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Preface | |

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Mathematical Preliminaries | |

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Vectors and Tensors | |

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Vector Algebra | |

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Coordinate Transformation: Rotation of Axes | |

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Second-Rank Tensors | |

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Symmetric and Antisymmetric Tensors | |

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Prelude to Invariants of Tensors | |

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Inverse of a Tensor | |

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Additional Proofs | |

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Additional Lemmas for Vectors | |

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Coordinate Transformation of Tensors | |

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Some Identities with Indices | |

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Tensor Product | |

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Orthonormal Basis | |

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Eigenvectors and Eigenvalues | |

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Symmetric Tensors | |

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Positive Definiteness of a Tensor | |

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Antisymmetric Tensors | |

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Orthogonal Tensors | |

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Polar Decomposition Theorem | |

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Polar Decomposition: Physical Approach | |

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The Cayley-Hamilton Theorem | |

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Additional Lemmas for Tensors | |

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Identities and Relations Involving [down triangle, open] Operator | |

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Suggested Reading | |

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Basic Integral Theorems | |

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Gauss and Stokes's Theorems | |

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Vector and Tensor Fields: Physical Approach | |

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Surface Integrals: Gauss Law | |

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Evaluating Surface Integrals | |

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The Divergence | |

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Divergence Theorem: Relation of Surface to Volume Integrals | |

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More on Divergence Theorem | |

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Suggested Reading | |

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Fourier Series and Fourier Integrals | |

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Fourier Series | |

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Double Fourier Series | |

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Integral Transforms | |

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Dirichlet's Conditions | |

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Integral Theorems | |

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Convolution Integrals | |

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Fourier Transforms of Derivatives of f(x) | |

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Fourier Integrals as Limiting Cases of Fourier Series | |

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Dirac Delta Function | |

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Suggested Reading | |

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Continuum Mechanics | |

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Kinematics of Continuum | |

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Preliminaries | |

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Uniaxial Strain | |

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Deformation Gradient | |

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Strain Tensor | |

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Stretch and Normal Strains | |

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Angle Change and Shear Strains | |

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Infinitesimal Strains | |

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Principal Stretches | |

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Eigenvectors and Eigenvalues of Deformation Tensors | |

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Volume Changes | |

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Area Changes | |

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Area Changes: Alternative Approach | |

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Simple Shear of a Thick Plate with a Central Hole | |

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Finite vs. Small Deformations | |

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Reference vs. Current Configuration | |

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Material Derivatives and Velocity | |

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Velocity Gradient | |

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Deformation Rate and Spin | |

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Rate of Stretching and Shearing | |

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Material Derivatives of Strain Tensors: E vs. D | |

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Rate of F in Terms of Principal Stretches | |

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Additional Connections Between Current and Reference State Representations | |

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Transport Formulae | |

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Material Derivatives of Volume, Area, and Surface Integrals: Transport Formulae Revisited | |

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Analysis of Simple Shearing | |

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Examples of Particle and Plane Motion | |

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Rigid Body Motions | |

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Behavior under Superposed Rotation | |

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Suggested Reading | |

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Kinetics of Continuum | |

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Traction Vector and Stress Tensor | |

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Equations of Equilibrium | |

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Balance of Angular Momentum: Symmetry of [sigma] | |

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Principal Values of Cauchy Stress | |

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Maximum Shear Stresses | |

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Nominal Stress | |

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Equilibrium in the Reference State | |

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Work Conjugate Connections | |

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Stress Deviator | |

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Frame Indifference | |

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Continuity Equation and Equations of Motion | |

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Stress Power | |

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The Principle of Virtual Work | |

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Generalized Clapeyron's Formula | |

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Suggested Reading | |

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Thermodynamics of Continuum | |

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First Law of Thermodynamics: Energy Equation | |

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Second Law of Thermodynamics: Clausius-Duhem Inequality | |

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Reversible Thermodynamics | |

