Keskin - Ordinary differential equations for engineers : problems with MATLAB solutions

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The theory of ODEs is a well-established field, and there are quite a number of excellent books on ODEs. The aim of this book (which is written from the viewpoint of the applied mathematics in engineering) is to teach some of its fundamental ideas, results, and applications in different engineering fields. However, the style of this book is centered on the learning procedure that is based upon improving problem-solving techniques using a modern software tool. In most of these (over 600 all-solved problems that are included in this book), each relevant concept is introduced within the problem statement and solutions are illustrated computationally with the help of short software scripts in MATLAB . This kind of approach to learn and apply ODEs in particular cases makes everything practical and easy to grasp, demystifying existing theoretical complexities of the subject via the numerical experiments.

As the advent of computers has changed many things in the world, they also influenced perceptions of many engineers. Because modern computers crunch numbers of big data, carry out symbolic manipulations, and put the results of these computations into graphical form easily, many of the earlier difficult and hard-to-solve problems of ODEs are best approached with computational techniques.

Most of the problems on the applications of ODEs concentrate on various engineering projects that are aimed to engage students in the understanding and application of ODEs using MATLAB . These may illustrate direct numerical applications of the explicit formulas or more complicated methods using iterative algorithms or symbolic MATLAB solutions.

Engineers are rather interested in the solution of an ODE describing a model and the physical interpretations of the solution. Therefore, many problems and their solutions presented here are designed to provide the engineers gain best possible understanding.

The originator of each of the main ideas was cited as a historical footnote. Almost all of the chapters in the book include sufficient amount of useful references that have been cited in the related problems of the book. The readers who wish to delve deeper into a specific topic can then follow these (more than 200) references.

There are no problems left to students as homework assignments or do it by yourself studies in the book. An outstanding feature of the book is the large number and variety of the all-solved problems that are included in it. Some of these problems can be found relatively simple, while others are more challenging and used for research projects. All solutions to the problems and scripts introduced in the book have been tested using MATLAB .

Mathematical models lead to ODEs, and they are part of research in many different fields; once a particular solution method of a model equation is well understood, it can be used in any other field of application in which an ODE arises. This book presents a quantitative treatment of ODEs that arise from these models in various areas of engineering.

This book was evolved from the courses taught at Yeditepe University, Biomedical Engineering Department. The book endeavors to prepare the reader to solve realistic problems, answer the needs in the field, and it is expected to be helpful for undergraduate students as well as to graduates and experts. It is assumed that the reader is comfortable with fundamental mathematical principles and basic MATLAB use.

Acknowledgements I would like to thank Prof. A.Okay elebi of Yeditepe University, Head of Mathematics Department, for his fruitful discussions, and Prof. Lawrence F. Shampine (Mathematics Department, Southern Methodist University, Dallas, TX) for his correspondence and material supply. I also thank our research assistants and graduate students in Biomedical Engineering Department; Sibel Ozbal, Kubra Ozturk, Ibrahim Kapici, Ilayda Hasdemir, Hayrettin Can Sudor, and Ahmet Yetkin who all have offered valuable opinions and suggestions, worked with the problems and proofreading.

Finally, I would like to express my special thanks to my wife Naciye, for her endless patience, encouragement, and support.

The software presented in this book is provided as is and for academic purpose. Any express or implied warranties, including, but not limited to, the implied warranties of merchantability and fitness for a particular purpose are disclaimed. In no event shall the copyright owner or publisher be liable for any direct, indirect, incidental, special, exemplary, or consequential damages (including, but not limited to, procurement of substitute goods or services; loss of use, data, or profits; or business interruption) however, caused and on any theory of liability, whether in contract, strict liability, or tort (including negligence or otherwise) arising in any way out of the use of this software, even if advised of the possibility of such damage.

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