Linear System Applications
This chapter presents four applications involving the solution to linear systems. The first of these is Fourier series that introduce the concept of an infinite-dimensional vector space with a basis of orthonormal functions. In this case, the functions are sines and cosines. The Fourier series for a periodic square wave is computed and convergence of its partial sums to the square wave is demonstrated by a graph. The second example is the use of finite differences to approximate the solution of the heat equation in time and one space variable. A tridiagonal system of equations must be solved for every time step, the right-hand side of which is determined by the initial and boundary conditions. ...
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