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Thermodynamic Relationships with p, V, T, and s | |

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Theoretical Calculations of Heat Capacity | |

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Third Law of Thermodynamics | |

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Irreversible Thermodynamics | |

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Gibbs Conditions of Thermodynamic Equilibrium | |

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Linear Thermoelasticity | |

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Thermodynamic Potentials in Linear Thermoelasticity | |

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Uniaxial Loading and Thermoelastic Effect | |

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Thermodynamics of Open Systems: Chemical Potentials | |

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Gibbs-Duhem Equation | |

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Chemical Potentials for Binary Systems | |

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Configurational Entropy | |

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Ideal Solutions | |

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Regular Solutions for Binary Alloys | |

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Suggested Reading | |

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Nonlinear Elasticity | |

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Green Elasticity | |

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Isotropic Green Elasticity | |

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Constitutive Equations in Terms of B | |

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Constitutive Equations in Terms of Principal Stretches | |

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Incompressible Isotropic Elastic Materials | |

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Elastic Moduli Tensors | |

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Instantaneous Elastic Moduli | |

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Elastic Pseudomoduli | |

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Elastic Moduli of Isotropic Elasticity | |

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Elastic Moduli in Terms of Principal Stretches | |

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Suggested Reading | |

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Linear Elasticity | |

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Governing Equations of Linear Elasticity | |

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Elementary Theory of Isotropic Linear Elasticity | |

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Elastic Energy in Linear Elasticity | |

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Restrictions on the Elastic Constants | |

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Compatibility Relations | |

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Compatibility Conditions: Cesaro Integrals | |

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Beltrami-Michell Compatibility Equations | |

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Navier Equations of Motion | |

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Uniqueness of Solution to Linear Elastic Boundary Value Problem | |

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Potential Energy and Variational Principle | |

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Betti's Theorem of Linear Elasticity | |

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Plane Strain | |

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Governing Equations of Plane Elasticity | |

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Thermal Distortion of a Simple Beam | |

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Suggested Reading | |

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Elastic Beam Problems | |

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A Simple 2D Beam Problem | |

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Polynomial Solutions to [down triangle, open superscript 4 phi] = 0 | |

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A Simple Beam Problem Continued | |

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Beam Problems with Body Force Potentials | |

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Beam under Fourier Loading | |

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Complete Boundary Value Problems for Beams | |

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Suggested Reading | |

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Solutions in Polar Coordinates | |

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Polar Components of Stress and Strain | |

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Plate with Circular Hole | |

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Degenerate Cases of Solution in Polar Coordinates | |

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Curved Beams: Plane Stress | |

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Axisymmetric Deformations | |

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Suggested Reading | |

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Torsion and Bending of Prismatic Rods | |

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Torsion of Prismatic Rods | |

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Elastic Energy of Torsion | |

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Torsion of a Rod with Rectangular Cross Section | |

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Torsion of a Rod with Elliptical Cross Section | |

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Torsion of a Rod with Multiply Connected Cross Sections | |

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Bending of a Cantilever | |

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Elliptical Cross Section | |

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Suggested Reading | |

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Semi-Infinite Media | |

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Fourier Transform of Biharmonic Equation | |

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Loading on a Half-Plane | |

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Half-Plane Loading: Special Case | |

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Symmetric Half-Plane Loading | |

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Half-Plane Loading: Alternative Approach | |

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Additional Half-Plane Solutions | |

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Infinite Strip | |

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Suggested Reading | |

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Isotropic 3D Solutions | |

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Displacement-Based Equations of Equilibrium | |

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Boussinesq-Papkovitch Solutions | |

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Spherically Symmetrical Geometries | |

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Pressurized Sphere: Stress-Based Solution | |

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Spherical Indentation | |

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Point Forces on Elastic Half-Space | |

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Suggested Reading | |

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Anisotropic 3D Solutions | |

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Point Force | |

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Green's Function | |

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Isotropic Green's Function | |

