The necessities in Numerical Methods

Calculus

Numerical Differentiation

• 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

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

Numerical Integration

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

Matrix Algebra

Simultaneous Linear Equations

• A system of linear equations (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.

• 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

• 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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