Implementation of Small Term Reduction in Taylor Series in Analytical Physics Problem
DOI:
https://doi.org/10.37891/kpej.v7i1.646Keywords:
Analytic physics, physics problems, small term, small term reduction, Taylor seriesAbstract
This research is motivated by the low ability of students to apply mathematical solving methods to analytic physics. The purpose of this research is to show the implementation of small term reduction in Taylor series on analytic physics problems. The analytical physics material described in this study is the pendulum oscillation material, heat conduction and the perturbation quantum state function. This research method involves a mathematical derivation of the Taylor series formation. The epicenter of the idea of reducing the Taylor series in this study is the use of very small terms in the Taylor series to reduce terms with values reaching towards zero, namely the third term and the fourth term. This small term reduction method is spread into problems of mechanics, oscillations, heat, electricity, magnetism and quantum mechanics. The results of this study show that after using the small term reduction principle, the equations to be solved are like first-order and second-order differential equations. By solving these equations we get a variable physical quantity.References
Anisa, A., Medriati, R., & Putri, D. H. (2019). Pengaruh Model Quantum Learning Terhadap Pemahaman Konsep dan Hasil Belajar Siswa Kelas X. Jurnal Kumparan Fisika, 2(3), 201–208. https://doi.org/10.33369/jkf.2.3.201-208
Antera, S. (2021). Professional Competence of Vocational Teachers: a Conceptual Review. Vocations and Learning, 14(3), 459–479. https://doi.org/10.1007/s12186-021-09271-7
Ariani, T. (2020). Analysis of Students’ Critical Thinking Skills in Physics Problems. Kasuari: Physics Education Journal (KPEJ), 3(1), 1–17. https://doi.org/10.37891/kpej.v3i1.119
Chen, H. (2006). A Power Series Expansion and Its Applications. International Journal of Mathematical Education in Science and Technology, 37(3), 362–368. https://doi.org/10.1080/00207390500433384
Chen, P., Villa, U., & Ghattas, O. (2019). Taylor Approximation and Variance Reduction for PDE-Constrained Optimal Control Under Uncertainty. Journal of Computational Physics, 385, 163–186. https://doi.org/10.1016/j.jcp.2019.01.047
Djesse, A., Tufukama, M., Mele, F. M., & Mabe, P. M. (2023). Vérification de la loi de fourrier dans la conduction thermique des métaux : Etude Expérimentale [Verification of Fourier ’ s Law in Heat Cnduction of Metals : Experimental study]. 41(2), 580–587.
Frhan Al-Maaitah, I. (2021). Taylor Series and Getting the General Solutions for the Equations of Motion Using Poisson Bracket Relations. World Journal of Applied Physics, 6(3), 47. https://doi.org/10.11648/j.wjap.20210603.12
Goudsmit, S. A. (1929). Quantum mechanics. Journal of the Franklin Institute, 207(4), 523–524. https://doi.org/10.1016/S0016-0032(29)91835-4
Motlan, H., Sinulinggga, K., & Siagian, H. (2016). Inquiry and Blended Learning Based Learning Material Development for Improving Student Achievement on General Physics I of Mathematics and Natural Science of State University of Medan. Journal of Education and Practice, 7(28), 171–176.
He, J. H. (2020). Taylor Series Solution for a Third Order Boundary Value Problem Arising in Architectural Engineering. Ain Shams Engineering Journal, 11(4), 1411–1414. https://doi.org/10.1016/j.asej.2020.01.016
Kereh, C. T., Tjiang, P. C., & Sabandar, J. (2014). Korelasi Penguasaan Materi Matematika Dasar dengan Penguasaan Materi Pendahuluan Fisika Inti. Indonesian Journal of Physics Education, 10(2), 140–149. https://doi.org/10.15294/jpfi.v10i2.3449
Kouki, R., & Griffiths, B. J. (2020). Introducing Taylor Series and Local Approximations using a Historical and Semiotic Approach. International Electronic Journal of Mathematics Education, 15(2). https://doi.org/10.29333/iejme/6293
Mazzolani, A., Macdonald, C. M., & Munro, P. R. T. (2022). Application of a Taylor Series Approximation to the Debye–Wolf Integral in Time-Domain Numerical Electromagnetic Simulations. Journal of the Optical Society of America A, 39(5), 927. https://doi.org/10.1364/josaa.448797
Mohiuddin, A. M., & Saha, B. K. (2023). A Comparative Study Amoong Perturbation Method, Taylor Series Method, Adomian Decomposition Method, for Solving Airy Diferential Equ. December 2020.
