Courses:

The Art of Approximation in Science and Engineering >> Content Detail



Study Materials



Readings



Singing Logarithms and Physical Constants


Calculating logarithms using musical intervals (PDF)

Constants for back-of-the-envelope calculations (PDF)



Required Text


The course readings were taken from a manuscript for the course notes. The manuscript is available as one file or broken up into its four major parts. Chapter 3 in Part 1 is unavailable.

Entire book (PDF - 1.2 MB)


PARTSTOPICS
 Preview (PDF)
1Divide and conquer (PDF)
2Symmetry and invariance (PDF)
3Discarding information (PDF)
4Backmatter (PDF)



Readings by Session


Readings given in the table below were designed to be read after that session's discussion and are taken from the manuscript above.


SES #READINGS

Introduction:

1Preview (PDF)

Managing complexity (PDF)

Pit spacing (PDF)

Managing complexity:

Heterogeneous hierarchies:
2Tree representations (PDF)

Oil imports (PDF)
3Gold or bills? (PDF)
4Random walks (PDF)

Random walks for accuracy (PDF)
5UNIX (PDF)

Removing spurious complexity:

Proportional reasoning:
6Triangle bisection (PDF)
7Pentagonal heat flow (PDF)

Introduction plus spring mass period (PDF)

Mountain heights (PDF)
8Animal jump heights (PDF)

Calculus (maximizing a quadratic) (PDF)

Jump heights (PDF)
9Calculus (maximizing gain of a second-order system) (PDF)

Power limits to jumping (PDF)
10Falling cones (PDF)

Calculus (maximizing a quadratic) (PDF)
11Drag and jumping (PDF)
12-14Cycling, swimming, flying (PDF)
Conservation/box models:
15Conservation cube (PDF)
16Flight (PDF)
17Flight (scaling) (PDF)
18Flight (explicit range and speed) (PDF)
Dimensions and afterword:
19Algebraic symmetry (PDF)
20Economics example; pyramid example (PDF)
21Dimensionless groups (PDF)

Hydrogen size (PDF)
22Densities (PDF)

Hydrogen size by physics (PDF)
23Long-lasting learning 1 (PDF)
24-25Bending of light (PDF)
26-29Long-lasting learning 2 (PDF)

Buckingham Pi Theorem (PDF)

Discarding actual complexity:

Special cases:
30-31Pyramid volume (PDF)

Pulley acceleration (PDF)
32-34Drag! (PDF)
Discretization:
35-36Random walks and keeping warm (PDF)
Spring models:
37-38Waves (PDF)

 








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