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This book is for people who need to solve ordinary differential equations (ODEs), both initial value problems (IVPs) and boundary value problems (BVPs) as well as delay differential equations (DDEs). These topics are usually taught in separate courses of length one semester each, but Solving ODEs with MATLAB provides a sound treatment of all three in about… (More)
We consider the question of characterizing the behavior of parametric curves whose components are cubic polynomials. When there is no chance of confusion, we will refer to such curves as cubic curves with the understanding that each of x(t) and y(t) are themselves cubic polynomials. We classify various types of parametric cubics using their defining… (More)
We show snapshots of magnetic flux lines in a simulated 10x10x150 nm 3 iron pillar undergoing magnetization reversal in an applied magnetic field that makes an angle of 75 o with the pillar's axis. 1 Finite-temperature micromagnetics simulations 2 were performed on an IBM SP3 supercomputer and the results visualized with the Tecplot ® graphics package. Red:… (More)
Moving averages of the solution of an initial value problem for a system of ordinary differential equations are used to extract the general behavior of the solution without following it in detail. They can be computed directly by solving delay differential equations. Because they vary much less rapidly and are smoother, they are easier to compute.
This paper explores some of the basic and most interesting facts about quadric surfaces. It describes the canonical coordinate transformations required to eliminate cross terms from the equation of a general quadric equation. It explains how to use these coordinates to obtain each of the seventeen canonical quadrics. It further describes the determination… (More)