Research Article
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Year 2025, Volume: 8 Issue: 1, 17 - 43, 30.06.2025

Abstract

References

  • Apaydın, G., Sevgi, G. (2014). MATLAB-based FEM -parabolic-equation tool for path loss calculations along multi-mixed-terrain paths. IEEE Antennas and Propagation Magazine. 56(3), 221-236.
  • Bayen, A. M. and Siauw T. (2015). An introduction to MatlabR programming and numerical methods for engineers. USA: Academic Press, Elsevier.
  • Bishay, P. L., (2016). FEApps: Boosting students' enthusiasm for coding and App designing, with a deeper learning experience in engineering fundamentals. Computer Applications in Engineering Education, 24, 456-463. https://doi.org/10.1002/cae.21723
  • Chapra, S. C., Canale, R. P. (2010). Numerical methods for engineers. Sixth Edition. New York, NY: McGraw Hill.
  • Chow, J. C. L. (2016). Some computer graphical user interfaces in radiation therapy. World Journal of Radiology. 8(3), 255-267.
  • Dinçkal, Ç. (2018). Design of integral spreadsheet calculator for engineering applications. Computer Applications in Engineering Education. Special Issue, 1-14. https://doi.org/10.1002/cae.21947
  • Dinçkal, Ç. (2025). New approaches for evaluation indeterminate limits for multivariable functions in undergraduate mathematics courses. Natural Sciences and Engineering Bulletin. 2(1), 56-74.
  • Fine, A. I., Kass S. (1966). Indeterminate forms for multi-place functions. Ann. Polon. Math. 18(1), 59-64.
  • Gulmaro, C. C. (2018). About the proof of the L’Hôpital's rule. American Scientific Research Journal for Engineering, Technology and Sciences. 41(1), 240-245.
  • Gupta, P. K., Patel R. N. (2017). A Teaching-learning tool for elementary psychrometric processes on psychrometric chart using MATLAB. Computer Applications in Engineering Education. 25, 458-467. https://doi.org/10.1002/cae.21813.
  • Hartig, D. (1991). L’Hôpital’s rule via integration. Amer. Math. Monthly. 98(3), 156– 157.
  • Huang, X. C. (1988). A discrete L’Hôpital’s rule. College Math. J. 19(4), 321–329.
  • John, T. M., Wara, S. T. (2018). A tutorial on the development of a Smart Calculator to determine the Installed Solar requirements for Households and Small businesses. IEEE PES/IAS PowerAfrica Conference, 319-323.
  • Ivlev, V. V. (2013). Mathematical analysis: multivariable functions. Moskow, IKAR in Russian.
  • Ivlev, V. V., Shilin I. A., (2014). On generalization of L’Hôpital’s rule for multivariable functions. Retrieved from https://arxiv.org/pdf/1403.3006.
  • Lawlor, G. R. (2020). L’Hôpital’s rule for multivariable functions. American Mathematical Monthly. 127(8), 717-725. https://doi.org/10.1080/00029890.2020.1793635.
  • Malehmir, R. D., Schmitt R. (2016). ARTc: anisotropic reflectivity and transmissivity calculator. Computers & Geosciences. 93, 114-126. https://doi.org/10.1016/j.cageo.2016.05.008 ·
  • Mitchell, R. J. (2014). A Matlab GUI for learning controller design in the frequency domain. International Conference on Control (UKACC), 279-284.
  • Mohamed, T. L. T., Mohamed, R. H.,& Mohamed, A., Z. (2010). Development of auto tuning PID controller using Graphical User Interface (GUI). 2010 Second International Conference on Computer Engineering and Applications (ICCEA 2010). 491-495.
  • Oke, E. O., Jimoda, L. A. & Araromi, D. O. (2018). Determination of biocoagulant dosage for water clarification using developed neuro-fuzzy network integrated with user interface-based calculator. Water Science and Technology-Water Supply. 18(5), 1783-1792. https://doi.org/10.2166/ws.2017.241.
  • Piris G., et al. (2021). 3DHIP-Calculator-A new tool to stochastically assess deep geothermal potential using the heat-in-place method from Voxel-based 3D geological models. Energies. 14(21), 7338. https://doi.org/10.3390/en14217338.
  • Sheldon, P. G. (2017). Visualizing and understanding L’Hôpital’s rule. International Journal of Mathematical Education in Science and Technology. 48(7), 1096-1105. https://doi.org/10.1080/0020739X.2017.1315187.
  • Singh, M., Deepika, Kumar, M. (2014). Economic load dispatch calculator. 6th IEEE Power India International Conference (PIICON).
  • Song, X. W. Z., Dong, Y. & Zang, Y. F. (2011). REST: A Toolkit for resting-state functional magnetic resonance imaging data processing. Plos One. 6(9), e25031.
  • Szabó, G. (1989). A note on the L’Hôpital’s rule. Elem. Math. 44(6), 150–153.
  • Takeuchi, Y. (1995). L’Hôpital’s rule for series. Bol. Mat. ½. 2(1), 17-33.
  • Výborný, R., Nester, R. (1989). L’Hôpital’s rule, a counterexample. Elem. Math. 44(5), 116–121.
  • Yogesh, J. (2012). Computer methods for engineering with MATLAB applications. New York, NY: Taylor & Francis.
  • Young, W. H. (1910). On indeterminate forms. Proc. Lond. Math. Soc. 2(1), 40-76.

