Physics Derivation Graph: July 2017

I've decided to focus on building content for the Physics Derivation Graph. Since I don't think it's reasonable to enter all the mathematical physics content manually on my own, in this post I'll define some bounds.

Step 1: identify major fields in Physics

Electromagnetism
relativity

astrophysics

quantum mechanics
classical mechanics

thermodynamics

Step 2: identify top derivations associated with each area

Electromagnetism: Maxwell's equations
Relativity: Lorentz (time dilation, length contraction)

astrophysics:

Quantum mechanics: Schrodinger, Uncertainty
Classical mechanics: F=ma, conservation of energy and momentum

thermodynamics: entropy

Step 3:

There are expressions, domains, and notations that need to be included to demonstrate the comprehensive nature of the project and the capability of the framework.

Expressions	Domains	Notation
Schrodinger's equation	Quantum	Dirac/bra-ket

Maxwell's equations	Electromagnetics	differentiation, vectors
contravariant/covariant	Electrodynamics	Einstein notation
Navier Stokes	Fluid Mechanics	differentiation, vectors
mass-energy relation
	Special Relativity
	Thermodynamics
Uncertainty relation	Quantum Mechanics
energy conservation	classical mechanics
	string theory
wave equation
	statistical mechanics
	aerodynamics
simple harmonic oscillator

Other comprehensive lists of "things to know" in Physics

https://www.staff.science.uu.nl/~gadda001/goodtheorist/

https://news.ycombinator.com/item?id=10714048

http://www.physics.uoguelph.ca/poisson/research/notes.html

https://www.physics.uoguelph.ca/poisson/research/mech.pdf

http://theoreticalminimum.com/courses

https://github.com/allofphysicsgraph/proofofconcept/wiki/All-Branches-of-Physics

The Physics Derivation Graph has a few pertinent scales:

topics within physics, ie thermodynamics, quantum mechanics, classical mechanics

major (often named) expressions within a domain, ie "E=mc^2", Schrodinger's equation, Maxwell's equations

derivations linking the major expressions

abstract syntax trees of an expression

In this post, I'll focus on finding examples of derivations linking the major expressions

