6.084 The Art of Approximation in Engineering and Science (U)

L MWF1, Room 4-265
Professor Sanjoy Mahajan, sanjoy@mrao.cam.ac.uk
Prereq.: 8.01 or equivalent
3-0-9
Course website (from FT06): http://web.mit.edu/sanjoy/www/6.084-F2006/

How far can birds (and 747's) fly without eating? How does their design affect their optimum cruising speeds, and vice versa? How high can animals jump? Why are random walks recurrent in two dimensions but non-recurrent in three dimensions? How tall can mountains rise? How hot is the interior of the sun? How do trees avoid snapping in high winds? How fast do rivers flow? How much energy do gravitational waves carry? How (and why!) does the retinal rod use enzyme kinetics to compute a logarithm of light intensity?

Even when these questions have exact answers, they are buried in the solution of complicated, often nonlinear differential equations. But by skillful lying -- the art of approximation -- you can understand these and other phenomena. The approximation techniques taught include divide-and-conquer reasoning, kitchen-sink experiments, thought experiments, dimensional analysis, limiting cases, and calculus on the cheap. These techniques are illustrated using physics, chemistry, biology, and engineering examples in the world around us. A theme of the examples is the connections between form and function in natural and engineered systems and their consequences for design.

Grading: reading memos, class participation, problem sets, midterm, and a final.

READINGS

Main text: Mahajan, Phinney, Goldreich, _The Art of Approximation in Science_.

Short course reader drawn from these books:

* Adrian Bejan, _Shape and Structure, from Engineering to Nature_ (CUP, 2000).

* Henk Tennekes, _The Simple Science of Flight: From Insects to Jumbo Jets_ (MIT Press, 1997).

* Thomas A. McMahon and John Tyler Bonner. _Size and Life_ (New York: Scientific American Library, 1983).

* Knut Schmidt-Nielsen, _Scaling: Why is Animal Size So Important?_ (CUP, 1984).

* George W. Hart, _Multidimensional Analysis: Algebras and Systems for Science and Engineering_ (Springer Verlag, 1995).

and articles:

* E. M. Purcell, 'Life at low Reynolds number', American Journal of Physics 45:3-11 (1977).

* "Search for Simplicity": Series of articles by Viktor Weisskopf in the American Journal of Physics.