An Expedition to Continuum Theory

ISBN-13: 9789402405330 / Angielski / Miękka / 2016 / 399 str.

Wolfgang H. Muller

Opis

This book introduces field theory as required in solid and fluid mechanics as well as in electromagnetism. It includes the necessary applied mathematical framework of tensor algebra and tensor calculus, using an inductive approach particularly suited to beginners. It is geared toward undergraduate classes in continuum theory for engineers in general, and more specifically to courses in continuum mechanics. Students will gain a sound basic understanding of the subject as well as the ability to solve engineering problems by applying the general laws of nature in terms of the balances for mass, momentum, and energy in combination with material-specific relations in terms of constitutive equations, thus learning how to use the theory in practice for themselves. This is facilitated by numerous examples and problems provided throughout the text.

Recenzje

"This book is a true experience, and I felt real pleasure in reading it. ... I warmly recommend this book to all graduate and PhD students, as well as to young and even less young researchers who want to enter the world of continuum field theory. It is true help in understanding the basic aspects and results of the subject and acquiring solid bases for continuing the study of this discipline further." (Paolo Vannucci, Mathematical Reviews, June, 2017)

"The book provides a lucid account on the subject of continuum mechanics illustrating various fields of application for undergraduate and graduate students of engineering and physics. ... this book, for providing vision and insight and providing a bridge between various subjects, can be recommended to students and teachers as well as to anyone interested in continuum mechanics." (M. Cengiz Dökmeci, zbMATH 1328.74001, 2016)

Spis treści

1 Prologue

2 Coordinate transformations

3 Balances (in particular in Cartesian systems

4 Spatial derivatives of fields

5 Balance equations in skew curvilinear coordinate systems

6 Constitutive equations in arbitrary coordinate systems

7 A first glance on field equations

8 Observers and frames of reference in classical continuum theory

9 Problems of linear elasticity

10 Selected problems for Newtonian and Maxwellian fluids

11 Introduction to time-independent plasticity theory

12 Entropy

13 Fundamentals of electromagnetic field theory

Picture sources

Subject index

Blurb

This book introduces field theory as required in solid and fluid mechanics as well as in electromagnetism. It also presents the necessary mathematical framework, namely tensor algebra and tensor calculus, by using an inductive approach, which makes it particularly suitable for beginners. In general, the book can be used in undergraduate classes on continuum theory and, more specifically, in courses on continuum mechanics, for students of physics and engineering alike. The benefits for the readers consist of providing a sound basis of the subject as a whole and of training their ability for solving specific problems in a rational manner.  For this purpose the general laws of nature in terms of the balances for mass, momentum, and energy are applied and combined with constitutive relations, which are material specific. Various examples and homework problems illustrate how to use the theory in daily practice. Numerous mini-biographies have been added to the mathematical text for diversion and amusement.