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This seventh edition of Advanced Engineering Mathematics differs from the sixth in four ways. First, based on reviews and user comments, new material has been added, including the following. • Orthogonal projections and least squares approximations of vectors and functions. This provides a unifying theme in recognizing partial sums of eigenfunction expansions as projections onto subspaces, as well as understanding lines of best fit to data points. • Orthogonalization and the production of orthogonal bases. • LU factorization of matrices. • Linear transformations and matrix representations. • Application of the Laplace transform to the solution of Bessel’s equation and to problems involving wave motion and diffusion. • Expanded treatment of properties and applications of Legendre polynomials and Bessel functions, including a solution of Kepler’s problem and a model of alternating current flow. • Heaviside’s formula for the computation of inverse Laplace transforms. • A complex integral formula for the inverse Laplace transform, including an application to heat diffusion in a slab. • Vector operations in orthogonal curvilinear coordinates. • Application of vector integral theorems to the development of Maxwell’s equations. • An application of the Laplace transform convolution to a replacement scheduling problem.

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