2. Review of Basic Fluid Dynamics 11 --
2.1. Forces and Moments Due to Pressure 11 --
2.2. Basic Conservation Laws of Fluid Mechanics 14 --
2.3. Vector Calculus 18 --
2.4. Differential Forms of the Conservation Laws 21 --
2.5. Rotational Velocity and Irrotational Flow 23 --
2.6. Two-Dimensional Incompressible Flow 25 --
3. Incompressible Irrotational Flow About Symmetric Airfoils at Zero Lift 32 --
3.1. Uniform Two-Dimensional Irrotational Incompressible Flow About an Isolated Body 33 --
3.2. Superposition of Fundamental Solutions 34 --
3.3. Dimensionless Variables 38 --
3.5. Line Source Distributions 43 --
3.6. Flow Past Thin Symmetric Airfoils 46 --
3.7. Errors Near The Stagnation Points 52 --
3.8. Numerical Solution Based on Line Doublet Distributions 55 --
3.9. Relation of Numerical to Analytical Solutions 58 --
3.10. Complex-Variable Methods 60 --
4. Lifting Airfoils in Incompressible Irrotational Flow 80 --
4.1. Thin Airfoil: Thickness and Camber Problems 80 --
4.2. Forces and Moments on a Thin Airfoil 85 --
4.3. Kutta Condition 91 --
4.4. Circulation Specification 93 --
4.5. Cambered Thin Airfoil 94 --
4.6. Aerodynamics of The Thin Airfoil 97 --
4.7. Lumped-Vortex Method 101 --
4.8. Panel Methods 103 --
4.9. Complex-Variables Methods 112 --
5. Wings of Finite Span 124 --
5.1. Vortex System for a Thin Planar Wing of Finite Span 124 --
5.2. Vortex-Lattice Method 130 --
5.4. Lifting-Line Theory 135 --
5.5. Elliptic Lift Distribution 138 --
5.7. Nonelliptic Lift Distributions 144 --
6. Navier-Stokes Equations 154 --
6.1. Stress at a Point 154 --
6.2. Newton's Second Law For Fluids 158 --
6.3. Symmetry of Stresses 160 --
6.4. Molecular View of Stress in a Fluid 161 --
6.5. No-Slip Condition 166 --
6.6. Unidirectional Flows 168 --
6.7. Viscosity Coefficient 170 --
6.9. Strain Versus Rotation 173 --
6.11. Vectors and Tensors 179 --
6.12. Stress Tensor 182 --
6.13. Rate-of-Strain Tensor 184 --
6.14. Two Coefficients of Viscosity 185 --
6.15. Navier-Stokes Equations 187 --
7.1. Laminar Boundary Layer 191 --
7.2. Use of the Boundary-Layer Equations 197 --
7.3. Momentum Integral Equation 203 --
7.4. Velocity Profile Fitting: Laminar Boundary Layers 204 --
7.5. Thwaites's Method For Laminar Boundary Layers 206 --
7.7. Turbulent Flows 210 --
7.8. Velocity Profile Fitting: Turbulent Boundary Layers 215 --
7.9. Head's Method For Turbulent Boundary Layers 219 --
7.10. Transition From Laminar to Turbulent Flow 220 --
7.11. Boundary Layer Separation 222 --
7.12. Airfoil Performance Characteristics 225 --
7.13. Development of Circulation About a Sharp-Tailed Airfoil 244 --
7.14. Computation of Boundary Layer Growth Along An Airfoil 247 --
8.1. Mathematical Foundations: Green's Identity 260 --
8.2. Potential-Based Panel Methods 266 --
8.3. Vortex-Based Panel Methods 280 --
8.4. Source-Based Panel Methods 282 --
8.5. Comparisons of Source-, Doublet-, and Vortex-Based Methods 285 --
9. Finite Difference Methods 289 --
9.1. Boundary-Value Problems in One Dimension 289 --
9.2. Convergence and Order of Accuracy 295 --
9.3. Incompressible Potential Flow Past a Thin Symmetric Airfoil 299 --
9.4. Initial Problems: The Heat Equation 308 --
10. Finite-Difference Solution of the Boundary Layer Equations 335 --
10.1. Statement of The Problem 335 --
10.2. Similar Solutions of The Laminar Incompressible Boundary Layer 337 --
10.3. Transformation of The Laminar Boundary-Layer Equations For Arbitrary Pressure Gradients 354 --
10.4. Turbulent Boundary Layers 360 --
10.5. Separated Flows 366 --
11. Compressible Potential Flow Past Airfoils 381 --
11.1. Shock Waves and Sound Waves 381 --
11.2. Equations of Compressible Steady Potential Flow 385 --
11.3. Prandtl-Glauert Equation 388 --
11.4. Subsonic Flow Past Thin Airfoils 390 --
11.5. Supersonic Flow Past Thin Airfoils 393 --
11.6. Transonic Flow Past Thin Airfoils 399 --
Appendix C. Potential Flow Past a Corner 429 --
Appendix D. Uniqueness of Solutions of Laplace Equation 433 --
Appendix E. Fourier-Series Expansions 438 --
Appendix F. Downwash Due to a Horseshoe Vortex 442 --
Appendix G. Geometrical Demonstration That Strain is a Tensor 446 --
Appendix H. Optimization of the SOR Method for the Laplace Equation 449 --
Appendix I. Structure of a Weak Shock Wave 456.
