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ЭHТКp=ТКpSџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџАšŠzTangent?ё™™™™™–?№ТКgТКpV?м#?€?€УdWMT0IGR0)NotesNotebook0NotesЈЯЯУ9љ HHк(џсџтљFg(ќHHи(dh  ‘>ž? ‘>ž?$Normalџџџџд џќџџџџџџџџ< BШHHHH$$ъ4Z ))))))))VThe function is K1+K2*exp(-x/Tau), that is, the sum of a constant and an exponential. UThe time units of the Time Constant (Tau) and the graph are arbitrary, but the same.  eChanging any of the parameters changes the function, and removes the derivative and integral traces.  mDraw tangent draws two straight line segments, the tangent and the final value of the exponential component.  Notice that: TShorter time constants (smaller Tau) give larger derivatives and smaller integrals. >A non-zero value for K1 leads to an ever increasing integral. hDerivative always tends to zero when time is long compared to Tau, that is, steady state is approached. $K2=-K1 gives initial value of zero. A tangent drawn at any point on any exponential plot intersects the final value one time constant after the point at with the tangent is drawn.ZЖ†Ž xМ*TGenevaв// Platform=Macintosh, IGORVersion=6.010, architecture=PowerPC Silent 101 // use | as bitwise or -- not comment. DefaultFont "Helvetica" MoveWindow/C 2,591,950,735 MoveWindow/P 398,389,898,684 OpenNotebook/N=Notebook0/W=(463,424,963,719)/J=68903 "Notes" as "Notes" graph0_1() Window graph0_1() : Graph PauseUpdate; Silent 1 // building window... Display /W=(31,63,805,617)/B=HorizCrossing Func,Deriv,Integ,Tangent as "Exponentials" ModifyGraph margin(bottom)=50 ModifyGraph mode(Tangent)=4 ModifyGraph marker(Tangent)=19 ModifyGraph lStyle(Deriv)=2,lStyle(Integ)=8 ModifyGraph rgb(Deriv)=(3,52428,1),rgb(Integ)=(0,0,65535),rgb(Tangent)=(0,0,0) ModifyGraph msize(Tangent)=2 ModifyGraph lblPos(HorizCrossing)=46 ModifyGraph lblLatPos(HorizCrossing)=-1 ModifyGraph freePos(HorizCrossing)={0,left} Label left "Function\\s(Func) Derivative\\s(Deriv) Integral\\s(Integ)" Label HorizCrossing "Time (units of the time constant)" SetAxis/A/N=1 left ControlBar 25 SetVariable K1,pos={1,5},size={87,15},proc=SetFunc,title="K1",value= K1 SetVariable K2,pos={98,5},size={87,15},proc=SetFunc,title="K2",value= K2 SetVariable tau,pos={195,5},size={132,15},proc=SetFunc,title="Time Constant" SetVariable tau,limits={0.0001,inf,0.1},value= Tau Button Derivative,pos={337,2},size={78,21},proc=Derivative,title="Derivative" Button Integral,pos={425,2},size={70,20},proc=Integral,title="Integral" Button DrawTan,pos={505,2},size={94,20},proc=DrawTan,title="Draw tangent" EndMacro Ц#pragma rtGlobals=1 // Use modern global access method. Function SetFunc(ctrlName,varNum,varStr,varName) : SetVariableControl String ctrlName //Standard parameters of a SetVariableControl Variable varNum String varStr String varName WAVE Func, Deriv, Integ, Tangent NVAR Tau //Time constant Func=K1+K2*exp(-x/Tau) //Sets function Deriv=NaN //makes trace invisible Integ=NaN Tangent=NaN End Function Derivative(ctrlName) : ButtonControl String ctrlName Wave Func, Deriv Differentiate Func/D=Deriv //restores Derivative End Function Integral(ctrlName) : ButtonControl String ctrlName WAVE Func, Integ Integrate/METH=1 Func/D=Integ //restores Integral End Function DrawTan(ctrlName) :ButtonControl String ctrlName String Curve="junk" Variable Point=1 NVAR Tau WAVE Func, Integ, Deriv, Tangent Prompt Curve, "to:", popup "Function;Derivative;Integral" Prompt Point, "at time:" DoPrompt "Draw a tangent" Curve, Point SetScale/P x Point,Tau,"", Tangent // SetScale/I x Point,Point+Tau,"", Tangent strswitch(Curve) case "Function": Tangent[0]=Func(Point) Tangent[1]=K1 Tangent[2]=K1 break case "Derivative": Differentiate Func/D=Deriv //restores Derivative Tangent[0]=Deriv(Point) Tangent[1]=0 Tangent[2]=0 Break case "Integral": Integrate/METH=1 Func/D=Integ //restores Integral Tangent[0]=Integ(Point) Tangent[1]=K1*(Point+Tau)+K2*Tau Tangent[2]=K1*(Point+2*Tau)+K2*Tau endswitch End