Function In this case we want to enter the equation for the right hand side of

Function in this case we want to enter the equation

This preview shows page 3 - 5 out of 5 pages.

Function . In this case, we want to enter the equation for the right hand side of the differential equation (1) and below we see the M-file (stored murder.m ). function yp = murder(t,y) % Model for Newton’s Law of Cooling % Parameters for the model
Image of page 3

Subscribe to view the full document.

k = log(4/3); Te = 22; yp = -k*(y - Te); % This is the RHS of the DE end Note that MatLab uses % beginning any comments that are not executed. The next step is to use MatLab’s numerical ODE solver to create the solution of the differential equation from the time of death, t d , found earlier for about 12 hours after the murder. Below we show the solving of the model and plotting of the graph. [t1,y1] = ode23(@murder,[0,td],30); [t2,y2] = ode23(@murder,[0,12],30); plot(t1,y1,’b-’,t2,y2,’b-’);grid; This produces a blue solution from the time of death until 12 hours after t = 0. This is quick way to produce a graph, but we want to illustrate the power of MatLab to produce a very good looking, professional graph. Below we present an M-file, Script , which executes a series of commands to produce a good graph. There are comments interior to the program to help understand what is happening, and clearly one could explore other options to improve the graph. clear % Clear previous definitions figure(1) % Assign figure number clf % Clear previous figures hold off % Start with fresh graph mytitle = ’Body Temperature’; % Title xlab = ’$t$’; % X-label ylab = ’$T(t)$’; % Y-label f = @(k) 22+8*exp(-k)-28; % Function for finding heat coefficient k = fzero(f,0.3); % Find the heat coefficient ft = @(t) 22+8*exp(-k*t)-37; % Function for finding the time of death td = fzero(ft,-5); % Find the time of death [t1,y1] = ode23(@murder,[0,td],30); % Simulate the heat equation [t2,y2] = ode23(@murder,[0,12],30); % Simulate the heat equation plot(t1,y1,’k-’,’LineWidth’,1.5); % Plot from death to t = 0 hold on % Plots Multiple graphs plot(t2,y2,’k-’,’LineWidth’,1.5); % Plot from t = 0 to 12 plot([-9,td],[37,37],’r-’,’LineWidth’,1.5); % Plot from t = -9 to td plot([-9,12],[22,22],’b:’,’LineWidth’,1.5); % Plot room temperature plot([td,td],[20,40],’k:’,’LineWidth’,1.5); % Plot time of murder grid % Adds Gridlines text(-2.7,28,’Time of death, $t_d$’,’rot’,90,’FontSize’,14,...
Image of page 4
Image of page 5
  • Fall '08
  • staff

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask You can ask ( soon) You can ask (will expire )
Answers in as fast as 15 minutes