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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 pada suatu permasalahan berbasis data apung.
Slide Materi -
Pertemuan 3 Solusi Persamaan Linear dengan metode Gaussian Elimination, LU Decomposition, Cholesky Decomposition, dan metode Iteratif beserta penerapan aplikasinya. . -
Pertemuan 4 Akar-Akar Persamaan Non-Linier: Bisection Method, Regula Falsi Method, Secant Method, dan Newton Method serta terampil dalam aplikasinya. -
Pertemuan 5 Serta terampil mempresentasikan Akar-Akar Persamaan Non-Linier: Fixed Point Iteration Method, Roots of Polynomials, Aitken’s Acccelerations, Implementation & Application. -
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 Penerapan Interpolation by Least Squares Methods: Fitting Straight Line, Fitting to a linear combinations of Functions, Implementation & Application. -
Pertemuan 10 Konsep Aproksimasi/Pencocokan Fungsi yang meliputi Piecewise Interpolation, Chebyshev Polynomials, Rational Aproximations, Implementation & Application. -
Pertemuan 11 Aproksimasi/Pencocokan (Fitting) Polinomial, yang meliputi: Piecewise Interpolations, Bezier Curves, B-Spline Curves, Implementation Applications. -
Pertemuan 12 Dengan terampil konsep Diferensiasi Numerik: Approximation Derivatives, Higher Derivatives, Implementations and Applications. -
Pertemuan 13 Secara terampil konsep Diferensiasi Numerik: Numerical Differentiation Formulas, Higher Derivatives, Implementations & Applications. -
Pertemuan 14 Dengan benar konsep dan teknik integrasi secara numerik (Definite Integration, Rectangle rules, Midpoint Rule, Trapezoidal Rule, Simpson’s Rules, Degree of Precession), implementasi dan aplikasinya dengan benar. -
Pertemuan 15 Dengan benar konsep Integrasi Numerik yang meliputi Gaussians Quadrature, Romberg Integration, Adaptive Integration, implementations, and Its Applications. -
Pertemuan 16 Soal-soal yang ditentukan secara benar.
References
- Fuad, Y. 2010. Metode Numerik. Unipress IKIP Surabaya.
- 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.
- Gezerlis, A. 2023. Numerical Methods in Physics with Python, 2nd Edition. Cambridge University Press.
- Fink, K.K. and Mathews H.J. 2004. Numerical Methods using MATLAB (4th Edition). New Jersey: Pearson Education Intern.
Lecturer
Difficult Things About Education.
$75$10
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