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Persamaan Diferensial

Persamaan Diferensial. MATA KULIAH : Persamaan Diferensial KODE / SKS : 307MKBM3 DESKRIPSI SINGKAT:

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Persamaan Diferensial

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  1. PersamaanDiferensial

  2. MATA KULIAH : PersamaanDiferensial • KODE / SKS : 307MKBM3 • DESKRIPSI SINGKAT: PersamaanDiferensial (PD), merupakanpersamaanmatematis yang diterapkanuntukmenentukanperubahan-perubahanyang terjadisecarajujuh (diskrit) maupun yang terjadisecaramalar (kontinyu). Persamaandiferensialdapatdijumpaidalamberbagaibentuk, sehinggametodepenyelesaianpersamaandiferensialjugaberbeda-beda, sesuaidenganbentuknya. • TIU: SetelahmengikutimatakuliahPersamaanDiferensialini, mahasiswadiharapkandapatmengidentifikasidanmenyelesaiakanberbagaibentukPersamaanDiferensial.

  3. PersamaanDifferensial PersamaanDifferensialBiasa PersamaanDifferensialParsial Perubahankonstan • Perubahantidakkonstan • NilaiAwaldanSyarat Batas • Geraklurusberaturan • Kemiringangaris • Geraklurusberubahberaturan • Perpindahanpanas

  4. Bentuk-bentukdasar

  5. Aturanrantai • Diterapkanpadafungsi-fungsikomposit (fungsididalamfungsi) • Misalnyasebuahbesaran𝒵 bergantungpadabesaranlainnya, , dan  bergantungpadabesaranx. • Dapatdituliskanbahwa𝒵=f(),  = g(x), sehingga𝒵=f(, x), dalambentuk𝒵=f(g(x)). Jadibesaran x dapatmempengaruhi𝒵.

  6. Notasi Leibniz Contoh

  7. Diferensialimplisit

  8. Referensi: • Kartono, PenuntunBelajarPersamaanDiferensial, Andi Offset Yogyakarta, 1994. • Diktat Kuliah Persamaan Diferensial, PMIPA – UKI Toraja, 2006 • Schaum’s Easy Outline, Differential Equations, McGraw Hill Companies, 2003. • Rudolph E. Langer, a First Course in Differential Equations, John Wiley & Sons, 1954. • Steven Holzner, Differential Equations for Dummies, Wiley Publishing Inc., Indiana, 2008. • Robert L. Borelli & Courtney S. Colemann, Differential Equations – a Modelling Perspective, John Wiley & Sons, 2004 • Morris Tenenbaum & Harry Pollard, Ordinary Differential Equations, Dover Publications Inc., New York, 1963. • Henry C. Richado, Modern Introduction to Differential Equations, 2nd Ed., Academic Press, 2009

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