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The Art of Approximation in Science and Engineering

 

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)

PARTS

TOPICS

 

Preview (PDF)

1

Divide and conquer (PDF)

2

Symmetry and invariance (PDF)

3

Discarding information (PDF)

4

Backmatter (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:

1

Preview (PDF)

Managing complexity (PDF)

Pit spacing (PDF)

Managing complexity:

Heterogeneous hierarchies:

2

Tree representations (PDF)

Oil imports (PDF)

3

Gold or bills? (PDF)

4

Random walks (PDF)

Random walks for accuracy (PDF)

5

UNIX (PDF)

Removing spurious complexity:

Proportional reasoning:

6

Triangle bisection (PDF)

7

Pentagonal heat flow (PDF)

Introduction plus spring mass period (PDF)

Mountain heights (PDF)

8

Animal jump heights (PDF)

Calculus (maximizing a quadratic) (PDF)

Jump heights (PDF)

9

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

Power limits to jumping (PDF)

10

Falling cones (PDF)

Calculus (maximizing a quadratic) (PDF)

11

Drag and jumping (PDF)

12-14

Cycling, swimming, flying (PDF)

Conservation/box models:

15

Conservation cube (PDF)

16

Flight (PDF)

17

Flight (scaling) (PDF)

18

Flight (explicit range and speed) (PDF)

Dimensions and afterword:

19

Algebraic symmetry (PDF)

20

Economics example; pyramid example (PDF)

21

Dimensionless groups (PDF)

Hydrogen size (PDF)

22

Densities (PDF)

Hydrogen size by physics (PDF)

23

Long-lasting learning 1 (PDF)

24-25

Bending of light (PDF)

26-29

Long-lasting learning 2 (PDF)

Buckingham Pi Theorem (PDF)

Discarding actual complexity:

Special cases:

30-31

Pyramid volume (PDF)

Pulley acceleration (PDF)

32-34

Drag! (PDF)

Discretization:

35-36

Random walks and keeping warm (PDF)

Spring models:

37-38

Waves (PDF)

Assignments

Problem set 7 was optional. No solution was given.

ASSIGNMENTS

SOLUTIONS

Homework 1 (PDF)

(PDF)

Homework 2 (PDF)

(PDF)

Homework 3 (PDF)

(PDF)

Homework 4 (PDF)

(PDF)

Homework 5 (PDF)

(PDF)

Homework 6 (PDF)

(PDF)

Homework 7 (PDF)

N/A