentice-Hall, Inc., chap. 6, 1961.
[9]	L. Flatto, Advanced Calculus, The Williams & Wilkins Co., chap. 11, 1976.
[10]	S, Lang, Undergraduate Analysis, Springer-Verlag, chap. 19, 1983.
[11]	T. M. Apostol, Mathematical Analysis, 2nd ed., Addison-Wesley Publishing Co., Inc., chap. 14, 1975.
[12]	C. H. Jr. Edwards and D. E. Penney, Calculus and Analytic Geometry, 2nd ed., Prentice-Hall, Inc, chap. 16, 1986.
[13]	S. I. Grossman, Calculus, 5th ed., Saunders College Publishing, chap. 14, 1992.
[14]	R. Larson, R. P. Hostetler, and B. H. Edwards, Calculus with Analytic Geometry, 8th ed., Houghton Mifflin, chap. 14, 2006.
[15]	C.-H., Yu,"Application of Maple:Using the evaluation of double integrals for an example,"2013 International Conference on Intercultural Communication, Nan Jeon Institute of Technology, Taiwan, pp. 294-302, February 2013.
[16]	C.-H., Yu, "Application of Maple on evaluation of four types of double integrals,"2013 Business Innovation and Development Symposium, Mingdao University, Taiwan, B20130117002, March 2013.
[17]	C.-H., Yu, "Application of Maple on solving double integral problems,"2012 cross-strait Electromechanical and Industry Cooperation Conference, Ta Hwa University of Science and Technology, Taiwan, O06, November 2012.
[18]	C.-H., Yu, "Application of Maple: Taking the study of two types of double integrals as an example,"SAE Seventeenth Vehicle Engineering Symposium, Nan Kai University of Technology, Taiwan, pp.856-860, November 2012.
[19]	C.-H., Yu, "Application of Maple: Using the infinite series expressions of double integrals for an example," UHC2012 Sixth High Quality Family Life Key Technology Symposium, Kun Shan University, Taiwan, pp. 211-214, October 2012.
[20]	C.-H., Yu,"Application of Maple: Taking the evaluation of double integrals by Fourier series as an example," ISC2012 Sixth Intelligent Application of Systems Engineering Symposium, Far East University, Taiwan, H2-6, May 2012.

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APA Style

Chii-Huei Yu. (2013). Using Maple to Study the Double Integral Problems. Applied and Computational Mathematics, 2(2), 28-31. https://doi.org/10.11648/j.acm.20130202.12

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ACS Style

Chii-Huei Yu. Using Maple to Study the Double Integral Problems. Appl. Comput. Math. 2013, 2(2), 28-31. doi: 10.11648/j.acm.20130202.12

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AMA Style

Chii-Huei Yu. Using Maple to Study the Double Integral Problems. Appl Comput Math. 2013;2(2):28-31. doi: 10.11648/j.acm.20130202.12

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@article{10.11648/j.acm.20130202.12,
  author = {Chii-Huei Yu},
  title = {Using Maple to Study the Double Integral Problems},
  journal = {Applied and Computational Mathematics},
  volume = {2},
  number = {2},
  pages = {28-31},
  doi = {10.11648/j.acm.20130202.12},
  url = {https://doi.org/10.11648/j.acm.20130202.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20130202.12},
  abstract = {This paper uses the mathematical software Maple as the auxiliary tool to study the evaluation of two types of double integrals. We can find the closed forms of these two types of double integrals by using Euler's formula and finite geometric series. On the other hand, we propose four examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions by using Maple. This type of research method not only allows the discovery of calculation errors, but also helps modify the original directions of thinking from manual and Maple calculations. For this reason, Maple provides insights and guidance regarding prob-lem-solving methods.},
 year = {2013}
}

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TY  - JOUR
T1  - Using Maple to Study the Double Integral Problems
AU  - Chii-Huei Yu
Y1  - 2013/04/02
PY  - 2013
N1  - https://doi.org/10.11648/j.acm.20130202.12
DO  - 10.11648/j.acm.20130202.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 28
EP  - 31
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20130202.12
AB  - This paper uses the mathematical software Maple as the auxiliary tool to study the evaluation of two types of double integrals. We can find the closed forms of these two types of double integrals by using Euler's formula and finite geometric series. On the other hand, we propose four examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions by using Maple. This type of research method not only allows the discovery of calculation errors, but also helps modify the original directions of thinking from manual and Maple calculations. For this reason, Maple provides insights and guidance regarding prob-lem-solving methods.
VL  - 2
IS  - 2
ER  -

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Author Information

Chii-Huei Yu

Department of Management and Information, Nan Jeon Institute of Technology, Tainan City, Taiwan

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APA Style

Chii-Huei Yu. (2013). Using Maple to Study the Double Integral Problems. Applied and Computational Mathematics, 2(2), 28-31. https://doi.org/10.11648/j.acm.20130202.12

Copy | Download

ACS Style

Chii-Huei Yu. Using Maple to Study the Double Integral Problems. Appl. Comput. Math. 2013, 2(2), 28-31. doi: 10.11648/j.acm.20130202.12

Copy | Download

AMA Style

Chii-Huei Yu. Using Maple to Study the Double Integral Problems. Appl Comput Math. 2013;2(2):28-31. doi: 10.11648/j.acm.20130202.12

Copy | Download

@article{10.11648/j.acm.20130202.12,
  author = {Chii-Huei Yu},
  title = {Using Maple to Study the Double Integral Problems},
  journal = {Applied and Computational Mathematics},
  volume = {2},
  number = {2},
  pages = {28-31},
  doi = {10.11648/j.acm.20130202.12},
  url = {https://doi.org/10.11648/j.acm.20130202.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20130202.12},
  abstract = {This paper uses the mathematical software Maple as the auxiliary tool to study the evaluation of two types of double integrals. We can find the closed forms of these two types of double integrals by using Euler's formula and finite geometric series. On the other hand, we propose four examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions by using Maple. This type of research method not only allows the discovery of calculation errors, but also helps modify the original directions of thinking from manual and Maple calculations. For this reason, Maple provides insights and guidance regarding prob-lem-solving methods.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - Using Maple to Study the Double Integral Problems
AU  - Chii-Huei Yu
Y1  - 2013/04/02
PY  - 2013
N1  - https://doi.org/10.11648/j.acm.20130202.12
DO  - 10.11648/j.acm.20130202.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 28
EP  - 31
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20130202.12
AB  - This paper uses the mathematical software Maple as the auxiliary tool to study the evaluation of two types of double integrals. We can find the closed forms of these two types of double integrals by using Euler's formula and finite geometric series. On the other hand, we propose four examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions by using Maple. This type of research method not only allows the discovery of calculation errors, but also helps modify the original directions of thinking from manual and Maple calculations. For this reason, Maple provides insights and guidance regarding prob-lem-solving methods.
VL  - 2
IS  - 2
ER  -

Copy | Download