E-ISBN: E 978-81-8487-479-2
Publication Year: 2014
Binding: Paper Back Dimension: 160mm x 240mm Weight: 400
About the book
After presenting the theory in engineers‘ language without the unfriendly abstraction of pure mathematics, several illustrative examples are discussed in great detail to see how the various functions of the Bessel family enter into the solution of technically important problems. Axisymmetric vibrations of a circular membrane, oscillations of a uniform chain, heat transfer in circular fins, buckling of columns of varying cross-section, vibrations of a circular plate and current density in a conductor of circular cross-section are considered. The problems are formulated purely from physical considerations (using, for example, Newton’s law of motion, Fourier’s law of heat conduction electromagnetic field equations, etc.) Infinite series expansions, recurrence relations, manipulation of expressions involving Bessel functions, orthogonality and expansion in Fourier-Bessel series are also covered in some detail.
Some important topics such as asymptotic expansions, generating function and Sturm-Lioville theory are relegated to a last chapter. Perhaps the reader will see how physical ideas are beautifully incorporated into mathematics and vice versa, and appreciate the compelling beauty of applied mathematics in action.
“This book beautifully blends mathematics and engineering and is a must read for advanced engineering students.”
Table of Contents
Preface / Introduction / Bessel's Equation and its Two Linearly Independent Solutions / Bessel Functions of Zero Order, J0(x) and Y0(x) / Bessel Functions of Higher, Negative and Non-integral Orders / Orthogonality Property and Expansion in a Fourier-Bessel Series / Modified Bessel Functions Iv (x) and Kv (x) / Ber, Bei; Ker, Kei Functions / Applications to Engineering: A Few More Illustrative Problems / A Brief Introduction to MAPLE / Some Additional Information, Closing Comments and Suggestions / Appendixes / Index.
Undergraduate and Postgraduate Students and Researchers