This book is a text and reference book on methods of numerical analysis applied with GNU Octave and Matlab at college entry level. The book describes linear algebra, polynomials and polynomial interpolations, numerical integration, difference approximation, roots finding for non-linear equations, and curve fitting to experimental data. Numerical methods described are all applied on GNU Octave and Matlab with ample explanations about the GNU Octave and Matlab commands. Each chapter has exercise problems which are fully answered in the back of the book along with the lists of programs used to answer the problems. This book is seamlessly continued from author's other books, GNU Octave Primer for Beginners or Octave/Matlab Primer and Applications. For more information about these books, please visit http: //octave.ismr.us