Book - MIT OpenCourseWare http/ocw.mit.edu 6.055J 2.038J The Art of Approximation in Science and Engineering Spring 2008 For information about

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MIT OpenCourseWare http://ocw.mit.edu 6.055J / 2.038J The Art of Approximation in Science and Engineering Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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Back-of-the-envelope numbers Symbol What Value Units π pi 3 G Newton’s constant 7 · 10 11 kg 1 m 3 s 1 c speed of light 3 · 10 8 ms 1 k B Boltzmann’s constant 10 4 eV K 1 e electron charge 1 . 6 · 10 19 C σ Stefan–Boltzmann constant 6 · 10 8 Wm 2 K 4 m sun Solar mass 2 · 10 30 kg R earth Earth radius 6 · 10 6 m θ moon / sun angular diameter 10 2 ρ air air density 1 kg m 3 ρ rock rock density 5 g cm 3 c 200 eV nm L water vap heat of vaporization 2 MJ kg 1 γ water surface tension of water 10 1 Nm 1 a 0 Bohr radius 0 . 5 Å a typical interatomic spacing 3 Å N A Avogadro’s number 6 · 10 23 E fat combustion energy density 9 kcal g 1 E bond typical bond energy 4 eV e 2 / 4 π± 0 fine-structure constant α 10 2 c p 0 air pressure 10 5 Pa ν air kinematic viscosity of air 1 . 5 · 10 5 m 2 s 1 ν water kinematic viscosity of water 10 6 m 2 s 1 day 10 5 s year π · 10 7 s F solar constant 1 . 3 k W m 2 AU distance to sun 1 . 5 · 10 11 m P basal human basal metabolic rate 100 W K air thermal conductivity of air 2 · 10 2 1 K 1 K ... of non-metallic solids/liquids 1 W m 1 K 1 K metal of metals 10 2 1 K 1 air c p specific heat of air 1 J g 1 K 1 c p of solids/liquids 25 J mole 1 K 1
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Handling complexity: The art of approximation how to handle complexity organizing complexity discarding complexity divide and conquer abstraction discarding fake complexity (symmetry) discarding actual complexity (lossless compression) (lossy compression) proportional reasoning conservation dimensional analysis special cases discretization springs
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Contents 1. Preview 4 Part 1 Divide and conquer 6 2. Assorted subproblems 7 3. Alike subproblems 19 Part 2 Symmetry and Invariance 20 4. Symmetry 21 5. Proportional reasoning 26 6. Box models and conservation 40 7. Dimensions 48 Part 3 Discarding Information 68 8. Special cases 69 9. Discretization 91 10.Springs 97 Part 4 Backmatter 129 11.Bon voyage! 130 Bibliography 133 Index 135
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Chapter 1 Preview An approximate model can be better than an exact model! This counterintuitive statement suggests a few questions. First, how can approximate mod- els be at all useful? Should we not strive for exactness? Second, what makes some models more useful than others? On the first question: An approximate answer is all that we can understand because our minds are a small part of the world itself. So when we represent or model the world, we have to throw away aspects of the world in order for our minds to contain the model.
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This note was uploaded on 02/24/2012 for the course MECHANICAL 6.055J taught by Professor Sanjoymahajan during the Spring '08 term at MIT.

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Book - MIT OpenCourseWare http/ocw.mit.edu 6.055J 2.038J The Art of Approximation in Science and Engineering Spring 2008 For information about

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