Numbers and Factoring

Absolute Value


Trigonometric Identities

Vector Calculus

Domain for Roots of Polynomial




Characteristic Polynomial

Inequalities for Eigenvalues

Singular-Value Decomposition

Jordan Canonical Form

Matrix Exponential

Simplex Method

Artificial Variables

Dual Simplex Method

Duality Theorem

Final Tableau

Sensitivity Analysis

Complementary Slackness Theorem

Ordinary Differential Equations

Linear Differential Equations

Series Solutions of LDE

Numerical Solution of ODE

Laplace Transform

Nonlinear Systems

Equilibrium Point

Linear System

Picard's Method

Roots of Polynomials

Root Finding Methods

Interpolation Theory

and Integration

Numerical Solution
of ODE

Approximation Theory

LU Decomposition

Pivoting Strategies

Power Method

Iterative Method for Solving Linear Systems

QR Decomposition

Householder Algorithm

Vector and Matrix Norms

Inverse of triangle Matrices


Linear Codes

Cyclic Codes

Hadamard Codes

Decimal Codes

Hamming Codes

Perfect Codes

BCH Codes

Golay Codes

Shift Registers

Reed-Muller Codes

Finite Fields

Chinese Remainder Theorem

Matlab Commands

Homework I

Homework II

Homework III

Solution to the Midterm

Homework IV

Homework V


GNU Octave is a high-level language, primarily intended for numerical computations. It provides a convenient command line interface for solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with Matlab.

Octave is an open source with great tools. The commands are identical to those of MatLab.

Application: GNU Octave

Official Site:

Download Site: Link.

For convenience Octave-Forge supplies pre-built installers for Octave:

  • Windows installer (Octave and Octave-Forge).

  • for Mac OS X is a ready to run binary version of GNU Octave. It runs on most of Apple's Mac OS X computers and comes with all the free libraries that are needed. The application can also be expanded by downloading and installing further packages as described before.

Documentation: there are several good tutorials out there: In Octave Wiki, you will find user-contributed advice, examples, tips and tricks as well as links to code that is too specialized or premature to be integrated in Octave.