Research and Demonstration of the Refraction Problems

Xiao Hu; Lintong Zhang; Jixun Chu

doi:doi:10.11648/j.ajam.20180602.19

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Research and Demonstration of the Refraction Problems

Xiao Hu, Lintong Zhang, Jixun Chu

Published in American Journal of Applied Mathematics (Volume 6, Issue 2)

Received: 25 June 2018 Published: 26 June 2018

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Abstract

The introduction of function extremum promotes the development of calculus, which is the prerequisite and important condition for the development and development of many mathematical ideas. Except for extreme problems in social life or science and technology, the issue of cost in economic issues, the shortest distance in mathematics problem can be solved by the function extreme value thought. However, because the extreme value problem is not well described, learners cannot easily observe and learn. This paper takes the uniform speed and uniform acceleration and descent in the descent model as an example. In the uniform acceleration, the dichotomy is introduced to solve the function extremum problem. Through MATLAB simulation, the position of the steepest descent point is found intuitively and relevant conclusions are obtained. It is hoped that the research process of the problem can be helpful to the study of refractive problems, and it is hoped that the visually intuitive simulation results can enable learners to understand the descent model more objectively.

Published in	American Journal of Applied Mathematics (Volume 6, Issue 2)
DOI	10.11648/j.ajam.20180602.19
Page(s)	87-96
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), 2018. Published by Science Publishing Group

Keywords

Refractive Problems, Function Extremum, Dichotomy, MATLAB Simulation

References

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APA Style

Xiao Hu, Lintong Zhang, Jixun Chu. (2018). Research and Demonstration of the Refraction Problems. American Journal of Applied Mathematics, 6(2), 87-96. https://doi.org/10.11648/j.ajam.20180602.19

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ACS Style

Xiao Hu; Lintong Zhang; Jixun Chu. Research and Demonstration of the Refraction Problems. Am. J. Appl. Math. 2018, 6(2), 87-96. doi: 10.11648/j.ajam.20180602.19

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AMA Style

Xiao Hu, Lintong Zhang, Jixun Chu. Research and Demonstration of the Refraction Problems. Am J Appl Math. 2018;6(2):87-96. doi: 10.11648/j.ajam.20180602.19

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@article{10.11648/j.ajam.20180602.19,
  author = {Xiao Hu and Lintong Zhang and Jixun Chu},
  title = {Research and Demonstration of the Refraction Problems},
  journal = {American Journal of Applied Mathematics},
  volume = {6},
  number = {2},
  pages = {87-96},
  doi = {10.11648/j.ajam.20180602.19},
  url = {https://doi.org/10.11648/j.ajam.20180602.19},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20180602.19},
  abstract = {The introduction of function extremum promotes the development of calculus, which is the prerequisite and important condition for the development and development of many mathematical ideas. Except for extreme problems in social life or science and technology, the issue of cost in economic issues, the shortest distance in mathematics problem can be solved by the function extreme value thought. However, because the extreme value problem is not well described, learners cannot easily observe and learn. This paper takes the uniform speed and uniform acceleration and descent in the descent model as an example. In the uniform acceleration, the dichotomy is introduced to solve the function extremum problem. Through MATLAB simulation, the position of the steepest descent point is found intuitively and relevant conclusions are obtained. It is hoped that the research process of the problem can be helpful to the study of refractive problems, and it is hoped that the visually intuitive simulation results can enable learners to understand the descent model more objectively.},
 year = {2018}
}

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TY  - JOUR
T1  - Research and Demonstration of the Refraction Problems
AU  - Xiao Hu
AU  - Lintong Zhang
AU  - Jixun Chu
Y1  - 2018/06/26
PY  - 2018
N1  - https://doi.org/10.11648/j.ajam.20180602.19
DO  - 10.11648/j.ajam.20180602.19
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 87
EP  - 96
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20180602.19
AB  - The introduction of function extremum promotes the development of calculus, which is the prerequisite and important condition for the development and development of many mathematical ideas. Except for extreme problems in social life or science and technology, the issue of cost in economic issues, the shortest distance in mathematics problem can be solved by the function extreme value thought. However, because the extreme value problem is not well described, learners cannot easily observe and learn. This paper takes the uniform speed and uniform acceleration and descent in the descent model as an example. In the uniform acceleration, the dichotomy is introduced to solve the function extremum problem. Through MATLAB simulation, the position of the steepest descent point is found intuitively and relevant conclusions are obtained. It is hoped that the research process of the problem can be helpful to the study of refractive problems, and it is hoped that the visually intuitive simulation results can enable learners to understand the descent model more objectively.
VL  - 6
IS  - 2
ER  -

