Numerical analysis is one of the most important branches of mathematics. It is used for: i- Giving numerical answers needed to rely on approximate methods to obtain usable answers. ii- Evaluation of definite integrations which can not be computed analytically. iii- Solving non-linear equations such to any required degree of accuracy.These equations cant be solved analytically. iv- Solving large systems of simultaneous linear equations using computer. v- Moreover, boundary value differential equations which cant be solved analytically can be solved using numerical methods. This book ""NUMERICAL METHODS with MATLAB for APPLIED ENGINEERING"" lies in six Chapters. In each Chapter the scientific material is given and illustrated in a very simple method, covered with solved Examples which are suitable for students as well as for engineers who are interested in the topics of this book. Moreover, at the end of each Chapter there are additional flow chart accompanied by one MATLAB program or more for application in addition to unsolved problems for training and applications.