Using Maple to Study the Double Integral Problems
Applied and Computational Mathematics
Volume 2, Issue 2, April 2013, Pages: 28-31
Received: Mar. 22, 2013; Published: Apr. 2, 2013
Views 2651      Downloads 149
Author
Chii-Huei Yu, Department of Management and Information, Nan Jeon Institute of Technology, Tainan City, Taiwan
Article Tools
PDF
Follow on us
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.
Keywords
Double Integrals, Euler's Formula, Finite Geometric Series, Closed Forms, Maple
To cite this article
Chii-Huei Yu, Using Maple to Study the Double Integral Problems, Applied and Computational Mathematics. Vol. 2, No. 2, 2013, pp. 28-31. doi: 10.11648/j.acm.20130202.12
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.
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186