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The necessities in Numerical Methods

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Calculus

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Numerical Differentiation

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  • Background on Differentiation (pdf)
  • Continuous Function Differentiation (pdf)
  • Discrete Function Differentiation (pdf)
  • Forward, Backward, Central Divided Difference
  • High Accuracy Differentiation
  • Richardson Extrapolation
  • Unequal Spaced Data Differentiation
  • Numerical Differentiation with Octave


Non-linear Equations

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  • Bisection Method (pdf)
  • Newton-Raphson Method
  • Secant Method
  • False-Position Method


Numerical Integration

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  • Trapezoidal Rule
  • Simpson's 1/3 Rule
  • Romberg Rule
  • Gauss-Quadrature Rule
  • Adaptive Quadrature


Roots of a Nonlinear Equation

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Optimization

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Matrix Algebra

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Simultaneous Linear Equations

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  • A system of linear equations (pdf)



Gaussian Elimination

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LU Decomposition

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Cholesky Decomposition

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LDL Decomposition

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Gauss-Seidel method

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Adequacy of Solutions

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Eigenvalue and Singular Value

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Iterative methods

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Regression

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Linear Regression

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Non-linear Regression

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Linear Least Squares

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Interpolation

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Polynomial Interpolation

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Linear Splines

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Piecewise Interpolation

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Ordinary Differential Equation

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Partial Differential Equation

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FEM (Finite Element Method)

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Using Symbolic Package in Octave

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  • In Ubuntu, using the Ubuntu Software Center, I installed GiNac and CLN related software and symbolic package for Octave. But it did not properly installed.
  • After extracting files from symbolic-1.0.9.tar.gz, I followed the following steps.
./configure 
./make 
./make INSTALL_PATH=/usr/share/octave/packages/3.2/symbolic-1.0.9 
  • While doing this, I got an error message related to mkoctfile. So, I used the following command: sudo apt-get install ocatve3.2-headers. Then I was able to install the symbolic packages in the Ubuntu.

Read some tutorials about symbolic computation

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Using SymPy ( a Python library for symbolic mathematics)

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