format compact
more off
tMeasured=[0 0.5 1 1.5 2]
tMeasured =
         0    0.5000    1.0000    1.5000    2.0000
tMeasured=[0 0.5 1 1.5 2]';
TExactFun=@(t)14.6*exp(-1.1*t);
tPlot=linspace(0,2,100)';
TExactPlot=TExactFun(tPlot);
TMeasured=TExactFun(tMeasured);
TMeasured
TMeasured =
   14.6000
    8.4235
    4.8599
    2.8039
    1.6177
round(TMeasured)
ans =
    15
     8
     5
     3
     2
TMeasured=round(TMeasured);
t=0.7;
TLinear=interp1(TMeasured,TMeasured,t)
TLinear =
   NaN
TLinear=interp1(tMeasured,TMeasured,t)
TLinear =
    6.8000
TSpline=spline(tMeasured,TMeasured,t)
TSpline =
    6.5300
tMeasured=[0 0.5 1 1.5 2]';
TExactFun=@(t)14.6*exp(-1.1*t);
TMeasured=TExactFun(tMeasured);
tPlot=linspace(0,2,100)';
TExactPlot=TExactFun(tPlot);
TMeasured=round(TMeasured);
t=0.7;
TLinear=interp1(tMeasured,TMeasured,t);
TSpline=spline(tMeasured,TMeasured,t);
TLinear
TLinear =
    6.8000
TSpline
TSpline =
    6.5300
TExactFun(t)
ans =
    6.7600
TLinearPlot=interp1(tMeasured,TMeasured,tPlot);
TSplinePlot=spline(tMeasured,TMeasured,tPlot);
plot(tPlot,TExactPlot,'k:',tMeasured,TMeasured,'mo',...
tPlot,TLinearPlot,'r',tPlot,TSplinePlot,'b')
errLinear=max(abs(TLinearplot-TExactPlot));
{Undefined function or variable 'TLinearplot'.} 
errLinear=max(abs(TLinearPlot-TExactPlot));
errLinear=max(abs(TLinearPlot-TExactPlot))
errLinear =
    0.5255
errSpline=max(abs(TSplinePlot-TExactPlot))
errSpline =
    0.4445
CoefLin=polyfit(tMeasured,TMeasured,1)
CoefLin =
   -6.2000   12.8000
t=0.7
t =
    0.7000
polyval(CoefLin,t)
ans =
    8.4600
TLinFitPlot=polyval(CoefLin,tPlot);
plot(tPlot,TExactPlot,'k:',tMeasured,TMeasured,'mo',...
tPlot,TLinFitPlot,'r')
CoefPar=polyfit(tMeasured,TMeasured,2)
CoefPar =
    3.7143  -13.6286   14.6571
plot(tPlot,TExactPlot,'k:',tMeasured,TMeasured,'mo',...
TParFitPlot=polyval(CoefPar,tPlot);
polyval(CoefPar,t)
ans =
    6.9371
plot(tPlot,TExactPlot,'k:',tMeasured,TMeasured,'mo',...
tPlot,TParFitPlot,'r')
errPar=max(abs(TParFitPlot-TExactPlot))
errPar =
    0.6394
CoefCube=polyfit(tMeasured,TMeasured,3)
CoefCube =
   -2.0000    9.7143  -17.9286   14.9571
polyval(CoefCube,t)
ans =
    6.4811
TCubeFitPlot=polyval(CoefCube,tPlot);
plot(tPlot,TExactPlot,'k:',tMeasured,TMeasured,'mo',...
tPlot,TCubeFitPlot,'r')
errCube=max(abs(TCubeFitPlot-TExactPlot))
errCube =
    0.4838
CoefQuart=polyfit(tMeasured,TMeasured,4)
CoefQuart =
    2.0000  -10.0000   19.5000  -21.5000   15.0000
polyval(CoefQuart,t)
ans =
    6.5552
TQuartFitPlot=polyval(CoefQuart,tPlot);
plot(tPlot,TExactPlot,'k:',tMeasured,TMeasured,'mo',...
tPlot,TQuartFitPlot,'r')
errQuart=max(abs(TQuartFitPlot-TExactPlot))
errQuart =
    0.4732
derTExactPlot=-1.1*TExactPlot
derTExactPlot =
  -16.0600
  -15.7070
  -15.3619
  -15.0242
  -14.6941
  -14.3711
  -14.0553
  -13.7464
  -13.4443
  -13.1488
  -12.8598
  -12.5772
  -12.3008
  -12.0305
  -11.7661
  -11.5075
  -11.2546
  -11.0072
  -10.7653
  -10.5287
  -10.2974
  -10.0711
   -9.8497
   -9.6332
   -9.4215
   -9.2145
   -9.0120
   -8.8139
   -8.6202
   -8.4308
   -8.2455
   -8.0643
   -7.8870
   -7.7137
   -7.5442
   -7.3784
   -7.2162
   -7.0576
   -6.9025
   -6.7508
   -6.6025
   -6.4574
   -6.3154
   -6.1767
   -6.0409
   -5.9081
   -5.7783
   -5.6513
   -5.5271
   -5.4056
   -5.2868
   -5.1706
   -5.0570
   -4.9459
   -4.8372
   -4.7309
   -4.6269
   -4.5252
   -4.4258
   -4.3285
   -4.2334
   -4.1403
   -4.0493
   -3.9603
   -3.8733
   -3.7882
   -3.7049
   -3.6235
   -3.5439
   -3.4660
   -3.3898
   -3.3153
   -3.2425
   -3.1712
   -3.1015
   -3.0333
   -2.9667
   -2.9015
   -2.8377
   -2.7753
   -2.7144
   -2.6547
   -2.5964
   -2.5393
   -2.4835
   -2.4289
   -2.3755
   -2.3233
   -2.2723
   -2.2223
   -2.1735
   -2.1257
   -2.0790
   -2.0333
   -1.9886
   -1.9449
   -1.9022
   -1.8604
   -1.8195
   -1.7795
derTExactPlot=-1.1*TExactPlot;
derTExactPlot=-1.1*TExactPlot;
derCoefLin=polyder(CoefLin);
derCoefPar=polyder(CoefPar);
derCoefCube=polyder(CoefCube);
derTLinFitPlot=polyval(derCoefLin,tPlot);
derTParFitPlot=polyval(derCoefPar,tPlot);
derTCubeFitPlot=polyval(derCoefCube,tPlot);
derTQuartFitPlot=polyval(derCoefQuart,tPlot);
{Undefined function or variable 'derCoefQuart'.} 
derTQuartFitPlot=polyval(derCoefQuart,tPlot);
{Undefined function or variable 'derCoefQuart'.} 
derCoefQuart=polyder(CoefQuart);
derTQuartFitPlot=polyval(derCoefQuart,tPlot);
plot(tPlot,derTExactPlot,'k',...
tPlot,derTLinFitPlot,'r',...
tPlot,derTParFitPlot,'g',...
tPlot,derTCubeFitPlot,'b',...
tPlot,derTQuartFitPlot,'y')
exit