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This book is about a standard course of numerical methods and algorithms for all graduate students with the MATLAB Program executing these methods. The reader must understand the method or the algorithm first and then tracing its executing with a scientific calculator before running it using the given MATLAB Program.The command window is very important to be followed exactly and one must be cautious about the appearance of the semicolon. It can't display the output program. The MATLAB Software Program contains many built-in functions that are very useful to be executed and one can compare them within our programs , but usually some of these are inflexible to be executed or traced . However there are so many important built-in functions such as SOLVE or INT functions. The content of this book has excluded by faults Chapter Seven which is MATLAB Programs And Methods For Solving Linear Equations. All these methods are called direct methods such as Cramer's Rule or Inverse and The Gauss-Jordan Method. Chapter six deals with approximations in which software methods such as rlegendre(n)or ChebT(n)are important. Lastly ONE must look at GISMALLA in the References.