Novák, L., & Novák, D. (2020). On Taylor Series Expansion for Statistical Moments of Functions of Correlated Random Variables.. Symmetry, 12(8). https://doi.org/10.3390/SYM12081379
Ö?rekçi, S. (2015). Generalized Taylor Series Method for Solving Nonlinear Fractional Differential Equations with Modified Riemann-Liouville Derivative. Advances in Mathematical Physics, 2015. https://doi.org/10.1155/2015/507970
Paudel, A., Gupta, S., Thapa, M., Mulani, S. B., & Walters, R. W. (2022). Higher-Order Taylor Series Expansion for Uncertainty Quantification with Efficient Local Sensitivity. Aerospace Science and Technology, 126(April). https://doi.org/10.1016/j.ast.2022.107574
Rostikawati, D. A., & Saefullah, A. (2022). Analysis of the Needs Basic Physics Teaching Materials in Industrial Engineering Major. Gravity: Jurnal Ilmiah Penelitian Dan Pembelajaran Fisika, 8(1), 34–40. https://doi.org/10.30870/gravity.v8i1.14865
Sales, L. De, Silva, J. A., Decen, N., Ferros, P., Diego, A., Farias, S., Decen, N., Ferros, P., Decen, N., Ferros, P., De, C. M., & Silva, A. D. (2021). Gaussian integral by Taylor series and applications de Taylor e aplicac e Tecnologia Introduction Mathematics is present in the teaching and research of several other areas such as physics. 1–15.
Satek, V., Veigend, P., & Necasova, G. (2019). Taylor Series Based Integration in Electric Circuits Simulations. Advances in Electrical and Electronic Engineering, 17(3), 352–359. https://doi.org/10.15598/aeee.v17i3.3369
Simangunsong, S. (2022). Student ’ s Professional Competence Development Using the Blended Learning. 08(02), 70–77. https://doi.org/10.30870/gravity.v8i2.15932
Simangunsong, S., & Trisna, I. (2021). Analisa Kognitif Model Blended Learning dengan Pendekatan Kalkulus Dasar. Jurnal Pendidikan Fisika Dan Teknologi, 7(1), 11–16. https://doi.org/10.29303/jpft.v7i1.2580
Syukri, M., Putri, E. S., Halim, L., Kuala, U. S., & Mekah, U. S. (2023). Analysis of Solving Physics Problems Using The Minnesota Model for Mechanics Concepts. 8(3), 296–303.
Truchet, G., & Leconte, P. (2019). Small Sample Reactivity Worths Calculation: Exact Perturbation Theory and Monte Carlo transport. International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019, 1886–1894.
Downloads
Published
How to Cite
Issue
Section
License
License and Copyright Agreement
In submitting the manuscript to the journal, the authors certify that:
- They are authorized by their co-authors to enter into these arrangements.
- The work described has not been formally published before, except in the form of an abstract or as part of a published lecture, review, thesis, or overlay journal. Please also carefully read Kasuari: Physics Education Journal Posting Your Article Policy at http://journalfkipunipa.org/index.php/kpef/about
- That it is not under consideration for publication elsewhere,
- That its publication has been approved by all the author(s) and by the responsible authorities tacitly or explicitly of the institutes where the work has been carried out.
- They secure the right to reproduce any material that has already been published or copyrighted elsewhere.
- They agree to the following license and copyright agreement.
Copyright
Authors who publish with Kasuari: Physics Education Journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (CC BY-SA 4.0) that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
Whatsapp 
