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Course Description
This course examines linear and nonlinear phenomena that exist in the universe through mathematical models, especially through systems of ordinary differential equations. Lectures will involve students in understanding planar linear systems, plane and phase portraits, system equilibrium points, stability analysis, planar nonlinear systems, high-dimensional nonlinear systems, linearization, eigenvalue analysis, and bifurcation. Methods for solving the system are carried out analytically, geometrically, topologically and numerically using software assistance.
Program Objectives (PO)
- Mengkonstruksi sistem dinamik berdasarkan fenomena di dunia nyata melalui prinsip-prinsip pemodelan yang valid
- Menganalisis penyelesaian sistem dinamik (penentuan titik ekuilibrium dan (pendekatan) solusi umum, kestabilan solusi).
- Mampu melakukan analisis bifurkasi penyelesaian sistem dinamik.
- Menganalisis secara numerik berbasis IT (software) penyelesaian sistem dinamik.
- Mengintepretasikan hasil analisis analitik dan numerik dan mengkomunikasikannya.
Aktifitas Pembelajaran
-
Pertemuan 1 Mengingat kembali prinsip-prinsip pemodelan dan memberikan contoh. -
Pertemuan 2 Pengertian sistem dinamik -
Pertemuan 3 Titik ekuilibrium sistem dinamik, penyelesaian eksak dan pendekatan (aproksimasi) menggunakan teori perturbasi. -
Pertemuan 4 Titik ekuilibrium sistem dinamik, penyelesaian eksak dan pendekatan (aproksimasi) menggunakan teori perturbasi. -
Pertemuan 5 Titik equilibrium dan jenis-jenisnya pada sistem dinamik linear planar -
Pertemuan 6 -
Pertemuan 7 -
Pertemuan 8 UTS -
Pertemuan 9 Solusi periodik dari suatu sistem dinamik nonlinear -
Pertemuan 10 Solusi periodik dari suatu sistem dinamik nonlinear -
Pertemuan 11 Teori kestabilan suatu sistem dinamik nonlinear -
Pertemuan 12 Teori kestabilan suatu sistem dinamik nonlinear -
Pertemuan 13 Bifurkasi solusi sistem dinamik dan jenis-jenisnya -
Pertemuan 14 Bifurkasi solusi sistem dinamik dan jenis-jenisnya -
Pertemuan 15 Bifurkasi melalui pembahasan sistem dinamik yang diambil dari artikel jurnal -
Pertemuan 16 UAS
References
- F. Verhulst. 2000. Nonlinear Differential Equations and Dynamical Systems . Berlin: Springer-Verlag.
- J. D. Murray. 2002 . Mathematical Biology 1, An introduction . Berlin. Springer-Verlag
- Giordano, F. R., Fox, W. P., and Horton, S. B., 2014, A First Course in Mathematical Modeling, Fifth Edition, Brooks/Cole, Cengage Learning, Boston, MA, 02210, USA.
- G. C. Layek. 2015. An Introduction to Dynamical Systems. New Delhi. Springer.
- Meyer, Walter J., 1984, Concepts of Mathematical Modeling, Dover Publications Inc., Mineola, New York.
Lecturer
Difficult Things About Education.
$75$10
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