The necessities in Numerical Methods

Numerical Differentiation

 * Background on Differentiation ([[Media:NM.Diff.1Background.20240625.pdf |pdf]])
 * Continuous Function Differentiation ([[Media:NM.Diff.1ContDiff.20240711.pdf |pdf]])
 * Discrete Function Differentiation
 * Forward, Backward, Central Divided Difference
 * High Accuracy Differentiation
 * Richardson Extrapolation
 * Unequal Spaced Data Differentiation
 * Numerical Differentiation with Octave

Numerical Integration

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

Simultaneous Linear Equations

 * A system of linear equations ([[Media:SystemLinearEq.20240521.pdf |pdf]])

Using Symbolic Package in Octave

 * Visit http://octave.sourceforge.net/index.html
 * Download symbolic-1.0.9.tar.gz


 * 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.

./configure ./make ./make INSTALL_PATH=/usr/share/octave/packages/3.2/symbolic-1.0.9
 * After extracting files from symbolic-1.0.9.tar.gz, I followed the following steps.


 * 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

 * Symbolic Mathematics in Matlab/GNU Octave (http://faraday.elec.uow.edu.au/subjects/annual/ECTE313/Symbolic_Maths.pdf)


 * Symbolic Computations (http://www.math.ohiou.edu/courses/math344/lecture7.pdf)

Using SymPy ( a Python library for symbolic mathematics)
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