Calculus

Numerical Differentiation

  • Continuous Function Differentiation
  • 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


Roots of a Nonlinear Equation


Optimization




Matrix Computation

Simultaneous Linear Equations


Gausian Elimination


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

  • 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


Using SymPy ( a Python library for symbolic mathematics)




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