An Expedition to Continuum Theory [Hardcover]

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.

This robust introduction to the field theory required for solid and fluid mechanics, as well as electromagnetism, has a wealth of examples and problems. It adopts an inductive approach to the relevant applied mathematics that is especially suited to beginners.

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

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