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Author Information

Xiao Hu

School of Mathematics and Physics, University of Science & Technology Beijing, Beijing, China
Lintong Zhang

School of Mathematics and Physics, University of Science & Technology Beijing, Beijing, China
Jixun Chu

School of Mathematics and Physics, University of Science & Technology Beijing, Beijing, China

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APA Style

Xiao Hu, Lintong Zhang, Jixun Chu. (2018). Research and Demonstration of the Refraction Problems. American Journal of Applied Mathematics, 6(2), 87-96. https://doi.org/10.11648/j.ajam.20180602.19

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ACS Style

Xiao Hu; Lintong Zhang; Jixun Chu. Research and Demonstration of the Refraction Problems. Am. J. Appl. Math. 2018, 6(2), 87-96. doi: 10.11648/j.ajam.20180602.19

Copy | Download

AMA Style

Xiao Hu, Lintong Zhang, Jixun Chu. Research and Demonstration of the Refraction Problems. Am J Appl Math. 2018;6(2):87-96. doi: 10.11648/j.ajam.20180602.19

Copy | Download

@article{10.11648/j.ajam.20180602.19,
  author = {Xiao Hu and Lintong Zhang and Jixun Chu},
  title = {Research and Demonstration of the Refraction Problems},
  journal = {American Journal of Applied Mathematics},
  volume = {6},
  number = {2},
  pages = {87-96},
  doi = {10.11648/j.ajam.20180602.19},
  url = {https://doi.org/10.11648/j.ajam.20180602.19},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20180602.19},
  abstract = {The introduction of function extremum promotes the development of calculus, which is the prerequisite and important condition for the development and development of many mathematical ideas. Except for extreme problems in social life or science and technology, the issue of cost in economic issues, the shortest distance in mathematics problem can be solved by the function extreme value thought. However, because the extreme value problem is not well described, learners cannot easily observe and learn. This paper takes the uniform speed and uniform acceleration and descent in the descent model as an example. In the uniform acceleration, the dichotomy is introduced to solve the function extremum problem. Through MATLAB simulation, the position of the steepest descent point is found intuitively and relevant conclusions are obtained. It is hoped that the research process of the problem can be helpful to the study of refractive problems, and it is hoped that the visually intuitive simulation results can enable learners to understand the descent model more objectively.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Research and Demonstration of the Refraction Problems
AU  - Xiao Hu
AU  - Lintong Zhang
AU  - Jixun Chu
Y1  - 2018/06/26
PY  - 2018
N1  - https://doi.org/10.11648/j.ajam.20180602.19
DO  - 10.11648/j.ajam.20180602.19
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 87
EP  - 96
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20180602.19
AB  - The introduction of function extremum promotes the development of calculus, which is the prerequisite and important condition for the development and development of many mathematical ideas. Except for extreme problems in social life or science and technology, the issue of cost in economic issues, the shortest distance in mathematics problem can be solved by the function extreme value thought. However, because the extreme value problem is not well described, learners cannot easily observe and learn. This paper takes the uniform speed and uniform acceleration and descent in the descent model as an example. In the uniform acceleration, the dichotomy is introduced to solve the function extremum problem. Through MATLAB simulation, the position of the steepest descent point is found intuitively and relevant conclusions are obtained. It is hoped that the research process of the problem can be helpful to the study of refractive problems, and it is hoped that the visually intuitive simulation results can enable learners to understand the descent model more objectively.
VL  - 6
IS  - 2
ER  -

Copy | Download