Selcuk S. Bayin 
Mathematical Methods in Science and Engineering 

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.

Tabella dei contenuti

Preface xxi

Acknowledgment xxvii

1. Nature and Mathematics 1

2. Legendre Equation and Polynomials 9

3. Laguerre Polynomials 43

4. Hermite Polynomials 57

5. Gegenbauer and Chebyshev Polynomials 71

6. Bessel Functions 83

7. Gauss Equation and its Solutions 99

8. Sturm-Liouville Theory 107

9. Sturm-Liouville Systems anad the Factorization Method 121

10. Coordinates and Tensors 163

11. Continuous Group and Representations 223

12. Complex Variables and Functions 293

13. Complex Integrals and Series 335

14. Fractional Derivatives and Integrals: ‘Differintegrals’ 379

15. Infinite Series 431

16. Integral Transforms 477

17. Variational Analysis 517

18. Integral Equations 547

19. Green’s Functions 567

20. Green’s Functions and Path Integrals 633

References 665

Index 669

Circa l’autore

S. SELCUK BAYIN, PHD, is Professor in the Department of Physics at the Middle East Technical University in Ankara, Turkey. Dr. Bayin is a member of the Turkish Physical Society and the American Physical Society. He received his Ph D in physics from the University of Michigan in 1979. The author has been teaching mathematical methods for physics courses for the past eighteen years.