MA 433 Numerical Analysis


Image Enhancement for Non Destructive Testing
Original temperature data Enhanced data  

Numerical analysis is concerned with the study of algorithms that underlie scientific computation, the use of computers to solve practical problems in science and engineering. Examples include solving linear systems of equations (perhaps thousands, millions, or billions of equations!), solving nonlinear systems, approximating integrals, solving differential equations, etc. Google's PageRank algorithm, computing the trajectory of a spacecraft, approximating the deformation of a beam under loading, or analyzing the magnetic field of a black hole are all problems where these kinds of algorithms are needed (and need to be understood.) The image on the left above is a simulation of the temperature of an aluminum boat hull 3 seconds after a low power laser is shined on the hull; there are three defects (cracks) near the laser spot. Pretty hard to see them, huh? The image on the right is an enhanced version that makes use of some significant numerical integration to bring out the crack locations.

The course work will consist of primarily of homework assignments and small computational projects, occasional in-class computer projects, and a couple take-home exams. The primary computational tool will be Matlab, which every Rose grad really ought to know, at least a little. It is not necessary to know Matlab beforehand, though some computational expertise is expected (e.g. one of MATLAB, MAPLE, or C++). We'll be making use of Jeff Leader's nice textbook, "Numerical Analysis and Scientific Computation."

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