By Jon Davis
ISBN-10: 0817641815
ISBN-13: 9780817641818
ISBN-10: 1461213762
ISBN-13: 9781461213765
Differential equations is a topic of broad applicability, and data of dif Differential equations is a topic of extensive applicability, and data of dif ferential ferential equations equations subject matters subject matters permeates permeates all all parts components of of analysis learn in in engineering engineering and and utilized utilized arithmetic. arithmetic. a few a few differential differential equations equations are are vulnerable prone to to analytic analytic skill technique of of so so lution, lution, whereas whereas others others require require the the new release new release of of numerical numerical answer resolution trajectories trajectories to to determine see the the habit habit of of the the approach method less than less than examine. research. For For either either occasions, occasions, the the software program software program package deal package deal Maple Maple can could be be used used to to virtue. virtue. To To the the coed pupil Making Making powerful potent use use of of differential differential equations equations calls for calls for facility facility in in spotting spotting and and fixing fixing regular usual "tractable" "tractable" difficulties, difficulties, as besides good as as having having the the historical past history in within the the topic topic to to make make use use of of instruments instruments for for dealing facing with events occasions that which are aren't no longer amenable amenable to to easy uncomplicated analytic analytic techniques. approaches.
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Additional info for Differential Equations with Maple: An Interactive Approach
Example text
Taking the moments about the centroid of the cross section, the element of moment acting on a cross sectional strip of area dA is The total comes from integrating this over the area of the cross section, which gives the moment expression M(x) = = = 1 J { cross section area A -(y - Ym)2 E y"(x) dA y"(x)dA -E Iyy y"(x), y"(X), where I yy is the moment of inertia of the cross section. 77 Although some beam calcuJations calculations (support reaction forces) can be made working only with the moment and shear expressions, one can also consider the displacement y (x) as the primary variable, and compute the other quantities in terms of the displacement function.
16. A flow field in order to obtain a unique solution to such a problem. The equation above alone represents a family of solutions, and specifying a different point will result in a different solution curve. Several of the examples above involve derivatives of order higher than one. The mechanical examples naturally arrive with second order derivatives and are classified as second order equations. The order of a differential equation may hence be taken as the order of the highest derivative appearing in it.
11/// II! -----~ """"--__ "'i.... -~" ....... '\ -~ .......... \. \\ ......... "" '\"-. .................... -..... \\'\"-. " .......... " \\\\'\ ................ "" .......... ,,\\\\\""\\\\\'\ ....... ""-\ \ \ \ \ \ ................ \\\\ ,.............. --// . ~ ................ '\\\\\ .......... \\\\\ ................ 1. 1 to appear; the paths of solution trajectories are evident in the result. The appearance also is the source of the "flow field" terminology since the arrows resemble motion paths of particles moving with a fluid flow.
Differential Equations with Maple: An Interactive Approach by Jon Davis
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