Introduction -- Elements of vector algebra and calculus -- Stress in a fluid -- Description of fluid motion -- Eulerian equations for the motion of an ideal fluid -- Alternate forms of the equations -- Equations of discontinuous motion -- Integration of Euler's equation in special cases -- Irrotational motion -- Unsteady acyclic motion -- Steady acyclic motion -- Steady two-dimensional acyclic motion -- Circulation and lift for an infinite wing in steady flow -- Elements of the theory of functions of a complex variable -- Two-dimensional motion and the complex variable -- Problem of the airfoil -- Elements of thin airfoil theory -- some features of flow with vorticity -- Elements of finite wing theory -- Elements of the theory for the flow past a slender body of revolution.
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The prerequisite for the study of this book is a knowledge of matrices and the essentials of functions of a complex variable. It has been developed from courses given by the authors and probably contains more material than will ordinarily be covered in a one-year course. It is hoped that the book will be a useful text in the application of differential equations as well as for the pure mathematician.