Computation of Indeterminate Limit Forms for Multivariable Functions Using GUI_calcm in Calculus Education

Year 2025, Volume: 8 Issue: 1, 17 - 43, 30.06.2025

Abstract

Taking limit for multivariable functions is one of the essential topics of calculus courses in calculus education. When evaluating limits, one can frequently come across with the solution of indeterminate limit forms such as 0/0, c/0 (c can be any real number). Well-known L'Hopital rule has been employed in the literature. However, this rule is lengthy and complicated process in some cases. So, finite difference methods as numerical methods have been developed and employed to solve these limits. All of the methods take too much time by hand computations. Main aim of the study is to design an indeterminate limit calculator: 'GUI_calcm' by use of Matlab GUI and APPS. The results of this study is to display the outputs obtained by each run of the calculator. These outputs are the results of each method with use of step size. Comparison of each method and performance of GUI_calcm are also presented.

References

  • Apaydın, G., Sevgi, G. (2014). MATLAB-based FEM -parabolic-equation tool for path loss calculations along multi-mixed-terrain paths. IEEE Antennas and Propagation Magazine. 56(3), 221-236.
  • Bayen, A. M. and Siauw T. (2015). An introduction to MatlabR programming and numerical methods for engineers. USA: Academic Press, Elsevier.
  • Bishay, P. L., (2016). FEApps: Boosting students' enthusiasm for coding and App designing, with a deeper learning experience in engineering fundamentals. Computer Applications in Engineering Education, 24, 456-463. https://doi.org/10.1002/cae.21723
  • Chapra, S. C., Canale, R. P. (2010). Numerical methods for engineers. Sixth Edition. New York, NY: McGraw Hill.
  • Chow, J. C. L. (2016). Some computer graphical user interfaces in radiation therapy. World Journal of Radiology. 8(3), 255-267.
  • Dinçkal, Ç. (2018). Design of integral spreadsheet calculator for engineering applications. Computer Applications in Engineering Education. Special Issue, 1-14. https://doi.org/10.1002/cae.21947
  • Dinçkal, Ç. (2025). New approaches for evaluation indeterminate limits for multivariable functions in undergraduate mathematics courses. Natural Sciences and Engineering Bulletin. 2(1), 56-74.
  • Fine, A. I., Kass S. (1966). Indeterminate forms for multi-place functions. Ann. Polon. Math. 18(1), 59-64.
  • Gulmaro, C. C. (2018). About the proof of the L’Hôpital's rule. American Scientific Research Journal for Engineering, Technology and Sciences. 41(1), 240-245.
  • Gupta, P. K., Patel R. N. (2017). A Teaching-learning tool for elementary psychrometric processes on psychrometric chart using MATLAB. Computer Applications in Engineering Education. 25, 458-467. https://doi.org/10.1002/cae.21813.
  • Hartig, D. (1991). L’Hôpital’s rule via integration. Amer. Math. Monthly. 98(3), 156– 157.
  • Huang, X. C. (1988). A discrete L’Hôpital’s rule. College Math. J. 19(4), 321–329.
  • John, T. M., Wara, S. T. (2018). A tutorial on the development of a Smart Calculator to determine the Installed Solar requirements for Households and Small businesses. IEEE PES/IAS PowerAfrica Conference, 319-323.
