DATA observations experiments and measurements Real world phenomenon

Data observations experiments and measurements real

This preview shows page 2 - 4 out of 13 pages.

DATA observations, experiments, and measurements. Real-world phenomenon Qualitative predictions Quantitative predictions Re fi ne model Determine dependent and independent variables Assign symbols to variables, Choose sensible units of measurement for variables Apply principles, laws and assumptions Mathematical inferences Analysis Computing Graphics Mathematical representation A diagram of the Modeling Process Joseph M. Mahaffy, h [email protected] i Lecture Notes – Direction Fields and Phase Portraits - 1D — (5/50) Mathematical Modeling Introduction to MatLab Qualitative Behavior of Differential Equations More Examples Maple - Direction Fields Solution of Linear Growth and Decay Models Mathematical Modeling Newton’s Law of Cooling Murder Investigation Linear Differential Equation Newton’s Law of Cooling 1 Newton’s Law of Cooling: After a murder (or death by other causes), the forensic scientist takes the temperature of the body Later the temperature of the body is taken again to find the rate at which the body is cooling Two (or more) data points are used to extrapolate back to when the murder occurred This property is known as Newton’s Law of Cooling Joseph M. Mahaffy, h [email protected] i Lecture Notes – Direction Fields and Phase Port — (6/50) Mathematical Modeling Introduction to MatLab Qualitative Behavior of Differential Equations More Examples Maple - Direction Fields Solution of Linear Growth and Decay Models Mathematical Modeling Newton’s Law of Cooling Murder Investigation Linear Differential Equation Newton’s Law of Cooling 2 Newton’s Law of Cooling states that the rate of change in temperature of a cooling body is proportional to the difference between the temperature of the body and the surrounding environmental temperature If T ( t ) is the temperature of the body, then it satisfies the differential equation dT dt = - k ( T ( t ) - T e ) with T (0) = T 0 The parameter k is dependent on the specific properties of the particular object (body in this case) T e is the environmental temperature T 0 is the initial temperature of the object Joseph M. Mahaffy, h [email protected] i Lecture Notes – Direction Fields and Phase Portraits - 1D — (7/50) Mathematical Modeling Introduction to MatLab Qualitative Behavior of Differential Equations More Examples Maple - Direction Fields Solution of Linear Growth and Decay Models Mathematical Modeling Newton’s Law of Cooling Murder Investigation Linear Differential Equation Murder Example 1 Murder Example Suppose that a murder victim is found at 8:30 am The temperature of the body at that time is 30 C Assume that the room in which the murder victim lay was a constant 22 C Suppose that an hour later the temperature of the body is 28 C Normal temperature of a human body when it is alive is 37 C Use this information to determine the approximate time that the murder occurred Joseph M. Mahaffy, h [email protected] i Lecture Notes – Direction Fields and Phase Port — (8/50)
Image of page 2

Subscribe to view the full document.

Mathematical Modeling Introduction to MatLab
Image of page 3
Image of page 4
  • 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