Mathematics applied to continuum mechanics 9780898716207, 0898716209

This is my favorite text for continuum mechanics. It contains derivations not usually covered, and spends a lot of time

875 135 5MB

English Pages 613 Year 2007

Mathematics applied to continuum mechanics
9780898716207, 0898716209

Author / Uploaded
Lee A. Segel with additional material on elasticity by G. H. Handelman

Categories
Mathematics

Table of contents :
Mathematics Applied to Continuum Mechanics......Page 1
Contents......Page 9
Foreword to the Classics Edition......Page 17
Preface......Page 19
Conventions......Page 23
PART A Geometrical Prerequisites for Three-Dimensional Continuum Mechanics......Page 24
CHAPTER 1 Vectors, Determinants, and Motivation for Tensors......Page 26
CHAPTER 2 Cartesian Tensors......Page 56
PART B Problems in Continuum Mechanics......Page 98
CHAPTER 3 Viscous Fluids......Page 100
CHAPTER 4 Foundations of Elasticity......Page 167
CHAPTER 5 Some Examples of Static Problems in Elasticity......Page 216
CHAPTER 6 Introduction to Dynamic Problems in Elasticity......Page 282
PART C Water Waves......Page 320
CHAPTER 7 Formulation of the Theory of Surface Waves in an Inviscid Fluid......Page 322
CHAPTER 8 Solution in the Linear Theory......Page 358
CHAPTER 9 Group Speed and Group Velocity......Page 391
CHAPTER 10 Nonlinear Effects......Page 441
PART D Variational Methods and Extremum Principles......Page 468
CHAPTER 11 Calculus of Variations......Page 470
CHAPTER 12 Characterization of Eigenvalues and Equilibrium States as Extrema......Page 523
Bibliography......Page 593
Hints and Answers......Page 601
Authors Cited......Page 607
Subject Index......Page 608

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