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This book introduces applied numerical methods for engineering and science students in sophomore to senior levels; it targets the students of today who do not like and/or do not have time to derive and prove mathematical results. It can also serve as a reference to MATLAB applications for professional engineers and scientists, since many of the MATLAB codes presented after introducing each algorithm’s basic ideas can easily be modified to solve similar problems even by those who do not know what is going on inside the MATLAB routines and the algorithms they use. Just as most drivers have to know only where to go and how to drive a car to get to their destinations, most users have to know only how to formulate their problems that they want to solve using MATLAB and how to use the corresponding routines for solving them.We never deny that detailed knowledge about the algorithm (engine) of the program (car) is helpful for getting safely to the solution (destination); we only imply that one-time users of any MATLAB program or routine may use this book as well as the readers who want to understand the underlying principle/equations of each algorithm. This book mainly focuses on helping readers understand the fundamental mathematical concepts and practice problem-solving skills using MATLAB-based numerical methods, skipping some tedious derivations/proofs. Obviously, basic concepts must be taught so that readers can properly formulate the mathematics problems. Afterward, readers can directly use the MATLAB codes to solve practical problems. Almost every algorithm introduced in this book is followed by example MATLAB code with a friendly interface so that students can easily modify the code to solve their own problems. The selection of exercises follows the same philosophy of making the learning easy and practical. Readers should be able to solve similar problems immediately after reading the materials and codes listed in this book. For most students – and particularly non-math majors – understanding how to use numerical tools correctly in solving their problems of interest is more important than doing lengthy proofs and derivations.