  • Ivlev, V. V. (2013). Mathematical analysis: multivariable functions. Moskow, IKAR in Russian.
  • Ivlev, V. V., Shilin I. A., (2014). On generalization of L’Hôpital’s rule for multivariable functions. Retrieved from https://arxiv.org/pdf/1403.3006.
  • Lawlor, G. R. (2020). L’Hôpital’s rule for multivariable functions. American Mathematical Monthly. 127(8), 717-725. https://doi.org/10.1080/00029890.2020.1793635.
  • Malehmir, R. D., Schmitt R. (2016). ARTc: anisotropic reflectivity and transmissivity calculator. Computers & Geosciences. 93, 114-126. https://doi.org/10.1016/j.cageo.2016.05.008 ·
  • Mitchell, R. J. (2014). A Matlab GUI for learning controller design in the frequency domain. International Conference on Control (UKACC), 279-284.
  • Mohamed, T. L. T., Mohamed, R. H.,& Mohamed, A., Z. (2010). Development of auto tuning PID controller using Graphical User Interface (GUI). 2010 Second International Conference on Computer Engineering and Applications (ICCEA 2010). 491-495.
  • Oke, E. O., Jimoda, L. A. & Araromi, D. O. (2018). Determination of biocoagulant dosage for water clarification using developed neuro-fuzzy network integrated with user interface-based calculator. Water Science and Technology-Water Supply. 18(5), 1783-1792. https://doi.org/10.2166/ws.2017.241.
  • Piris G., et al. (2021). 3DHIP-Calculator-A new tool to stochastically assess deep geothermal potential using the heat-in-place method from Voxel-based 3D geological models. Energies. 14(21), 7338. https://doi.org/10.3390/en14217338.
  • Sheldon, P. G. (2017). Visualizing and understanding L’Hôpital’s rule. International Journal of Mathematical Education in Science and Technology. 48(7), 1096-1105. https://doi.org/10.1080/0020739X.2017.1315187.
  • Singh, M., Deepika, Kumar, M. (2014). Economic load dispatch calculator. 6th IEEE Power India International Conference (PIICON).
  • Song, X. W. Z., Dong, Y. & Zang, Y. F. (2011). REST: A Toolkit for resting-state functional magnetic resonance imaging data processing. Plos One. 6(9), e25031.
  • Szabó, G. (1989). A note on the L’Hôpital’s rule. Elem. Math. 44(6), 150–153.
  • Takeuchi, Y. (1995). L’Hôpital’s rule for series. Bol. Mat. ½. 2(1), 17-33.
  • Výborný, R., Nester, R. (1989). L’Hôpital’s rule, a counterexample. Elem. Math. 44(5), 116–121.
  • Yogesh, J. (2012). Computer methods for engineering with MATLAB applications. New York, NY: Taylor & Francis.
  • Young, W. H. (1910). On indeterminate forms. Proc. Lond. Math. Soc. 2(1), 40-76.
There are 29 citations in total.

Details

Primary Language English
Subjects Instructional Technologies, Educational Technology and Computing
Journal Section Research Article
Authors

Çiğdem Dinçkal 0000-0002-1201-0885

Submission Date November 1, 2024
Acceptance Date January 27, 2025
Publication Date June 30, 2025
Published in Issue Year 2025 Volume: 8 Issue: 1

Cite

APA Dinçkal, Ç. (2025). Computation of Indeterminate Limit Forms for Multivariable Functions Using GUI_calcm in Calculus Education. International Journal of Computers in Education, 8(1), 17-43.