MATA KULIAH KALKULUS-1
Dosen Pengampu : Widya Retno Prasinta, S.T,.M.T,.
Diferensial sendiri dapat diartikan sebagai tingkat perubahan suatu fungsi atas adanya perubahan variabel bebas dari fungsi tersebut. Maka diferensial dapat diartikan sebagai tingkat perubahan dari setiap variabel y sebagai tanggapan terhadap suatu perubahan dalam variabel x.
Misalkan fungsi :
(dengan y sebagai variabel terikat dan x sebagai variabel bebasnya, artinya nilai y dipengaruhi oleh nilai x).
Diferensial Aljabar
Turunan fungsi aljabar merupakan fungsi lain dari suatu fungsi sebelumnya, sebagai contoh fungsi f menjadi f’ yang memiliki nilai tidak beraturan.
In mathematics, differential algebra is, broadly speaking, the area of mathematics consisting in the study of differential equations and differential operators as algebraic objects in view of deriving properties of differential equations and operators without computing the solutions, similarly as polynomial algebras are used for the study of algebraic varieties, which are solution sets of systems of polynomial equations. Weyl algebras and Lie algebras may be considered as belonging to differential algebra.
A natural example of a differential field is the field of rational functions in one variable over the complex numbers, More generally, every differential equation may be viewed as an element of a differential algebra over the differential field generated by the (known) functions appearing in the equation.
Rumus Diferensial Aljabar :
ANALISIS AL-QUR’AN DIFERENSIAL ALJABAR
The application of differential equations is widely used in everyday life, one of which is to estimate the population in a certain area and time using the concept of differential equations.
اَلزَّانِيَةُ وَالزَّانِيْ فَاجْلِدُوْا كُلَّ وَاحِدٍ مِّنْهُمَا مِائَةَ جَلْدَةٍۖ وَّلَا تَأْخُذْكُمْ بِهِمَا رَأْفَةٌ فِيْ دِيْنِ اللّٰهِ اِنْ كُنْتُمْ تُؤْمِنُوْنَ بِاللّٰهِ وَالْيَوْمِ الْاٰخِرِۚ وَلْيَشْهَدْ عَذَابَهُمَا طَاۤىِٕفَةٌ مِّنَ الْمُؤْمِنِيْنَ
Artinya : “Pezina perempuan dan pezina laki-laki, deralah masing-masing dari keduanya seratus kali dan janganlah rasa belas kasihan kepada keduanya mencegah kamu untuk (melaksanakan) agama (hukum) Allah jika kamu beriman kepada Allah dan hari Kemudian. Hendaklah (pelaksanaan) hukuman atas mereka disaksikan oleh sebagian orang-orang mukmin.”
From the verse above we can interpret that by committing adultery you will receive a humiliating punishment and you will even give birth to an unplanned child, therefore this is related to differential material, one of the applications of which is to estimate the population in a certain area and time using the concept of differential equations.
Sumber:
( Jurnal Matematika Terapan Oleh :Fathan Mubina Dewadi Cynthia -Tri Octavianti Nanang, Joni Wilson Sitopu Novita, Aswan, Devi Eka Wardani Meganingtyas, Leny Dhianti Haeruman, Wilminche M. D. E. L. Kelen, Erwin Randjawali, Haris Suhendar, Nining Puji Lestari, Jan Setiawan Sediyanto
https://www.researchgate.net/profile/Fathan-Dewadi/publication/371170745_MATEMATIKA_TERAPAN_II/links/64777c76d702370600c50b8e/MATEMATIKA-TERAPAN-II.pdf#page=22 Tanggal akses: 01-02-2024 )
( Perbanas Institute by Muhammad Iqbal 26 Maret 2017 https://dosen.perbanas.id/diferensial-turunan-dalam-ilmu-ekonomi-dan-bisnis/#:~:text=Pengertian%20%3A,variabel%20bebas%20dari%20fungsi%20tersebut.&text=Maka%20diferensial%20dapat%20diartikan%20sebagai,suatu%20perubahan%20dalam%20variabel%20x )
Agus Wibowo. (2022). KALKULUS. Penerbit Yayasan Prima Agus Teknik, 8(1), 1-148. Retrieved from https://penerbit.stekom.ac.id/index.php/yayasanpat/article/view/382
https://books.google.co.id/books?id=vBpzMqTH1j4C&dq=info:3x49p5B2VHwJ:scholar.google.com/&lr=&source=gbs_navlinks_s ( Tanggal akses 5/2/2024 )
https://m.rctiplus.com/news/detail/inewsid/4096250/10-contoh-soal-turunan-fungsi-aljabar–lengkap-dengan-pembahasannya (diakses pada tanggal 3 Febuari 2024) Artikel
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