Useful places to search

Google Scholar
Arxiv
journals for Physics teachers

Useful search string: derivation of equation

Unsorted results

https://en.wikipedia.org/wiki/ADM_formalism
https://en.wikipedia.org/wiki/Abraham–Lorentz_force
https://en.wikipedia.org/wiki/Acoustic_wave_equation
https://en.wikipedia.org/wiki/Action-angle_coordinates
https://en.wikipedia.org/wiki/Adiabatic_process
https://en.wikipedia.org/wiki/Angular_momentum
https://en.wikipedia.org/wiki/Angular_momentum_operator
https://en.wikipedia.org/wiki/Appell's_equation_of_motion
https://en.wikipedia.org/wiki/Area_of_a_circle
https://en.wikipedia.org/wiki/Available_energy_(particle_collision)
https://en.wikipedia.org/wiki/Avrami_equation
https://en.wikipedia.org/wiki/Azimuthal_quantum_number
https://en.wikipedia.org/wiki/BET_theory
https://en.wikipedia.org/wiki/Backpropagation
https://en.wikipedia.org/wiki/Ballistic_pendulum
https://en.wikipedia.org/wiki/Beer–Lambert_law
https://en.wikipedia.org/wiki/Bell's_theorem
https://en.wikipedia.org/wiki/Bethe–Salpeter_equation
https://en.wikipedia.org/wiki/Bivector
https://en.wikipedia.org/wiki/Black–Scholes_model
https://en.wikipedia.org/wiki/Bloch_oscillations
https://en.wikipedia.org/wiki/Boltzmann_relation
https://en.wikipedia.org/wiki/Bose–Einstein_statistics
https://en.wikipedia.org/wiki/Braking_distance
https://en.wikipedia.org/wiki/CHSH_inequality
https://en.wikipedia.org/wiki/Capillary_wave
https://en.wikipedia.org/wiki/Catenary
https://en.wikipedia.org/wiki/Causal_dynamical_triangulation
https://en.wikipedia.org/wiki/Causality
https://en.wikipedia.org/wiki/Centimetre–gram–second_system_of_units
https://en.wikipedia.org/wiki/Centripetal_force
https://en.wikipedia.org/wiki/Charge_conservation
https://en.wikipedia.org/wiki/Classical_electron_radius
https://en.wikipedia.org/wiki/Clausius–Clapeyron_relation
https://en.wikipedia.org/wiki/Coefficient_of_restitution
https://en.wikipedia.org/wiki/Collective_noun
https://en.wikipedia.org/wiki/Collision_theory
https://en.wikipedia.org/wiki/Compton_scattering
https://en.wikipedia.org/wiki/Conductance_quantum
https://en.wikipedia.org/wiki/Confidence_interval
https://en.wikipedia.org/wiki/Convolution
https://en.wikipedia.org/wiki/Darcy's_law
https://en.wikipedia.org/wiki/Debye_model
https://en.wikipedia.org/wiki/Derivative
https://en.wikipedia.org/wiki/Diffusion_equation
https://en.wikipedia.org/wiki/Doppler_broadening
https://en.wikipedia.org/wiki/Drag_equation
https://en.wikipedia.org/wiki/Dynamic_mechanical_analysis
https://en.wikipedia.org/wiki/Eddington_luminosity
https://en.wikipedia.org/wiki/Effective_medium_approximations
https://en.wikipedia.org/wiki/Elastic_collision
https://en.wikipedia.org/wiki/Electrodynamic_tether
https://en.wikipedia.org/wiki/Equilibrium_constant
https://en.wikipedia.org/wiki/Euler–Bernoulli_beam_theory
https://en.wikipedia.org/wiki/Euler–Maclaurin_formula
https://en.wikipedia.org/wiki/Ewald_summation
https://en.wikipedia.org/wiki/Exponential_decay
https://en.wikipedia.org/wiki/Fermat's_principle
https://en.wikipedia.org/wiki/Feynman_parametrization
https://en.wikipedia.org/wiki/Fick's_laws_of_diffusion
https://en.wikipedia.org/wiki/Fictitious_force
https://en.wikipedia.org/wiki/Fisher_information
https://en.wikipedia.org/wiki/Flory–Huggins_solution_theory
https://en.wikipedia.org/wiki/Fluctuation-dissipation_theorem
https://en.wikipedia.org/wiki/Four-gradient
https://en.wikipedia.org/wiki/Four-momentum
https://en.wikipedia.org/wiki/Fourier_optics
https://en.wikipedia.org/wiki/Freund–Rubin_compactification
https://en.wikipedia.org/wiki/Gaussian_gravitational_constant
https://en.wikipedia.org/wiki/Geiger–Nuttall_law
https://en.wikipedia.org/wiki/Generalizations_of_the_derivative
https://en.wikipedia.org/wiki/Gibbs_free_energy
https://en.wikipedia.org/wiki/Gibbs–Duhem_equation
https://en.wikipedia.org/wiki/Giovanni_Semerano
https://en.wikipedia.org/wiki/Golden_ratio
https://en.wikipedia.org/wiki/Group_velocity
https://en.wikipedia.org/wiki/Group_velocity_dispersion
https://en.wikipedia.org/wiki/Gullstrand–Painlevé_coordinates
https://en.wikipedia.org/wiki/Gyroradius
https://en.wikipedia.org/wiki/Hamilton–Jacobi_equation
https://en.wikipedia.org/wiki/Harmonic_coordinate_condition
https://en.wikipedia.org/wiki/Haynes–Shockley_experiment
https://en.wikipedia.org/wiki/Heat_equation
https://en.wikipedia.org/wiki/Helmholtz_coil
https://en.wikipedia.org/wiki/Helmholtz_decomposition
https://en.wikipedia.org/wiki/Hyperfocal_distance
https://en.wikipedia.org/wiki/Interference_(wave_propagation)
https://en.wikipedia.org/wiki/Ion_acoustic_wave
https://en.wikipedia.org/wiki/Isotropic_radiator
https://en.wikipedia.org/wiki/Kalman_filter
https://en.wikipedia.org/wiki/Killing_vector_field
https://en.wikipedia.org/wiki/Kinetic_energy
https://en.wikipedia.org/wiki/Klein–Gordon_equation
