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Mata Kuliah : Metode Numerik�Minggu ke 1

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Capaian Pembelajaran Mata Kuliah

  • Mahasiswa mampu menjelaskan pentingnya metode numerik sebagai solusi keterbatasan pendekatan analitik.
  • Mahasiswa mampu melakukan komputasi & menemukan solusi dari sekumpulan data berdasarkan metode numerik.
  • Mahasiswa mampu menerapkan metode numerik dengan menggunakan program komputer.

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Mahasiswa dapat memahami definisi Numerical Methods (Metode Numerik) dan implementasinya

Tujuan perkuliahan

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Kontrak Perkuliahan

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What is Numerical Method

  • Using basic operation
  • Give an approximate solution

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Why Numerical Method

Help solving Mathematical Problem (a lot)

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Numerical Method vs Analytical Approach

Numerical Method

Analytical Approach

Approximate Solution

Exact Solution/True Solution

Has Error

No Error

Solve some Problem

Sometimes solve problem

Designed to do with Computer

Easier to do with Capable Human

Easy to understand

Hard to understand

Based on Hard Work

Based on mathematical manipulation

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Example

  •  

Numerical

Analytic

 

 

Main Method

Pivot

Iteration

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Example (Cont.)

  •  

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Numerical Method (Content)

Basic

Numerical Approach

Numerical Problem

Algorithm

Problem and Algorithm

Algebraic Equation

Interpolation

Matrix

Differentiation

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Numerical Method (term)

  • Numerical Problem�A problem that can be solved by numerical method
  • Approximate Solution�A solution that close to exact/true solution
  • Numerical Error�An Error that generated by Numerical Method�- Exact Error�- Relative Error

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Numerical Problem

  • Non linear equation
    • Metode Tertutup : Tabel, Biseksi, Regula Falsi,
    • Metode Terbuka : Secant, Newton Raphson, Iterasi Sederhana
  • Linear equation
    • Eliminasi Gauss, Eliminasi Gauss Jordan, Gauss Seidel
  • Differentiation
    • Selisih Maju, Selisih Tengahan, Selisih Mundur
  • Integration
    • Integral Reimann, Integrasi Trapezoida, Simpson, Gauss
  • Interpolation
    • Interpolasi Linier, Quadrat, Kubik, Polinom Lagrange, Polinom Newton
  • Regression
    • Regresi Linier dan Non Linier
  • Differential Equation
    • Euler, Taylor

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