Mathematica Tool 1

This Mathematica notebook is designed to be used with Checkpoint 2 in Section 2.5

Use this tool to add in several additional solution curves to the differential equation
				(∂/(∂ t)) P(t)=0.25P(t).

Needs["VectorFieldPlots`"]

The additional curves should be entered by their values at t=0. In this workbook, this is done by entering the value into the list of initial conditions below.

InitialConditions ={1,2,3};
Equation=P'[t]==0.25 P[t];
RHS =0.25 P;  

Plot1=VectorFieldPlot[((#)/(Norm[#]))&[{1,RHS}],{t,0,5.5},{P,0,5.5}, Axes->True,AxesLabel->{"t","P(t)"},ColorFunction->Hue];
DSolve[{Equation,P[0]==a},P,t]//Quiet;
Plot2=Plot[Evaluate[P[t]/.%/.{a->InitialConditions}],{t,0,6},PlotRange->{{0,6},{0,5.75}},PlotStyle->Thickness[0.01],AxesLabel->{"t","P(t)"}];
Show[Plot1,Plot2]