Items related to Mathematical Methods in Science and Engineering
Synopsis
This book is a textbook for courses on mathematical methods, written for a multidisciplinary audience. While preserving all the successful features of the First Edition, this Second Edition corresponds to a major overhaul of the entire book through new examples, figures, topics, and improved readability. This book is written in a modular way so that each chapter is also a review of its subject and can be read independently, which makes the book not only suitable as a self-study book for students and beginning researchers but also useful as a reference for scientists. This book contains 20 chapters. Chapter 1 starts with a philosophical prelude about physics, mathematics, and mind. Chapters 2-6 present a detailed discussion of the most frequently encountered special functions in science and engineering. Chapter 7 introduces hypergeometric equation and its solutions. Chapter 8 covers special functions and contains a systematic treatment of their common properties in terms of the Sturm- Liouville theory. Chapter 9 is a natural extension of the chapter on Sturm-Liouville theory and approaches second-order differential equations of physics and engineering from the viewpoint of the theory of factorization. Chapter 10 presents an extensive treatment of coordinates, their transformations, and tensors. Continuous groups, Lie algebras, and group representations are covered in Chapter 11. Chapters 12-13 deal with complex analysis. Chapter 14 introduces the basics of fractional calculus. A comprehensive discussion of infinite series is covered in Chapter 15. Next, Chapter 16 treats integral transforms, while Chapter 17 discusses variational analysis. Integral equations are introduced in Chapter 18, while Chapter 19 introduces Green's functions. Finally, Chapter 20 is an extensive discussion of path integrals and their relation to Green's functions.
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Review
"The book is written in a clear and attractive style. It is rich in content, with a wide–ranging covering, and will be useful not only as a textbook for students of physical sciences and engineering but also as a reference book for them." (Zentralblatt MATH Database, 2011)
"The book is well written and thorough " (CHOICE, February 2007)
"The book is well written and thorough " ( CHOICE, February 2007)
From the Back Cover
An innovative treatment of mathematical methods for a multidisciplinary audience
Clearly and elegantly presented, Mathematical Methods in Science and Engineering provides a coherent treatment of mathematical methods, bringing advanced mathematical tools to a multidisciplinary audience. The growing interest in interdisciplinary studies has brought scientists from many disciplines such as physics, mathematics, chemistry, biology, economics, and finance together, which has increased the demand for courses in upper–level mathematical techniques. This book succeeds in not only being tuned in to the existing practical needs of this multidisciplinary audience, but also plays a role in the development of new interdisciplinary science by introducing new techniques to students and researchers.
Mathematical Methods in Science and Engineering′s modular structure affords instructors enough flexibility to use this book for several different advanced undergraduate and graduate level courses. Each chapter serves as a review of its subject and can be read independently, thus it also serves as a valuable reference and refresher for scientists and beginning researchers.
There are a growing number of research areas in applied sciences, such as earthquakes, rupture, financial markets, and crashes, that employ the techniques of fractional calculus and path integrals. The book′s two unique chapters on these subjects, written in a style that makes these advanced techniques accessible to a multidisciplinary audience, are an indispensable tool for researchers and instructors who want to add something new to their compulsory courses.
Mathematical Methods in Science and Engineering includes:
- Comprehensive chapters on coordinates and tensors and on continuous groups and their representations
- An emphasis on physical motivation and the multidisciplinary nature of the methods discussed
- A coherent treatment of carefully selected topics in a style that makes advanced mathematical tools accessible to a multidisciplinary audience
- Exercises at the end of every chapter and plentiful examples throughout the book
Mathematical Methods in Science and Engineering is not only appropriate as a text for advanced undergraduate and graduate physics programs, but is also appropriate for engineering science and mechanical engineering departments due to its unique chapter coverage and easily accessible style. Readers are expected to be familiar with topics typically covered in the first three years of science and engineering undergraduate programs. Thoroughly class–tested, this book has been used in classes by more than 1,000 students over the past eighteen years.
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