| Introduction | p. ix |
| Functions of a Complex Variable | p. 1 |
| Basic definitions | p. 1 |
| Complex functions | p. 2 |
| Properties of holomorphic functions | p. 3 |
| Multiple-valued functions | p. 5 |
| Cauchy integrals | p. 9 |
| The Hilbert problem | p. 11 |
| Evaluation of the Plemelj functions | p. 17 |
| Evaluation of line integrals | p. 18 |
| The Basic Equations of Two-Dimensional Elasticity | p. 21 |
| Basic equations of elasticity | p. 21 |
| Plane strain | p. 23 |
| Boundary conditions | p. 24 |
| Generalized plane stress | p. 25 |
| Complex variable formulation | p. 28 |
| The body force potential | p. 32 |
| Resultant force over an arc | p. 33 |
| Arbitrariness of the complex potentials | p. 34 |
| Restrictions on the complex potentials | p. 35 |
| Conditions at infinity | p. 36 |
| Boundary conditions for the complex potentials | p. 40 |
| Stresses in curvilinear coordinates | p. 42 |
| Appendix | p. 44 |
| Examples | p. 46 |
| Plane and Half-Plane Problems | p. 50 |
| Infinite plane | p. 50 |
| Point forces and moments | p. 51 |
| Continuation of the complex potentials | p. 52 |
| Stress boundary value problem for a half-plane | p. 55 |
| Point forces and moments in a half-plane | p. 57 |
| Displacement boundary value problem for a half-plane | p. 58 |
| Mixed boundary value problems for a half-plane | p. 59 |
| Frictionless punch problems | p. 66 |
| A sliding punch with friction | p. 71 |
| Crack problems | p. 77 |
| Alternative methods of solution | p. 81 |
| Examples | p. 83 |
| Regions with Circular Boundaries | p. 87 |
| Introduction | p. 87 |
| Stress and displacement boundary value problems | p. 87 |
| Series method of solution | p. 90 |
| Direct method of solution | p. 97 |
| Stress and displacement continuations | p. 101 |
| Solutions to the stress and displacement problems by continuation | p. 104 |
| The mixed boundary value problem | p. 111 |
| An infinite medium with cracks along arcs of a circle | p. 114 |
| Frictionless boundary conditions | p. 118 |
| Examples | p. 125 |
| Regions with Curvilinear Boundaries | p. 129 |
| Introduction | p. 129 |
| Conformal transformations | p. 129 |
| Basic formulae | p. 137 |
| Direct method of solution | p. 141 |
| Stress and displacement continuations | p. 149 |
| Stress and displacement problems | p. 152 |
| The mixed boundary value problem | p. 158 |
| Frictionless boundary conditions | p. 161 |
| Concluding remarks | p. 169 |
| Examples | p. 170 |
| Bibliography | p. 174 |
| Summary of Formulae | p. 177 |
| Answers to the Examples | p. 178 |
| Index | p. 193 |
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