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

Roots of a Nonlinear Equation

Optimization

Matrix Algebra

Simultaneous Linear Equations

A system of linear equations (pdf)

Gaussian Elimination

LU Decomposition

Cholesky Decomposition

LDL Decomposition

Gauss-Seidel method

Adequacy of Solutions

Eigenvalue and Singular Value

QRD

SVD

Iterative methods

Regression

Linear Regression

Non-linear Regression

Linear Least Squares

Interpolation

Polynomial Interpolation

Linear Splines

Piecewise Interpolation

Ordinary Differential Equation

Partial Differential Equation

FEM (Finite Element Method)

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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