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Syahrini, Intan
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Computer Science & IT Economics, Econometrics & Finance Environmental Science Mathematics Physics

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Penerapan Teorema Residu Cauchy dalam Integral Tak Wajar Hanim, Safiatun; Murida, Eva; Ramadhani, Rizka Aulia; Yuni, Syarifah Meurah; Syahrini, Intan
Transcendent Journal of Mathematics and Applications Vol 3, No 2 (2024)
Publisher : Syiah Kuala University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24815/tjoma.v3i2.39119

Abstract

This article discusses the application of Cauchy's Residue Theorem to improper integrals of real functions. The theorem states that the integral along a simple closed contour is equal to 2i times the sum of the residues of the function at single points located inside the contour. Furthermore, the article describes various methods for determining the residues, including the use of Laurent series and Taylor series. In addition, Jordan's lemma is also referenced in this article. Cauchy's Residue Theorem on improper integrals can be employed to resolve integrals that are challenging to compute using traditional real analysis methods. By identifying the residue of the integral at a singularity within a closed contour, the integral along the contour can be evaluated. The application of the residue theorem to improper integrals can be expressed in a specific form to facilitate calculation. This method offers several advantages over conventional methods. Some of the sources consulted in the preparation of this article include the following publications: Complex Analysis, Residue Theorem and Its Applications, and Calculus Applications in Physics Lectures.
Application of The Autoregressive Integrated Moving Average (ARIMA) Box-Jenkins Method in Forecasting Inflation Rate in Aceh Syahrini, Intan; Radhiah, Radhiah; Damanik, Wirda Fadhila
Transcendent Journal of Mathematics and Applications Vol 2, No 1 (2023)
Publisher : Syiah Kuala University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24815/tjoma.v2i1.31702

Abstract

Inflation is an increase in the price of goods and services, in general that occurs continuously over a certain period. The government in a country or region needs to examine and pay attention to inflation data in the past to find out the inflation rate movement in a region. This study aims to predict the inflation rate in Aceh Province in the period September 2021 to January 2022 using the Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) method. The best model obtained in this study is the ARIMA(2,0,2) model, which has a reasonably good forecasting accuracy value. The accuracy measured using the RMSE (Root of Mean Square) and MAE (Mean Absolute Error) values are close to zero, namely 0.474 and 0.373, respectively. The forecast results from inflation value this period classified into the category of mild inflation, where the increase in the price of goods that occurred during that period was still below 10%, so it did not impact the regional economy.
Comparison Of Fuzzy Time Series Chen and Fuzzy Time Series Markov Chain Methods in Forecasting Consumer Price Index in Banda Aceh Syahrini, Intan; Tamimi, Afifah; Zuhra, Rahma; Amri, Saiful; Oktavia, Rini
Transcendent Journal of Mathematics and Applications Vol 4, No 1 (2025)
Publisher : Syiah Kuala University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24815/tjoma.v4i1.46243

Abstract

The Consumer Price Index (CPI) is utilized to determine a country's inflation and deflation rate. Inflation decreases the buying power of consumers; meanwhile, continuous deflation will lead to a recession. characterized by a stagnant economy and a diminished willingness among manufacturers to innovate. The CPI trends serve as a valuable economic indicator and a standard for manufacturing costs that reflect price fluctuations at the consumer level for specific goods and services. This study aims to forecast the CPI in Banda Aceh, Indonesia, utilizing CPI data in the region from January 2017 to October 2022 by applying the Fuzzy Time Series Chen and Fuzzy Time Series Markov Chain methods. Forecasting accuracy is assessed by the Mean Absolute Percentage Error (MAPE) and Mean Absolute Error (MAE). The Fuzzy Time Series Chen method obtained a MAPE of 2.98% and an MAE of 3.64, whereas the Fuzzy Time Series Markov Chain method attained a MAPE of 1.07% and an MAE of 1.27. This indicates that the predicting accuracy of the Fuzzy Time Series Markov Chain surpasses that of Chen's Fuzzy Time Series, leading to the conclusion that CPI forecasting in Banda Aceh City utilizing the Fuzzy Time Series Markov Chain approach is more precise.
Co-Authors Damanik, Wirda Fadhila Hanim, Safiatun Murida, Eva Oktavia, Rini Rahma Zuhra Ramadhani, Rizka Aulia Saiful Amri Sukamto, Ika Sumiyarsi Syarifah Meurah Yuni Tamimi, Afifah