Mathematical Explorations with MATLAB

Abstract

This 1999 book is about the kind of mathematics usually encountered in first year university courses. A key feature of the book is that this mathematics is explored in depth using the popular and powerful package MATLAB. The emphasis is on understanding and investigating the mathematics, and putting it into practice in a wide variety of modelling situations. In the process, the reader will gain some fluency with MATLAB, no starting knowledge of the package being assumed. The range of material is wide: matrices, whole numbers, complex numbers, geometry of curves and families of lines, data analysis, random numbers and simulations, and differential equations form the basic mathematics. This is applied to a large number of investigations and modelling problems, from sequences of real numbers to cafeteria queues, from card shuffling to models of fish growth. All extras to the standard MATLAB package are supplied on the World Wide Web.

Analysis of Dallara T12 Race Car Front Wing Vibrations

“…Calculation of the spectral power density of oscillations was performed using the calculation module "sptool" of the MATLAB software [12,13].…”

Modelling and simulation of the intervertebral movements of the lumbar spine using an inverse kinematic algorithm

“…An iterative refinement algorithm was used to improve the solution (CHEN et aL, 1999). The positions of the spinous processes were predicted using the approximate solution of co and (1).…”

“…The solution was accepted if the residual was less than its 2-norm II r II 2. if not, the inverse kinematic problem was considered to be ill-conditioned. Singular value decomposition was employed (GoLus and VAN LOAN, 1996;CHEN et al, 1999) to estimate the error. The approximate solution of co was adjusted accordingly.…”

“…An iterative procedure was employed to minimise the residuals, thus ensuring the optimum solution was obtained. The 2-norm of the residuals was used as the optimisation criterion as it was most computationally efficient when compared with the 1-norm and infinity-norm (GOLUB and VAN LOAN, 1996;CHEN et al, 1999).…”

Visualization for fisheries management from a spatiotemporal perspective

“…The ever-increasing popularity and use of geographical information systems (GIS) and proprietary graphics and visualization systems is, in part, due to the sophisticated capabilities they provide for displaying georeferenced data in two and three dimensions (ESRI, 1996;Chen et al, 1999). Customized applications based on such systems have been used in many marine information and analysis systems to gain insights and understanding of the ecosystem being studied (Ault, 1996;Hatcher et al, 1997;Garibaldi and Caddy, 1998;Megrey and Hinckley, 2001).…”