Lectures: Back of the envelope calculations, 2013
Dimensional Analysis
- L1: Introducing dimensional analysis
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Dimensional analysis, similarity, scaling, Pythagoras' theorem,
radius of curvature, choice of units, dimensional analysis, vector spaces,
homogeneous functions, slenderness ratio, fracture, buckling, elasticity,
diastolic pressure, cardiac output, giraffe, Brachiosaurus.
[pdf, Mathematica notebook] - L2: Measurements and fundamental constants
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Principle of equivalence, Coulomb's law, Gaussian units, SI units, Lorentz
force, electric field, magnetic field, Biot-Savart law, Maxwell's equations,
speed of light, Joule's constant, Boltzmann's constant, Planck's constant,
black body, Planck spectrum, Stefan-Boltzmann constant, ultraviolet
catastrophe, Compton wavelength, Bohr radius, Rydberg's constant, Thompson
scattering, protein folding, vacuum decay, Planck mass.
[pdf, Mathematica notebook] - L3: The physics of plasmas
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Plasma, electrical resistance, Ohm's law, resistivity, conductivity,
ballistic transport, collisions, Rutherford scattering, plasma
parameter, space charge, screening, Debye screening length, plasma
oscillations, Langmuir waves, plasmon, Landau damping, quantum plasmas,
diffractive scattering, relativistic plasmas, plasmas in quantum field
theory.
[pdf] - L4: Similarity and incomplete similarity
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Convection, Fourier's law, Boussinesq's approximation, shear viscosity,
Joule's constant, Boltzmann's constant, Prandtl number, Rayleigh
number, Rayleigh-Benard convection, scaling, incomplete scaling,
anomalous dimension, fractal, fractal dimension, broken scale invariance,
scaling and the renormalization group, quantum field theory, ultraviolet
divergence, broken scale invariance, renormalized coupling, renormalized
mass, renomalization group equations.
[pdf]
Statistical inference
- L5: Informal problems of inference
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Cards, cheating, prior knowledge, probability, inference, Monty Hall,
Rolls Royce, Martin Gardner, AIDS testing, search engine terms, tossing
a coin, angular momentum, phase space, symmetry.
[pdf] - L6: Inference and probability
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Logic, syllogism, Boolean algebra, uncertain propositions, plausibility,
information and implication, common sense, consistency, fairness, equivalence,
probability, Bayesian reasoning, jumping to conclusions, Bernoulli's urn,
randomness.
[pdf] - L7: Testing hypotheses
- Sampling distribution, prior probability, posterior probability, odds, evidence, sampling without replacement, sampling with replacement, level of significance, zombie hypotheses.
- L7: Estimation of parameters
- Bernoulli urn, sampling theory, hidden symmetry, hypergeometric distribution, fitting, frequentist result, prior dependence.
Approximation methods
Copyright: Sourendu Gupta; Last modified on 19 Apr, 2024.