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Suggested Reading | |

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Plane Contact Problems | |

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Wedge Problem | |

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Distributed Contact Forces | |

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Displacement-Based Contact: Rigid Flat Punch | |

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Suggested Reading | |

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Deformation of Plates | |

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Stresses and Strains of Bent Plates | |

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Energy of Bent Plates | |

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Equilibrium Equations for a Plate | |

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Shear Forces and Bending and Twisting Moments | |

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Examples of Plate Deformation | |

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Rectangular Plates | |

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Suggested Reading | |

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Micromechanics | |

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Dislocations and Cracks: Elementary Treatment | |

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Dislocations | |

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Tensile Cracks | |

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Suggested Reading | |

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Dislocations in Anisotropic Media | |

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Dislocation Character and Geometry | |

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Dislocations in Isotropic Media | |

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Planar Geometric Theorem | |

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Applications of the Planar Geometric Theorem | |

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A 3D Geometrical Theorem | |

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Suggested Reading | |

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Cracks in Anisotropic Media | |

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Dislocation Mechanics: Reviewed | |

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Freely Slipping Crack | |

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Crack Extension Force | |

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Crack Faces Loaded by Tractions | |

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Stress Intensity Factors and Crack Extension Force | |

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Crack Tip Opening Displacement | |

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Dislocation Energy Factor Matrix | |

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Inversion of a Singular Integral Equation | |

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2D Anisotropic Elasticity - Stroh Formalism | |

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Suggested Reading | |

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The Inclusion Problem | |

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The Problem | |

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Eshelby's Solution Setup | |

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Calculation of the Constrained Fields: u[superscript c], e[superscript c], and [sigma superscript c] | |

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Components of the Eshelby Tensor for Ellipsoidal Inclusion | |

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Elastic Energy of an Inclusion | |

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Inhomogeneous Inclusion: Uniform Transformation Strain | |

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Nonuniform Transformation Strain Inclusion Problem | |

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Inclusions in Isotropic Media | |

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Suggested Reading | |

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Forces and Energy in Elastic Systems | |

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Free Energy and Mechanical Potential Energy | |

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Forces of Translation | |

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Interaction Between Defects and Loading Mechanisms | |

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Elastic Energy of a Dislocation | |

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In-Plane Stresses of Straight Dislocation Lines | |

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Chemical Potential | |

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Applications of the J Integral | |

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Suggested Reading | |

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Micropolar Elasticity | |

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Introduction | |

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Basic Equations of Couple-Stress Elasticity | |

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Displacement Equations of Equilibrium | |

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Correspondence Theorem of Couple-Stress Elasticity | |

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Plane Strain Problems of Couple-Stress Elasticity | |

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Edge Dislocation in Couple-Stress Elasticity | |

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Edge Dislocation in a Hollow Cylinder | |

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Governing Equations for Antiplane Strain | |

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Antiplane Shear of Circular Annulus | |

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Screw Dislocation in Couple-Stress Elasticity | |

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Configurational Forces in Couple-Stress Elasticity | |

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Energy-Momentum Tensor of a Couple-Stress Field | |

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Basic Equations of Micropolar Elasticity | |

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Noether's Theorem of Micropolar Elasticity | |

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Conservation Integrals in Micropolar Elasticity | |

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Conservation Laws for Plane Strain Micropolar Elasticity | |

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M Integral of Micropolar Elasticity | |

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Suggested Reading | |

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Thin Films and Interfaces | |

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Dislocations in Bimaterials | |

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Introduction | |

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Screw Dislocation Near a Bimaterial Interface | |

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Edge Dislocation (b[subscript x]) Near a Bimaterial Interface | |

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Edge Dislocation (b[subscript y]) Near a Bimaterial Interface | |

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Strain Energy of a Dislocation Near a Bimaterial Interface | |

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Suggested Reading | |

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Strain Relaxation in Thin Films | |

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Dislocation Array Beneath the Free Surface | |

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Energy of a Dislocation Array | |

