This book is a text and reference book on numerical methods 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. The book is written carefully so that the readers can read without guidance by an instructor. Each chapter has exercise problems which are answered in the back of the book. This book is seamlessly continued from author’s previous book, GNU Octave Primer for beginners.