The art of insight in science and engineering : mastering complexity / Sanjoy Mahajan.

Format:

Book

Author/Creator:

Mahajan, Sanjoy, 1969- author.

Language:

English

Subjects (All):

Statistical physics.

Estimation theory.

Hypothesis.

Problem solving.

Physical Description:

xvi, 389 pages : illustrations ; 24 cm

Place of Publication:

Cambridge, Massachusetts : The MIT Press, [2014]

Contents:

Part I Organizing complexity 1

1 Divide and conquer 3

1.1 Warming up 3

1.2 Rails versus roads 6

1.3 Tree representations 7

1.4 Demand-side estimates 10

1.5 Multiple estimates for the same quantity 16

1.6 Talking to your gut 17

1.7 Physical estimates 20

1.8 Summary and further problems 25

2 Abstraction 27

2.1 Energy from burning hydrocarbons 28

2.2 Coin-flip game 31

2.3 Purpose of abstraction 34

2.4 Analogies 36

2.5 Summary and further problems 53

Part II Discarding complexity without losing information 55

3 Symmetry and conservation 57

3.1 Invariants 57

3.2 From invariant to symmetry operation 66

3.3 Physical symmetry 73

3.4 Box models and conservation 75

3.5 Drag using conservation of energy 84

3.6 Lift using conservation of momentum 93

3.7 Summary and further problems 99

4 Proportional reasoning 103

4.1 Population scaling 103

4.2 Finding scaling exponents 105

4.3 Scaling exponents in fluid mechanics 117

4.4 Scaling exponents in mathematics 123

4.5 Logarithmic scales in two dimensions 126

4.6 Optimizing flight speed 128

4.7 Summary and further problems 135

5 Dimensions 137

5.1 Dimensionless groups 139

5.2 One dimensionless group 147

5.3 More dimensionless groups 152

5.4 Temperature and charge 165

5.5 Atoms, molecules, and materials 175

5.6 Summary and further problems 192

Part III Discarding complexity with loss of information 197

6 Lumping 199

6.1 Approximate! 199

6.2 Rounding on a logarithmic scale 200

6.3 Typical or characteristic values 203

6.4 Applying lumping to shapes 212

6.5 Quantum mechanics 229

6.6 Summary and further problems 234

7 Probabilistic reasoning 235

7.1 Probability as degree of belief: Bayesian probability 235

7.2 Plausible ranges: Why divide and conquer works 239

7.3 Random walks: Viscosity and heat flow 249

7.4 Transport by random walks 263

7.5 Summary and further problems 276

8 Easy cases 279

8.1 Warming up 279

8.2 Two regimes 281

8.3 Three regimes 291

8.4 Two dimensionless quantities 308

8.5 Summary and further problems 312

9 Spring models 317

9.1 Bond springs 317

9.2 Energy reasoning 321

9.3 Generating sound, light, and gravitational radiation 331

9.4 Effect of radiation: Blue skies and red sunsets 345

9.5 Summary and further problems 353.

Notes:

Includes bibliographical references (pages 359-361) and index.

ISBN:

9780262526548

0262526549

OCLC:

875770923