Essentials of Applied Mathematics for Engineers and Scientists, Second Edition

ISBN-13: 9783031012761 / Angielski / Miękka / 2012 / 185 str.

Robert Watts

Opis

The Second Edition of this popular book on practical mathematics for engineers includes new and expanded chapters on perturbation methods and theory. This is a book about linear partial differential equations that are common in engineering and the physical sciences. It will be useful to graduate students and advanced undergraduates in all engineering fields as well as students of physics, chemistry, geophysics and other physical sciences and professional engineers who wish to learn about how advanced mathematics can be used in their professions. The reader will learn about applications to heat transfer, fluid flow and mechanical vibrations. The book is written in such a way that solution methods and application to physical problems are emphasized. There are many examples presented in detail and fully explained in their relation to the real world. References to suggested further reading are included. The topics that are covered include classical separation of variables and orthogonal functions, Laplace transforms, complex variables and Sturm-Liouville transforms. This second edition includes two new and revised chapters on perturbation methods, and singular perturbation theory of differential equations. Table of Contents: Partial Differential Equations in Engineering / The Fourier Method: Separation of Variables / Orthogonal Sets of Functions / Series Solutions of Ordinary Differential Equations / Solutions Using Fourier Series and Integrals / Integral Transforms: The Laplace Transform / Complex Variables and the Laplace Inversion Integral / Solutions with Laplace Transforms / Sturm-Liouville Transforms / Introduction to Perturbation Methods / Singular Perturbation Theory of Differential Equations / Appendix A: The Roots of Certain Transcendental Equations

Spis treści

Partial Differential Equations in Engineering.- The Fourier Method: Separation of Variables.- Orthogonal Sets of Functions.- Series Solutions of Ordinary Differential Equations.- Solutions Using Fourier Series and Integrals.- Integral Transforms: The Laplace Transform.- Complex Variables and the Laplace Inversion Integral.- Solutions with Laplace Transforms.- Sturm-Liouville Transforms.- Introduction to Perturbation Methods.- Singular Perturbation Theory of Differential Equations.- Appendix A: The Roots of Certain Transcendental Equations.

O autorze

Dr. Robert G. Watts is the Cornelia and Arthur L. Jung Professor of Mechanical Engineering at Tulane University. He holds a BS (1959) in mechanical engineering from Tulane, an MS (1960) in nuclear engineering from the Massachusetts Institute of Technology and a PhD (1965) from Purdue University in mechanical engineering. He spent a year as a Postdoctoral associate studying atmospheric and ocean science at Harvard University. He has taught advanced applied mathematics and thermal science at Tulane for most of his 43 years of service to that university. Dr. Watts is the author of Keep Your Eye on the Ball: The Science and Folklore of Baseball (W. H. Freeman) and the editor of Engineering Response to Global Climate Change (CRC Press) and Innovative Energy Strategies for CO2 Stabilization (Cambridge University Press) as well as many papers on global warming, paleoclimatology energy and the physic of sport. He is a Fellow of the American Society of Mechanical Engineers.