| Foreword | p. v |
| Preface | p. vii |
| Some Notation | p. xi |
| Models and Ideas of Classical Mechanics | p. 1 |
| Orientation | p. 1 |
| Some Words on the Fundamentals of Our Subject | p. 2 |
| Metric Spaces and Spaces of Particles | p. 4 |
| Vectors and Vector Spaces | p. 8 |
| Normed Spaces and Inner Product Spaces | p. 11 |
| Forces | p. 16 |
| Equilibrium and Motion of a Rigid Body | p. 21 |
| D' Alembert's Principle | p. 23 |
| The Motion of a System of Particles | p. 25 |
| The Rigid Body | p. 31 |
| Motion of a System of Particles; Comparison of Trajectories; Notion of Operator | p. 33 |
| Matrix Operators and Matrix Equations | p. 40 |
| Complete Spaces | p. 44 |
| Completion Theorem | p. 48 |
| Lebesgue Integration and the Lp Spaces | p. 54 |
| Orthogonal Decomposition of Hilbert Space | p. 60 |
| Work and Energy | p. 63 |
| Virtual Work Principle | p. 67 |
| Lagrange's Equations of the Second Kind | p. 70 |
| Problem of Minimum of a Functional | p. 74 |
| Hamilton's Principle | p. 83 |
| Energy Conservation Revisited | p. 85 |
| Simple Elastic Models | p. 89 |
| Introduction | p. 89 |
| Two Main Principles of Equilibrium and Motion for Bodies in Continuum Mechanics | p. 89 |
| Equilibrium of a Spring | p. 91 |
| Equilibrium of a String | p. 95 |
| Equilibrium Boundary Value Problems for a String | p. 100 |
| Generalized Formulation of the Equilibrium Problem for a String | p. 105 |
| Virtual Work Principle for a String | p. 108 |
| Riesz Representation Theorem | p. 112 |
| Generalized Setup of the Dirichlet Problem for a String | p. 115 |
| First Theorems of Imbedding | p. 116 |
| Generalized Setup of the Dirichlet Problem for a String, Continued | p. 120 |
| Neumann Problem for the String | p. 122 |
| The Generalized Solution of Linear Mechanical Problems and the Principle of Minimum Total Energy | p. 126 |
| Nonlinear Model of a Membrane | p. 128 |
| Linear Membrane Theory: Poisson's Equation | p. 131 |
| Generalized Setup of the Dirichlet Problem for a Linear Membrane | p. 132 |
| Other Membrane Equilibrium Problems | p. 145 |
| Banach's Contraction Mapping Principle | p. 151 |
| Theory of Elasticity: Statics and Dynamics | p. 157 |
| Introduction | p. 157 |
| An Elastic Bar Under Stretching | p. 158 |
| Bending of a beam | p. 168 |
| Generalized Solutions to the Equilibrium Problem for a Beam | p. 175 |
| Generalized Setup: Rough Qualitative Discussion | p. 179 |
| Pressure and Stresses | p. 181 |
| Vectors and Tensors | p. 188 |
| The Cauchy Stress Tensor, Continued | p. 196 |
| Basic Tensor Calculus in Curvilinear Coordinates | p. 202 |
| Euler and Lagrange Descriptions of Continua | p. 207 |
| Strain Tensors | p. 208 |
| The Virtual Work Principle | p. 214 |
| Hooke's Law in Three Dimensions | p. 218 |
| The Equilibrium Equations of Linear Elasticity in Displacements | p. 221 |
| Virtual Work Principle in Linear Elasticity | p. 224 |
| Generalized Setup of Elasticity Problems | p. 227 |
| Existence Theorem for an Elastic Body | p. 231 |
| Equilibrium of a Free Elastic Body | p. 232 |
| Variational Methods for Equilibrium Problems | p. 235 |
| A Brief but Important Remark | p. 243 |
| Countable Sets and Separable Spaces | p. 243 |
| Fourier Series | p. 245 |
| Problem of Vibration for Elastic Structures | p. 249 |
| Self-Adjointness of A and Its Consequences | p. 252 |
| Compactness of A | p. 255 |
| Riesz-Fredholm Theory for a Linear, Self-Adjoint, Compact Operator in a Hilbert Space | p. 262 |
| Weak Convergence in Hilbert Space | p. 267 |
| Completeness of the System of Eigenvectors of a Self-Adjoint, Compact, Strictly Positive Linear Operator | p. 272 |
| Other Standard Models of Elasticity | p. 277 |
| Hints for Selected Exercises | p. 281 |
| Bibliography | p. 293 |
| Index | p. 295 |
| Table of Contents provided by Ingram. All Rights Reserved. |
