Mathematical methods in science and engineering (Second edition.)

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.