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Strained-Layer Epitaxy | |

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Conditions for Dislocation Array Formation | |

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Frank and van der Merwe Energy Criterion | |

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Gradual Strain Relaxation | |

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Stability of Array Configurations | |

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Stronger Stability Criteria | |

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Further Stability Bounds | |

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Suggested Reading | |

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Stability of Planar Interfaces | |

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Stressed Surface Problem | |

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Chemical Potential | |

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Surface Diffusion and Interface Stability | |

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Volume Diffusion and Interface Stability | |

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2D Surface Profiles and Surface Stability | |

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Asymptotic Stresses for 1D Surface Profiles | |

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Suggested Reading | |

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Plasticity and Viscoplasticity | |

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Phenomenological Plasticity | |

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Yield Criteria for Multiaxial Stress States | |

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Von Mises Yield Criterion | |

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Tresca Yield Criterion | |

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Mohr-Coulomb Yield Criterion | |

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Gurson Yield Criterion for Porous Metals | |

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Anisotropic Yield Criteria | |

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Elastic-Plastic Constitutive Equations | |

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Isotropic Hardening | |

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Kinematic Hardening | |

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Constitutive Equations for Pressure-Dependent Plasticity | |

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Nonassociative Plasticity | |

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Plastic Potential for Geomaterials | |

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Rate-Dependent Plasticity | |

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Deformation Theory of Plasticity | |

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J[subscript 2] Corner Theory | |

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Rate-Dependent Flow Theory | |

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Elastic and Plastic Constitutive Contributions | |

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A Rate Tangent Integration | |

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Plastic Void Growth | |

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Suggested Reading | |

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Micromechanics of Crystallographic Slip | |

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Early Observations | |

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Dislocations | |

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Other Strengthening Mechanisms | |

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Measurements of Latent Hardening | |

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Observations of Slip in Single Crystals and Polycrystals at Modest Strains | |

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Deformation Mechanisms in Nanocrystalline Grains | |

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Suggested Reading | |

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Crystal Plasticity | |

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Basic Kinematics | |

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Stress and Stress Rates | |

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Convected Elasticity | |

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Rate-Dependent Slip | |

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Crystalline Component Forms | |

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Suggested Reading | |

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The Nature of Crystalline Deformation: Localized Plastic Deformation | |

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Perspectives on Nonuniform and Localized Plastic Flow | |

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Localized Deformation in Single Slip | |

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Localization in Multiple Slip | |

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Numerical Results for Crystalline Deformation | |

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Suggested Reading | |

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Polycrystal Plasticity | |

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Perspectives on Polycrystalline Modeling and Texture Development | |

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Polycrystal Model | |

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Extended Taylor Model | |

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Model Calculational Procedure | |

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Deformation Theories and Path-Dependent Response | |

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Suggested Reading | |

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Laminate Plasticity | |

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Laminate Model | |

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Additional Kinematical Perspective | |

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Final Constitutive Forms | |

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Suggested Reading | |

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Biomechanics | |

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Mechanics of a Growing Mass | |

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Introduction | |

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Continuity Equation | |

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Reynolds Transport Theorem | |

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Momentum Principles | |

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Energy Equation | |

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Entropy Equation | |

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General Constitutive Framework | |

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Multiplicative Decomposition of Deformation Gradient | |

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Density Expressions | |

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Elastic Stress Response | |

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Partition of the Rate of Deformation | |

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Elastic Moduli Tensor | |

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Elastic Strain Energy Representation | |

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Evolution Equation for Stretch Ratio | |

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Suggested Reading | |

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Constitutive Relations for Membranes | |

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Biological Membranes | |

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Membrane Kinematics | |

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Constitutive Laws for Membranes | |

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Limited Area Compressibility | |

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Simple Triangular Networks | |

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Suggested Reading | |

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Solved Problems | |

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Solved Problems for Chapters 1-33 | |

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Bibliography | |

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Index | |