| Wings | p. 1 |
| Function | p. 1 |
| Geometry | p. 4 |
| References | p. 9 |
| Problems | p. 10 |
| Review of Basic Fluid Dynamics | p. 11 |
| Forces and Moments Due to Pressure | p. 11 |
| The Basic Conservation Laws of Fluid Mechanics | p. 14 |
| Vector Calculus | p. 18 |
| Differential Forms of the Conservation Laws | p. 21 |
| Rotational Velocity and Irrotational Flow | p. 23 |
| Two-Dimensional Incompressible Flow | p. 25 |
| Uniform Flow | p. 27 |
| Source Flow | p. 27 |
| Vortex Flow | p. 28 |
| Bibliography | p. 29 |
| Problems | p. 29 |
| Incompressible Irrotational Flow About Symmetric Airfoils at Zero Lift | p. 32 |
| Uniform Two-Dimensional Irrotational Incompressible Flow About an Isolated Body | p. 33 |
| Superposition of Fundamental Solutions | p. 34 |
| Dimensionless Variables | p. 38 |
| Rankine Ovals | p. 39 |
| Line Source Distributions | p. 43 |
| Flow Past Thin Symmetric Airfoils | p. 46 |
| Errors Near The Stagnation Points | p. 52 |
| Numerical Solution Based on Line Doublet Distributions | p. 55 |
| Relation of Numerical to Analytical Solutions | p. 58 |
| Complex-Variable Methods | p. 60 |
| Flow Past an Ellipse | p. 63 |
| Joukowsky Airfoils | p. 66 |
| Problems | p. 70 |
| Computer Programs | p. 75 |
| Lifting Airfoils in Incompressible Irrotational Flow | p. 80 |
| The Thin Airfoil: Thickness and Camber Problems | p. 80 |
| Forces and Moments on a Thin Airfoil | p. 85 |
| The Kutta Condition | p. 91 |
| Circulation Specification | p. 93 |
| The Cambered Thin Airfoil | p. 94 |
| Aerodynamics of The Thin Airfoil | p. 97 |
| The Lumped-Vortex Method | p. 101 |
| Panel Methods | p. 103 |
| Program PANEL | p. 110 |
| Complex-Variables Methods | p. 112 |
| References | p. 117 |
| Problems | p. 117 |
| Computer Program | p. 118 |
| Wings of Finite Span | p. 124 |
| The Vortex System for a Thin Planar Wing of Finite Span | p. 124 |
| The Vortex-Lattice Method | p. 130 |
| Induced Drag | p. 134 |
| Lifting-Line Theory | p. 135 |
| The Elliptic Lift Distribution | p. 138 |
| The Optimal Wing | p. 141 |
| Nonelliptic Lift Distributions | p. 144 |
| References | p. 148 |
| Problems | p. 149 |
| Computer Program | p. 151 |
| The Navier-Stokes Equations | p. 154 |
| The Stress at a Point | p. 154 |
| Newton's Second Law For Fluids | p. 158 |
| Symmetry of Stresses | p. 160 |
| Molecular View of Stress in a Fluid | p. 161 |
| The No-Slip Condition | p. 166 |
| Unidirectional Flows | p. 168 |
| The Viscosity Coefficient | p. 170 |
| Pascal's Law | p. 171 |
| Strain Versus Rotation | p. 173 |
| Isotropy | p. 177 |
| Vectors and Tensors | p. 179 |
| The Stress Tensor | p. 182 |
| The Rate-of-Strain Tensor | p. 184 |
| The Two Coefficients of Viscosity | p. 185 |
| The Navier-Stokes Equations | p. 187 |
| Problems | p. 189 |
| The Boundary Layer | p. 191 |
| The Laminar Boundary Layer | p. 191 |
| Use of the Boundary-Layer Equations | p. 197 |
| Skin Friction | p. 198 |
| Displacement Thickness | p. 199 |
| Momentum Thickness | p. 202 |
| The Momentum Integral Equation | p. 203 |
| Velocity Profile Fitting: Laminar Boundary Layers | p. 204 |
| Thwaites's Method For Laminar Boundary Layers | p. 206 |
| Form Drag | p. 209 |
| Turbulent Flows | p. 210 |
| Velocity Profile Fitting: Turbulent Boundary Layers | p. 215 |
| Head's Method For Turbulent Boundary Layers | p. 219 |
| Transition From Laminar to Turbulent Flow | p. 220 |
