202_2017_1_b.pdf - APM2616/202/1/2017 Tutorial letter...

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BARCODEDefine tomorrow.universityof south africaTutorial letter 202/1/2017COMPUTER ALGEBRAAPM2616Semester 1Department of Mathematical SciencesIMPORTANT INFORMATION:This tutorial letter contains solutions to assignment 2, Sem 1.APM2616/202/1/2017
Question 1:18 MarksWrite MuPAD code to draw a graph that plots the functionsf(t) =esinxandg(t) =t21 +t2in theranget=-1 to 5.The axes should be appropriately labelled, and horizontal directions should be thesame. The graph offis to be blue and that ofggreen.f:=plot::Function2d(exp(sin(t)),t= 1..5,Color=RGB::Blue):g:=plot::Function2d(t^2/(1+t^2),t= 1..5,Color=RGB::Green):plot(f,g,Scaling=Constrained,Labels=["t","f, g"]):Question 2:17 MarksProduce a plot demonstrating the behaviour ofy(x) in the rangex= 1 to 50 wheny(x) satisfies thedifferential equationx2y00(x) +xy0(x) +x2y(x) = 0, withy(1) = 1 andy0(1) = 0.f:=(x,Y)->[Y[2],-Y[1]-Y[2]/x]:Y0:=[1,0]:G:=(x,Y)->[x,Y[1]]:p:=plot::ode([i $ i=1..50],f,Y0,[G, Style = Splines]):plot(p);2
APM2616/202/1/2017Question 3:25 MarksPlot the following on a 3-DgraphSphere, centred at the origin and radius 2Surfacez=x-y+ 1 +xy5.Cylindrical surface (x-10)2+y2= 81, zany valueEstimate the points at which all three surfaces intersect, and then use this information as startingpoint in a numerical procedure to find accurately (to 10 significant figures) the coordinates of thepoints at which the surfaces intersect.

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