Some Applications of Elliptic Integrals of First Kind

Authors

  • Yasamin Barakat Islamic Azad University-Ahvaz Branch
  • Nor Haniza Sarmin Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Malaysia

DOI:

https://doi.org/10.11113/jt.v65.1711

Keywords:

Elliptic integral, first kind, Legendre's form

Abstract

One of the most important applications of elliptic integrals in engineering mathematics is their usage to solve integrals of the form  (Eq. 1), where  is a rational algebraic function and  is a polynomial of degree  with no repeated roots. Nowadays, incomplete and complete elliptic integrals of first kind are estimated with high accuracy using advanced calculators.  In this paper, several techniques are discussed to show how definite integrals of the form (Eq. 1) can be converted to elliptic integrals of the first kind, and hence be estimated for optimal values. Indeed, related examples are provided in each step to help clarification.

Author Biographies

  • Yasamin Barakat, Islamic Azad University-Ahvaz Branch
    PHD student of Universiti Teknologi Malaysia
  • Nor Haniza Sarmin, Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Malaysia
    Deputy Dean (Admission & Customer Relation)School of Graduate Studies (SPS)

References

Casio Computer Co., Ltd. Retrieved on 16/9/2011. http://keisan.casio.com/exec/system/1244989500.

Casio Computer Co., Ltd. Retrieved on 16/9/2011. http://keisan.casio.com/exec/system/1180573451.

P. F. Byrd, M. D. Friedman. 1971. Handbook of Elliptic Integrals for Engineering and Scientists. 2nd Ed. New York: Springer-Verlag.

G. Almkvist, B. Berndt. 1988. The American Mathematical monthly. 95(7): 585.

Y. Barakat, N. H. Sarmin. 2011. Proc. of ISASM 2011. UTHM University, KL, Malaysia, 1-3 November 2011, No. 83.

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Published

2013-10-25

Issue

Vol. 65 No. 1: Nov. 2013

Section

Science and Engineering

License

Copyright of articles that appear in Jurnal Teknologi belongs exclusively to Penerbit Universiti Teknologi Malaysia (Penerbit UTM Press). This copyright covers the rights to reproduce the article, including reprints, electronic reproductions, or any other reproductions of similar nature.

How to Cite

Some Applications of Elliptic Integrals of First Kind. (2013). Jurnal Teknologi, 65(1). https://doi.org/10.11113/jt.v65.1711