The ubiquitous role of linear algebra within applied mathematics

Bayram Ülgen
2011 unpublished
This thesis combines Linear Algebra with Applied Mathematics. The author presents mathematical applications from physics and electrical engineering, statistics and demography, signal and image processing by means of linear algebra. The first chapter presents three fundamental laws of Kirchhoff and Ohm, respectively, which combine into the fundamental network equation. Therefore, the author considers the four subspaces, graphs and incidence matrices. The second chapter is all about applications
more » ... o eigenvalues and eigenvectors. The author introduces Markov chains, the singular value decomposition and the method of (minimal norm) least squares. Statistics and demographic processes, image compres- sion and (minimal norm) least squares applications, respectively, are among mathematical applications introduced in this chapter. The third chapter deals with basics of signal and image processing. The author provides an introduction to Fourier analysis and discusses some important tools for signal processing, e.g., filters. The last chapter constitutes an attempt to review this thesis with respect to mathematics education, teaching and, in general, didactics.
doi:10.25365/thesis.15605 fatcat:j3wwhghfhreb7k3ihb26xn6aym