About The Book
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.