| Preface |
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vii | |
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Chapter 1 The Tools of Calculus |
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1 | (66) |
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1.1 Is Mathematical Proof Necessary? |
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2 | (4) |
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1.2 Abstraction, Understanding, Infinity |
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6 | (2) |
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8 | (3) |
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11 | (4) |
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15 | (4) |
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19 | (2) |
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1.7 How to Measure Length |
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21 | (12) |
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33 | (2) |
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35 | (7) |
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1.10 The Length of a Curve |
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42 | (2) |
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1.11 Multidimensional Integrals |
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44 | (3) |
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1.12 Approximate Integration |
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47 | (5) |
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1.13 On the Notion of a Function |
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52 | (1) |
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1.14 Differential Equations |
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53 | (6) |
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59 | (2) |
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1.16 Petroleum Exploration and Recovery |
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61 | (2) |
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63 | (2) |
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65 | (2) |
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Chapter 2 The Mechanics of Continua |
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67 | (84) |
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67 | (4) |
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2.2 The Main Notions of Classical Mechanics |
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71 | (3) |
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2.3 Forces, Vectors, and Objectivity |
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74 | (2) |
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2.4 More on Forces; Statics |
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76 | (4) |
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80 | (4) |
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84 | (10) |
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94 | (6) |
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2.8 Principal Axes and Invariants of the Stress Tensor |
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100 | (2) |
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2.9 On the Continuum Model and Limit Passages |
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102 | (2) |
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2.10 Equilibrium Equations |
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104 | (4) |
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108 | (5) |
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2.12 Generalized Hooke's Law |
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113 | (1) |
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114 | (1) |
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2.14 Boundary Value Problems |
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115 | (3) |
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2.15 Setup of Boundary Value Problems of Elasticity |
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118 | (2) |
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2.16 Existence and Uniqueness of Solution |
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120 | (6) |
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2.17 Energy; Minimal Principle for a Spring |
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126 | (2) |
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2.18 Energy in Linear Elasticity |
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128 | (4) |
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2.19 Dynamic Problems of Elasticity |
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132 | (2) |
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2.20 Oscillations of a String |
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134 | (3) |
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2.21 Lagrangian and Eulerian Descriptions of Continuum Media |
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137 | (3) |
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2.22 The Equations of Hydrodynamics |
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140 | (2) |
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2.23 D'Alembert--Euler Equation of Continuity |
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142 | (2) |
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2.24 Some Other Models of Hydrodynamics |
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144 | (1) |
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2.25 Equilibrium of an Ideal Incompressible Liquid |
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145 | (3) |
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2.26 Force on an Obstacle |
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148 | (3) |
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Chapter 3 Elements of the Strength of Materials |
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151 | (50) |
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3.1 What Are the Problems of the Strength of Materials? |
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151 | (1) |
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3.2 Hooke's Law Revisited |
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152 | (5) |
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3.3 Objectiveness of Quantities in Mechanics Revisited |
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157 | (2) |
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159 | (2) |
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3.5 Saint-Venant's Principle |
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161 | (2) |
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163 | (2) |
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3.7 Linearity vs. Nonlinearity |
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165 | (1) |
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3.8 Dislocations, Plasticity, Creep, and Fatigue |
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166 | (6) |
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172 | (3) |
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175 | (2) |
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177 | (1) |
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3.12 A Few Words on the History of Thermodynamics |
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178 | (2) |
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3.13 Thermodynamics of an Ideal Gas |
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180 | (2) |
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3.14 Thermodynamics of a Linearly Elastic Rod |
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182 | (4) |
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186 | (2) |
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3.16 Static Stability of a Straight Beam |
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188 | (5) |
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3.17 Dynamical Tools for Studying Stability |
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193 | (2) |
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3.18 Additional Remarks on Stability |
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195 | (3) |
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198 | (3) |
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Chapter 4 Some Questions of Modeling in the Natural Sciences |
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201 | (18) |
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4.1 Modeling and Simulation |
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201 | (2) |
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4.2 Computerization and Modeling |
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203 | (3) |
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4.3 Numerical Methods and Modeling in Mechanics |
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206 | (2) |
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4.4 Complexity in the Real World |
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208 | (1) |
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4.5 The Role of the Cosine in Everyday Measurements |
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209 | (2) |
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4.6 Accuracy and Precision |
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211 | (2) |
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4.7 How Trees Stand Up against the Wind |
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213 | (3) |
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4.8 Why King Kong Cannot Be as Terrible as in the Movies |
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216 | (3) |
| Afterword |
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219 | (2) |
| Recommended Reading |
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221 | (2) |
| Index |
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223 | |
Lisainfo e-raamatute kohta