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Applied Numerical Methods Using MATLAB

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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 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 only have to know where to go and how to drive a car to get to their destinations, most users only have to know how to define the problems they want to solve using MATLAB and how to use the corresponding routines to solve their problems. 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 students who want to understand the underlying principle of each algorithm.

In this book, we focus on understanding the fundamental mathematical concepts and mastering problem-solving skills using numerical methods with the help of MATLAB and skip some tedious derivations. Obviously, basic concepts must be taught so that students can properly formulate the mathematics problems. Afterwards, students 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 real life problems. The selection of exercises follows the some philosophy of making the learning easy and practical. Students should be able to solve similar problems immediately after taking the class using the MATLAB codes we provide. For most students—and particularly nonmath majors—understanding how to use numerical tools correctly in solving their problems of interest is more important than studying lengthy proofs and derivations.
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