Week 4 - Curve fitting

%curve fitting of temperature vs specific heatclear allclose allclc%load the data which contains variation of specific heat with temperaturetemp_cp=load('data');temperature=temp_cp(:,1);cp=temp_cp(:,2);%%curve fit%%cp=a*t^2+b*t+ccoeff=polyfit(temperature,cp,2);predicted_cp=polyval(coeff,temperature);%plotting the datafigure(1)title('Second Order Fit')hold onxlabel('Temperature [K]','color','r')ylabel('Specific Heat [KJ/Kg-K]','color','r')plot(temperature,cp,'linewidth',1,'color','g')plot(temperature,predicted_cp,'linewidth',1,'color','r')legend('Original data set','curve fit')grid on%using third order polynomialcoeff_3=polyfit(temperature,cp,3)predicted_cp1=polyval(coeff_3,temperature)figure(2)title('Third Order Fit')hold onplot(temperature,cp,'linewidth',1,'color','g')plot(temperature,predicted_cp1,'linewidth',1,'color','r')xlabel('Temperature [K]','color','r')ylabel('Specific Heat [KJ/Kg-K]','color','r')legend('Original data set','curve fit') 

To get more smooth curve fit we can use higher order polynomials or splitwise polynomials which means using differents polynomials for different range of temperatures.