Course objectives: I want to acquaint attendees with the ways by which engineers analyze and predict the behavior of natural and engineered systems. The most interesting of these to me are dynamic systems and random systems. Dynamic systems display behavior that changes over time while random systems display dynamic behavior that cannot be predicted exactly. Our lives are full of such systems: the climate, the spread of diseases, rise and extinction of species, swaying of buildings in earthquakes. What limits the height of trees? Why is the Eiffel Tower swoop-shaped? Why don’t elephants look like big daddy longlegs? How many trucks does Amazon need to serve a given region? How can methods of modeling physical dynamic systems be used to model people interacting with machines and even interacting with each other? How do economists explain the business cycle? I will try to convey what it is like to design something so that it not only works but will not be subject to the many kinds of challenges that lurk in the design and its natural and human working environment. I will provide plenty of down-to-earth examples and will minimize the use of actual mathematics.
Topics:
• What is a math model and what kinds of things can be modeled
• Mathematical and pictorial models: explaining dynamic behavior without equations
• Continuity: persistence of stuff and energy – the most useful of all the Laws of Nature
• Static and dynamic systems: time delay, growth, shrinkage, oscillation
• Scaling laws, growth patterns, what happens when things get really big or really small
• Regularity and randomness, predictability within limits, mistakes people make
• How engineers think, what keeps them up at night
• What engineering designers do, with examples (Polaroid SX-70, Space Shuttle Booster rocket explosion)