The compound matrix method, which was first proposed for numerically integrating systems of differential equations in hydrodynamic stability on k = 2, 3 dimensional subspaces of C n , by using compound matrices as coordinates, is reformulated in a coordinate-free way using exterior algebra spaces, k (C n ).This formulation leads to a general framework for studying systems of differential equations on k-dimensional subspaces. The framework requires the development of several new ideas: the role of Hodge duality and the Hodge star operator in the construction, an efficient strategy for constructing the induced differential equations on k (C n ), general formulation of induced boundary conditions, the role of geometric integrators for preserving the manifold of k−dimensional subspaces -the Grassmann manifold, G k (C n ), and a formulation for induced systems on an unbounded interval.The numerical exterior algebra framework is most advantageous for numerical solution of differential eigenvalue problems on unbounded domains, where there are significant difficulties in setting up matrix discretizations.The formulation is presented for k-dimensional subspaces of systems on C n with k and n arbitrary, and examples are given for the cases of k = 2 and n = 4, and k = 3 and n = 6, with an indication of implementation details for systems of larger dimension.The theory is illustrated by application to four differential eigenvalue problems on unbounded intervals: hydrodynamic stablity of boundary-layer flow past a compliant surface, the eigenvalue problem associated with the stability of solitary waves, the stability of Bickley jet in oceanography, and

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Many aquatic species such as dolphins and whales have fins, which can be modeled as swept wings. Some of these fins, such as the dorsal fin of a dolphin, are semi-rigid and therefore can be modeled as a rigid swept wing with a compliant surface. An understanding of the hydrodynamics of the flow past swept compliant surfaces is of great interest for understanding potential drag reduction mechanisms, especially since swept wings are widely used in hydrodynamic and aerodynamic design. In this paper, the flow past a swept wing with a compliant surface is modeled by an attachment-line boundary layer flow, which is an exact similarity solution of the Navier-Stokes equations, flowing past a compliant surface modeled as an elastic plate. The hydrodynamic stability of the coupled problem is studied using a new numerical framework based on exterior algebra. The basic instability of the attachment line boundary layer on a rigid surface is a traveling wave instability that propagates along the attachment line, and numerical results show that the compliance results in a substantial reduction in the instability region. Moreover, the results show that, although the flow-field is three-dimensional, the qualitative nature of the instability suppression is very similar to the qualitative reduction of instability of the two-dimensional Tollmien-Schlichting modes in the classical boundary-layer flow past a compliant surface.

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Although primarily written for educationalists working in the area of second language teaching, Teaching the Spoken Language may surprise speech pathologists by the range of issues and concerns which are shared by educational and clinical linguists, and by the usefulness and applicability of much of the information which is presented for speech pathology practice. The authors intentionally maintain a foot in the classroom door with this book. Provision of a practical resource of strategies and tools for the field professional is given as the rationale for the writing of Teaching the Spoken Language. This applied emphasis is reflected both by the text's specificity and use of exemplification, and in the content included in its four chapters.