APPROXIMATING PERFECTION: CONTENTS
Preface
1. The Tools of Calculus
1.1 Is Mathematical Proof Necessary?
1.2 Abstraction, Understanding, Infinity
1.3 Irrational Numbers
1.4 What Is a Limit?
1.5 Series
1.6 Function Continuity
1.7 How to Measure Length
1.8 Antiderivatives
1.9 Definite Integral
1.10 The Length of a Curve
1.11 Multidimensional Integrals
1.12 Approximate Integration
1.13 On the Notion of a Function
1.14 Differential Equations
1.15 Optimization
1.16 Petroleum Exploration and Recovery
1.17 Complex Variables
1.18 Moving On
2. The Mechanics of Continua
2.1 Why Do Ships Float?
2.2 The Main Notions of Classical Mechanics
2.3 Forces, Vectors, and Objectivity
2.4 More on Forces; Statics
2.5 Hooke's Law
2.6 Bending of a Beam
2.7 Stress Tensor
2.8 Principal Axes and Invariants of the Stress Tensor
2.9 On the Continuum Model and Limit Passages
2.10 Equilibrium Equations
2.11 The Strain Tensor
2.12 Generalized Hooke's Law
2.13 Constitutive Laws
2.14 Boundary Value Problems
2.15 Setup of Boundary Value Problems of Elasticity
2.16 Existence and Uniqueness of Solution
2.17 Energy; Minimal Principle for a Spring
2.18 Energy in Linear Elasticity
2.19 Dynamic Problems of Elasticity
2.20 Oscillations of a String
2.21 Lagrangian and Eulerian Descriptions of Continuum Media
2.22 The Equations of Hydrodynamics
2.23 D'Alembert-Euler Equation of Continuity
2.24 Some Other Models of Hydrodynamics
2.25 Equilibrium of an Ideal Incompressible Liquid
2.26 Force on an Obstacle
3. Elements of the Strength of
Materials
3.1 What Are the Problems of the Strength of Materials?
3.2 Hooke's Law Revisited
3.3 Objectiveness of Quantities in Mechanics Revisited
3.4 Plane Elasticity
3.5 Saint-Venant's Principle
3.6 Stress Concentration
3.7 Linearity vs. Nonlinearity
3.8 Dislocations, Plasticity, Creep, and Fatigue
3.9 Heat Transfer
3.10 Thermoelasticity
3.11 Thermal Expansion
3.12 A Few Words on the History of Thermodynamics
3.13 Thermodynamics of an Ideal Gas
3.14 Thermodynamics of a Linearly Elastic Rod
3.15 Stability
3.16 Static Stability of a Straight Beam
3.17 Dynamical Tools for Studying Stability
3.18 Additional Remarks on Stability
3.19 Leak Prevention
4. Some Questions of Modeling in the
Natural Sciences
4.1 Modeling and Simulation
4.2 Computerization and Modeling
4.3 Numerical Methods and Modeling in Mechanics
4.4 Complexity in the Real World
4.5 The Role of the Cosine in Everyday Measurements
4.6 Accuracy and Precision
4.7 How Trees Stand Up against the Wind
4.8 Why King Kong Cannot Be as Terrible as in the Movies
Afterword
Recommended Reading
Index