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Numerical Computation for Engineers (Komputasi Numerik untuk Insinyur)

Kursus ini akan memberi pemahaman tentang Sistem Persamaan Linear dan Non Linear, Diferensial, Optimasi, persamaan Matematika yang Mewakili Fenomena Rekayasa serta Penggunaannya dalam Penyelesaian Numerik. pembelajaran ini akan mengajarkan dan menerapkan prinsip-prinsip koding sebagai alternatif untuk memecahkan masalah di bidang teknik kimia.

References:

  1. Constantinides, A. & Mostoufi, N. (1999). Numerical Methods for Chemical Engineers with MATLAB Applications. Prentice Hall.
  2. Finlayson, B. A. (2006). Introduction to Chemical Engineering Computing. John wiley & Sons, Inc.

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Samuel Pangeran Aletheia

Numerical Solutions of Nonlinear Equations

Complex nonlinear equations is often solved with numerical methods. This session includes materials about:

  1. Types of Roots and Their Approximation
  2. The Newton-Raphson Method
  3. Newton's Method for Simultaneous Nonlinear Equations
  4. Secant Method

Simultaneous Linear Algebraic Equations

Linear equations that contain more than 2 variables are often solved with numerical methods. The materials discussed includes:

  1. Review of Selected Matrix and Vector Operations
  2. Gauss' Elimination Method
  3. Gauss-Jordan Reduction Method
  4. Jacobi Method

Finite Differences Methods

Finite difference is used to solve differential equations numerically. The materials discussed includes:

  1. Backward Finite Differences
  2. Forward Finite Differences
  3. Central Finite Differences
  4. Difference Equations and the Solutions

Numerical Differentiation

This session is the continuation of finite difference session, which discuss:

  1. Differentiation by Backward Finite Differences
  2. Differentiation by Forward Finite Differences
  3. Differentiation by Central Finite Differences

Numerical Integration

Integrating complex equations mostly done by using numerical methods. This session discuss materials:

  1. Trapezoidal Rules
  2. Simpson's 1/3 Rule
  3. Simpson's 3/8 Rule

Numerical Solution of Ordinary Differential Equations: Initial-Value Problems

Ordinary differential equations need initial condition to solve numerically. This session will discuss initial value problems, which includes:

  1. "Linear Ordinary Differential Equations
  2. Euler and Modified Euler Methods
  3. Runge-Kutta Methods
  4. Simultaneous Differential Equations
  5. Stability and Error Propagation of Euler and Runge-Kutta Methods

Numerical Solution of Ordinary Differential Equations: Boundary-Value Problems

Another boundary condition to solve ODE numerically is by boundary-value. This sessions includes materials in:

  1. Shooting Method
  2. The Finite Difference Method
  3. Collocation Method

Numerical Solution of Partial Differential Equations

Partial differential equations solved numerically using finite difference. This session includes:

  1. Classification of Partial Differential Equations
  2. Initial and Boundary Conditions
  3. Solution Using Finite Differences