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Course Description
The Numerical Methods course aims to provide the basic principles of numerical solutions without abandoning the analytical proof scheme. Understanding numerical solutions includes the concept of error including sources and ways to prevent them, approximation of the roots of nonlinear equations including solution methods and analytical proof schemes, interpolation including approximation and smoothing of data, as well as numerical differentiation and integration with analytical proof schemes. Learning is carried out by applying a combination of problem-based learning approaches and collaborative learning based on problems determined based on eco-techno-entrepreneur-maths. The assessment is determined with proportional weights and is carried out during the learning process with active interactive participation, presentations, assignments and mid-semester exams, as well as final semester exams.
Program Objectives (PO)
- Memahami prinsip dasar paradigma numerik, estimasi galat yang fisibel dan skema pembuktian analitiknya, serta penyelesaian numerik dalam permasalahan berbasis techno-ecopreneur-maths.
- Menentukan aproksimasi akar-akar persamaan nonliner, estimasi galat dari akar-akar persamaan nonlinear beserta skema pembuktian analitiknya serta terampil mengaplikasikannya dalam penyelesaian permasalahan berbasis techno-ecopreneur-maths.
- Memahami prinsip pencocokan kurva, interpolasi polinom beserta skema pembuktian analitiknya dan terampil menerapkannya dalam penyelesaian permasalahan berbasis techno-ecopreneur-maths.
- Mengaplikasikan prinsip smoothing data, aproksimasi, spline kubik beserta skema pembuktian analitiknya dan terampil menerapkannya dalam penyelesaian permasalahan berbasis techno-ecopreneur-maths.
- Memahami direvatif dan integrasi numerik beserta skema pembuktian analitiknya serta terampil menerapkannya dalam penyelesaian permasalahan berbasis techno-ecopreneur-maths.
Aktifitas Pembelajaran
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Pertemuan 1 Perbedaan paradigma numerik vs paradigma analitik, sistem basis biner, konsep galat dan aplikasinya pada program Excel. -
Pertemuan 2 Konsep pembulatan, pemotongan, perambatan galat, galat maksimum, galat mutlak, galat relatif, pencegahan galat, serta implementasi dan aplikasinya.
Slide Materi -
Pertemuan 3 Solusi Persamaan Linear, dengan metode Gaussian Elimination, LU Decomposition, Cholesky Decomposition, dan Iterative. -
Pertemuan 4 Akar-Akar Persamaan Non-Linier: Bisection Method, Regula Falsi Method, Secant Method, dan Newton Method. -
Pertemuan 5 -
Pertemuan 6 Interpolasi Linier & Interpolasi Polinom: Interpolation, Data with Difference Uniform; Table of Difference, Linear Interpolation, Polynom Interpolation. -
Pertemuan 7 Interpolasi Invers and Spline Curves: Interpolation with Data Non Uniform, Lagrange Interpolation, Invers Interpolation, serta Implementation & Application. -
Pertemuan 8 -
Pertemuan 9 Prinsip penghalusan dan spline kubik serta terapannya -
Pertemuan 10 -
Pertemuan 11 -
Pertemuan 12 -
Pertemuan 13 -
Pertemuan 14 -
Pertemuan 15 -
Pertemuan 16
References
- Gerald, C.F. and Wheatley, P.O. 2004. Applied Numerical Analysis Seventh Edition. Boston: Pearson Education Inc.
- LeMesurier, B. 2024. Introduction to Numerical Methods and Analysis with Python. http://lemesurierb.people.cofc.edu/introduction-to-numerical-methods-and-analysis-python/
- Kharab, A. and Guenther, R.B. 2019. An Introduction to Numerical Methods a MATLAB Approach 4th Edition. Florida: CRC Press.
Lecturer
Difficult Things About Education.
$75$10
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