Classes: Tues/Thurs 1:30-3:05pm D250, E&MS.
Office hours: Tues/Thurs 12:30-1:30pm A219 (FN) and Thurs 11:30-1:30pm A254 (PC).
An important skill for graduate students is the ability to make “quick and dirty” calculations, to see whether a problem is worth investigating properly. Such “back of the envelope” techniques are a vital part of any working scientist’s intellectual toolbox. This class is designed to teach some of these techniques.
Classes will consist of a mixture of lectures, discussions and in-class problems. Problem sets will consist of both solving, and suggesting, suitable problems. There will be a final exam (oral).
We will discuss problems relating to: Planets, Oceans and Atmospheres, Energy and the Environment, and Real Life. Typical examples: How long does it take the Moon to cool? Do beaver dams affect global warming? How dense is a neutron star? What controls how tall trees (or mountains) grow? How small is the smallest mammal? How many piano tuners in New York City? (Aficionados will recognize the last question as the archetypcal Fermi Problem).
Very few textbooks are available on this kind of material, but two reasonable ones are Back of the Envelope Physics, C. Swartz, Johns Hopkins Univ. Press, 1993, and Guesstimation, L. Weinstein and J.A. Adam, Princeton Univ. Press, 2008. An outstanding guide to order of magnitude problems as applied to energy and the environment is Sustainable energy – without the hot air by D.J.C. McKay (UIT Press, 2009). By far the most entertaining “textbook” is What If?, R. Monroe, Houghton Mifflin, 2014. For the biologically-inclined, there are some useful problems in Cell Biology by the Numbers by R. Milo et al.
There are also several useful websites. By far the best is an excellent (if incomplete) textbook from Sanjoy Mahajan at MIT. Sanjoy has also published a related book, Street-Fighting Mathematics (MIT Press 2010) which is, however, not as useful. Eugene Chiang at Berkeley has a very useful home page for a course similar to this one; Sterl Phinney at Caltech has another. The University of Maryland has a good Fermi Problem site. And here are some astrophysical examples from Ohio State.
Here is the syllabus. This will only be approximate – we prefer covering a few topics in depth (lots of examples!) to more topics less carefully.
You can download the lecture handouts and problem sets (PDF format) below.
| Week 1 (10 Jan) | Basic concepts and more on basic concepts; Getting our feet wet |
| Week 2 (17 Jan) | Material properties Binding energies Sanjoy’s chapter |
| Week 3 (24 Jan) | Heat transfer and mass transfer |
| Weeks 4-5 (31 Jan) | Fluid mechanics Viscous flows |
| Week 6 (14 Feb) | Turbulence, more turbulence, and boundary layers |
| Week 7 (21 Feb) | Waves and Oscillators |
| Week 8 (28 Feb) | Energy and the environment |
| Week 9 (7 Mar) | Disasters More disasters |
Over the course of the term we will be compiling a list of useful numbers; there will also be a list of basic equations and some useful formulae to know.