Название: Applied Mathematics for Scientists and Engineers
Автор: Youssef N. Raffoul
Издательство: CRC Press
Год: 2024
Страниц: 442
Язык: английский
Формат: pdf (true)
Размер: 10.2 MB

After many years of teaching graduate courses in applied mathematics, Youssef N. Raffoul saw a need among his students for a book reviewing topics from undergraduate courses to help them recall what they had learned, while his students urged him to publish a brief and approachable book on the topic. Thus, the author used his lecture notes from his graduate course in applied mathematical methods, which comprises three chapters on linear algebra, calculus of variations, and integral equations, to serve as the foundation for this work. These notes have undergone continuous revision.

Applied Mathematics for Scientists and Engineers is designed to be used as a graduate textbook for one semester. The five chapters in the book can be used by the instructor to create a one-semester, three-chapter course. The only prerequisites for this self-contained book are a basic understanding of calculus and differential equations. In order to make the book accessible to a broad audience, the author endeavored to strike a balance between rigor and presentation of the most challenging content in a simple format by adopting friendlier, more approachable notations and using numerous examples to clarify complex themes. The hope is both instructors and students will find, in this single volume, a refresher on topics necessary to further their courses and study.

The book is self-contained, and no knowledge beyond an undergraduate course on ordinary differential equations is required. A couple of sections of Chapters 4 and 5 require knowledge of Fourier series. To make up for this deficiency, an appendix was added. The book should serve as a one-semester graduate textbook exploring the theory and applications of topics in applied mathematics. Educators have the flexibility to design their own three-chapter, one-semester course from Chapters 2–5. The first chapter is intended as a review on the subject of ordinary differential equations, and we refer to particular sections of it in later chapters when dealing with calculus of variations and integral equations. The author made every effort to create a balance between rigor and presenting the most difficult subject in an elementary language while writing the book in order to make it accessible to a wide variety of readers. The author’s main objective was to provide as many examples as possible to help make the theory reflected in the theorems more understandable. The purpose of the book is to provide a concise and well-organized study of the theoretical foundations for the development of mathematics and problem-solving methods. This book’s text is organized in a way that is both very readable and mathematically sound. A wide range of solution strategies are shown for a number of real-world challenges.