Students move their left arm in a circle to trace out the complex plane (Argand diagram). They then explore the rectangular and exponential representations of complex numbers by using their left arm to show given complex numbers on the complex plane. Finally they enact multiplication of complex numbers in exponential form and complex conjugation.

1. 1. Which pairs of events (if any) are simultaneous in the unprimed frame?

   2. Which pairs of events (if any) are simultaneous in the primed frame?

   3. Which pairs of events (if any) are colocated in the unprimed frame?

   4. Which pairs of events (if any) are colocated in the primed frame?

      

2. For each of the figures, answer the following questions:

   1. Which event occurs first in the unprimed frame?

   2. Which event occurs first in the primed frame?

      1. 

      2. 

      3. 

• The same model used in MacKay's book
• Introduce key ideas from thermodynamics
• A valuable model for figuring out how we're going to save the Earth

Let's start by visualizing the energy flow associated with driving a gasoline-powered car. We will use a box and arrow diagram, where boxes represent where energy can accumulate, and arrows show energy flow.

The energy clearly starts in the form of gasoline in the tank. Where does it go?

Actually ask this of students.

The heat can look like

• Hot exhaust gas
• The radiator (its job is to dissipate heat)
• Friction heating in the drive train

The work contribute to

• Rubber tires heated by deformation
• Wind, which ultimately ends up as heating the atmosphere

The most important factors for a coarse-grain model of highway driving:

1. The 75:25 split between “heat” and “work”
2. The trail of wind behind a car

What might we have missed? Where else might energy have gone? We ignored the kinetic energy of the car, and the energy dissipated as heat in the brakes. On the interstate this is appropriate, but for city driving the dominant “work” may be in accelerating the car to 30 mph, and with that energy then converted into heat by the brakes.

• Students evaluate two given partial derivatives from a system of equations.
• Students learn/review generalized Leibniz notation.
• Students may find it helpful to use a chain rule diagram.

Student consider several curves on a spacetime diagram and have to judge which curves could be worldlines for an object.

In this lecture, students see a geometric derivation of the Lorentz Transformation on a spacetime diagram.