| Boundary Layer Separation | p. 222 |
| Airfoil Performance Characteristics | p. 225 |
| The Development of Circulation About a Sharp-Tailed Airfoil | p. 244 |
| Computation of Boundary Layer Growth Along An Airfoil | p. 247 |
| References | p. 252 |
| Problems | p. 253 |
| Computer Program | p. 255 |
| Panel Methods | p. 260 |
| Mathematical Foundations: Green's Identity | p. 260 |
| Potential-Based Panel Methods | p. 266 |
| Constant-Potential Method | p. 264 |
| Linear-Potential Method | p. 273 |
| Equivalent Vortex Distributions | p. 276 |
| Vortex-Based Panel Methods | p. 280 |
| Source-Based Panel Methods | p. 282 |
| Comparisons of Source-, Doublet-, and Vortex-Based Methods | p. 285 |
| References | p. 287 |
| Problems | p. 287 |
| Finite Difference Methods | p. 289 |
| Boundary-Value Problems in One Dimension | p. 289 |
| Convergence and Order of Accuracy | p. 295 |
| Incompressible Potential Flow Past a Thin Symmetric Airfoil | p. 299 |
| Direct Methods | p. 303 |
| Iterative Methods | p. 304 |
| Initial Problems: The Heat Equation | p. 308 |
| An Explicit Finite-Difference Method | p. 310 |
| Stability | p. 312 |
| Convergence | p. 315 |
| The Crank-Nicolson Method | p. 317 |
| Backward-Difference Schemes | p. 320 |
| References | p. 322 |
| Problems | p. 322 |
| Computer Programs | p. 324 |
| Finite-Difference Solution of the Boundary Layer Equations | p. 335 |
| Statement of The Problem | p. 335 |
| Similar Solutions of The Laminar Incompressible Boundary Layer | p. 337 |
| Finite-Difference Methods for the Falkner-Skan Equation | p. 341 |
| Iterative Solution of Nonlinear Equations | p. 342 |
| A Finite-Difference Method Based on a Second-Order Differential Equation | p. 344 |
| A Finite-Difference Method Based on a System of First-Order Equations | p. 348 |
| Transformation of The Laminar Boundary-Layer Equations For Arbitrary Pressure Gradients | p. 354 |
| Program BDYLAY | p. 359 |
| Turbulent Boundary Layers | p. 360 |
| Separated Flows | p. 366 |
| References | p. 368 |
| Problems | p. 369 |
| Computer Programs | p. 371 |
| Compressible Potential Flow Past Airfoils | p. 381 |
| Shock Waves and Sound Waves | p. 381 |
| Equations of Compressible Steady Potential Flow | p. 385 |
| The Prandtl-Glauert Equation | p. 388 |
| Subsonic Flow Past Thin Airfoils | p. 390 |
| Supersonic Flow Past Thin Airfoils | p. 393 |
| Transonic Flow Past Thin Airfoils | p. 399 |
| Aerodynamics in the Transonic Range | p. 402 |
| Solution of the Transonic Small-Disturbance Equation: Subcritical Flow | p. 404 |
| Conservative versus Nonconservative Difference Schemes | p. 406 |
| Supercritical Flow and Upwind Differencing | p. 408 |
| The Relaxation Iteration | p. 413 |
| The Poisson Iteration | p. 415 |
| References | p. 417 |
| Problems | p. 417 |
| Computer Program | p. 418 |
| An Important Integral | p. 424 |
| The Integral [characters not reproducible] | p. 427 |
| Potential Flow Past a Corner | p. 429 |
| Uniqueness of Solutions of Laplace Equation | p. 433 |
| Fourier-Series Expansions | p. 438 |
| Downwash Due to a Horseshoe Vortex | p. 442 |
| Geometrical Demonstration That Strain is a Tensor | p. 446 |
| Optimization of the SOR Method for the Laplace Equation | p. 449 |
| Structure of a Weak Shock Wave | p. 456 |
| Index | p. 459 |
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