Calculation of Partial Derivatives of Two Variables Functions

Authors

  • Chii-Huei Yu  Department of Information Technology, Nan Jeon University of Science and Technology, Taiwan
  • Shih-Yin Huang  Department of Information Technology, Nan Jeon University of Science and Technology, Taiwan

Keywords:

Two Variables Functions, Partial Derivatives, Infinite Series Forms, Differentiation Term By Term Theorem, Maple.

Abstract

In this article, we study the partial differential problem of two types of two variables functions. The infinite series forms of any order partial derivatives of the two types of two variables functions can be obtained mainly using differentiation term by term theorem. Therefore, the difficulty of calculating higher order partial derivatives of these two variables functions can be greatly reduced. On the other hand, some examples are provided to do calculation practically. The research method adopted is to find solutions through manual calculations, and verify these solutions using Maple.

References

  1. H., Bischof, G. Corliss, and A. Griewank, "Structured second and higher-order derivatives through univariate Taylor series," Optimization Methods and Software, vol. 2, pp. 211-232, 1993.
  2. N. Richard, "An efficient method for the numerical evaluation of partial derivatives of arbitrary order, " ACM Transactions on Mathematical Software, vol. 18, no. 2, pp. 159-173, 1992.
  3. Griewank and A. Walther, Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, 2nd ed., Philadelphia: SIAM, 2008.
  4. E. Fraenkel, "Formulae for high derivatives of composite functions, " Mathematical Proceedings of the Cambridge Philosophical Society, vol. 83, pp. 159-165, 1978.
  5. T-W, Ma, "Higher chain formula proved by combinatorics," The Electronic Journal of Combinatorics , vol. 16, #N21, 2009.
  6. -H. Yu, "Partial derivatives of some types of two-variables functions," Pure and Applied Mathematics Journal, vol. 2, no. 2, pp. 56-61, 2013.
  7. -H. Yu, "Using Maple to evaluate the partial derivatives of two-variables functions," International Journal of Computer Science and Mobile Computing, vol. 2, issue. 6, pp. 225-232, 2013.
  8. -H. Yu, "A study of partial differential problem with Maple," International Journal of Research, vol. 3, issue. 4, pp. 101-108, 2016.
  9. -H. Yu, "Complex analysis method for evaluating the partial derivatives of two variables functions," International Journal of Research, vol. 3, issue. 4, pp. 154-160, 2016.
  10. -H. Yu, "Solving the partial differential problems using Maple," Journal of Applied Research and Technology, vol.12, no. 6, pp.1144-1153, 2014.
  11. -H. Yu, "Using Maple to study the partial differential problems," Applied Mechanics and Materials, vols. 479-480(2014), pp. 800-804, 2013.
  12. -H. Yu and B. -H. Chen, "The partial differential problem," Computational Research, vol.1, no.3, pp.53-60, 2013.
  13. -H. Yu, "Using differentiation term by term theorem to study the partial differential problems," Turkish Journal of Analysis and Number Theory, vol. 1, no. 1, pp. 63-68, 2013.
  14. -H. Yu, "Partial derivatives of three variables functions," Universal Journal of Computational Mathematics, vol. 2, no. 2, pp. 23-27, 2014.
  15. -H. Yu, "Application of differentiation term by term theorem on the partial differential problems," International Journal of Partial Differential Equations and Applications, vol. 2, no. 1, pp. 7-12, 2014.
  16. -H. Yu, "Evaluating the partial derivatives of some types of multivariable functions, " American Journal of Computing Research Repository, vol. 2, no. 1, pp. 15-18, 2014.
  17. -H. Yu, "Solving the partial differential problems using differentiation term by term theorem," Journal of Automation and Control, vol. 2, no. 1, pp. 8-14, 2014.
  18. -H. Yu, "Partial differential problems of four types of two-variables functions," American Journal of Numerical Analysis, vol. 2, no. 1, pp.4-10, 2014.
  19. -H. Yu and B. -H. Chen, "Studying the partial differential problem using Maple," Universal Journal of Engineering Science, vol. 2, no. 1, pp. 6-15, 2014.
  20. -H. Yu, "Evaluating partial derivatives of two-variables functions by using Maple," Proceedings of the 6th IEEE/International Conference on Advanced Infocomm Technology, Hsinchu, Taiwan, no. 00295, 2013.
  21. -H. Yu, "Application of Maple: taking the partial differential problem of some types of two-variables functions as an example," (in Chinese) Proceedings of the International Conference on e-Learning, New Taipei City, Taiwan, pp. 337-345, 2013.
  22. -H. Yu, "Application of Maple on the partial differential problem of four types of two-variables functions," (in Chinese) Proceedings of the International Conference on Advanced Information Technologies, Taichung, Taiwan, no.87, 2013.
  23. -H. Yu, "Application of Maple: taking the partial differential problem of two-variables functions as an example," (in Chinese) Proceedings of 2013 Business Innovation and Development Symposium, Changhua County, Taiwan, B20130113001, 2013.
  24. M. Apostol, Mathematical Analysis, 2nd ed., Massachusetts: Addison-Wesley, 1975.

IInternational Journal of Scientific Research in Computer Science, Engineering and Information Technology

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Published

2016-10-30

Issue

Volume 1, Issue 2, September-October-2016

Section

Research Articles

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Copyright (c) IJSRCSEIT

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

[1]
Chii-Huei Yu, Shih-Yin Huang, " Calculation of Partial Derivatives of Two Variables Functions, IInternational Journal of Scientific Research in Computer Science, Engineering and Information Technology(IJSRCSEIT), ISSN : 2456-3307, Volume 1, Issue 2, pp.54-58, September-October-2016.