https://en.wikipedia.org/wiki/Kramers–Kronig_relations
https://en.wikipedia.org/wiki/Kramers–Wannier_duality
https://en.wikipedia.org/wiki/Kutta–Joukowski_theorem
https://en.wikipedia.org/wiki/Lamb_shift
https://en.wikipedia.org/wiki/Landau_quantization
https://en.wikipedia.org/wiki/Langmuir_(unit)
https://en.wikipedia.org/wiki/Laplace_expansion_(potential)
https://en.wikipedia.org/wiki/Large_eddy_simulation
https://en.wikipedia.org/wiki/Larmor_formula
https://en.wikipedia.org/wiki/Leibniz_integral_rule
https://en.wikipedia.org/wiki/Length_contraction
https://en.wikipedia.org/wiki/Lie_algebra
https://en.wikipedia.org/wiki/Liénard–Wiechert_potential
https://en.wikipedia.org/wiki/Linear_least_squares_(mathematics)
https://en.wikipedia.org/wiki/Linearized_gravity
https://en.wikipedia.org/wiki/Lippmann–Schwinger_equation
https://en.wikipedia.org/wiki/Magic_number_(physics)
https://en.wikipedia.org/wiki/Magnetic_quantum_number
https://en.wikipedia.org/wiki/Mass–energy_equivalence
https://en.wikipedia.org/wiki/Maxwell–Boltzmann_statistics
https://en.wikipedia.org/wiki/Mean_effective_pressure
https://en.wikipedia.org/wiki/Mean_free_path
https://en.wikipedia.org/wiki/Metalloid
https://en.wikipedia.org/wiki/Mooney–Rivlin_solid
https://en.wikipedia.org/wiki/Newton's_theorem_of_revolving_orbits
https://en.wikipedia.org/wiki/Noether's_theorem
https://en.wikipedia.org/wiki/Non-associative_algebra
https://en.wikipedia.org/wiki/Optical_flat
https://en.wikipedia.org/wiki/Optical_theorem
https://en.wikipedia.org/wiki/Orbital_state_vectors
https://en.wikipedia.org/wiki/Parabola
https://en.wikipedia.org/wiki/Parallax
https://en.wikipedia.org/wiki/Parametric_oscillator
https://en.wikipedia.org/wiki/Particle_in_a_spherically_symmetric_potential
https://en.wikipedia.org/wiki/Paschen's_law
https://en.wikipedia.org/wiki/Path_integral_formulation
https://en.wikipedia.org/wiki/Perpendicular_axis_theorem
https://en.wikipedia.org/wiki/Pilot_wave
https://en.wikipedia.org/wiki/Planck's_law
https://en.wikipedia.org/wiki/Planck_particle
https://en.wikipedia.org/wiki/Plasmon
https://en.wikipedia.org/wiki/Poisson–Boltzmann_equation
https://en.wikipedia.org/wiki/Polarization_identity
https://en.wikipedia.org/wiki/Ponderomotive_energy
https://en.wikipedia.org/wiki/Ponderomotive_force
https://en.wikipedia.org/wiki/Potential_energy
https://en.wikipedia.org/wiki/Potential_temperature
https://en.wikipedia.org/wiki/Poynting's_theorem
https://en.wikipedia.org/wiki/Price_equation
https://en.wikipedia.org/wiki/Principal_quantum_number
https://en.wikipedia.org/wiki/Principle_of_maximum_entropy
https://en.wikipedia.org/wiki/Quadratic_equation
https://en.wikipedia.org/wiki/Quartz_crystal_microbalance
https://en.wikipedia.org/wiki/RRKM_theory
https://en.wikipedia.org/wiki/Radian
https://en.wikipedia.org/wiki/Radius_of_gyration
https://en.wikipedia.org/wiki/Rainbow
https://en.wikipedia.org/wiki/Read_(surname)
https://en.wikipedia.org/wiki/Redshift
https://en.wikipedia.org/wiki/Reduced_mass
https://en.wikipedia.org/wiki/Relational_quantum_mechanics
https://en.wikipedia.org/wiki/Richards_equation
https://en.wikipedia.org/wiki/Roche_limit
https://en.wikipedia.org/wiki/Rodrigues'_rotation_formula
https://en.wikipedia.org/wiki/Rotating_wave_approximation
https://en.wikipedia.org/wiki/Rutherford_scattering
https://en.wikipedia.org/wiki/Saha_ionization_equation
https://en.wikipedia.org/wiki/Scale_relativity
https://en.wikipedia.org/wiki/Schrödinger_equation
https://en.wikipedia.org/wiki/Schwinger–Dyson_equation
https://en.wikipedia.org/wiki/Second_law_of_thermodynamics
https://en.wikipedia.org/wiki/Shallow_water_equations
https://en.wikipedia.org/wiki/Shockley_diode_equation
https://en.wikipedia.org/wiki/Spin_connection
https://en.wikipedia.org/wiki/Spin_quantum_number
https://en.wikipedia.org/wiki/Stefan–Boltzmann_law
https://en.wikipedia.org/wiki/Stretch_rule
https://en.wikipedia.org/wiki/String_theory
https://en.wikipedia.org/wiki/Sverdrup_balance
https://en.wikipedia.org/wiki/Taylor's_theorem
https://en.wikipedia.org/wiki/Terminal_velocity
https://en.wikipedia.org/wiki/Tetum_language
https://en.wikipedia.org/wiki/Theorem
https://en.wikipedia.org/wiki/Torque

https://en.wikipedia.org/wiki/Torricelli%27s_equation#Derivation

https://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm#Derivation
tag: math

https://en.wikipedia.org/wiki/Tropical_cyclone#Maximum_potential_intensity
tag: weather

https://en.wikipedia.org/wiki/Twomey_effect#Derivation

https://en.wikipedia.org/wiki/Van_der_Waals_equation#Derivation

https://en.wikipedia.org/wiki/Variable-range_hopping#Derivation

https://en.wikipedia.org/wiki/Visibility#Derivation

https://en.wikipedia.org/wiki/Wallis_product#Derivation
tag: math

https://en.wikipedia.org/wiki/Washburn%27s_equation#Derivation

https://en.wikipedia.org/wiki/Wheeler%E2%80%93DeWitt_equation#Derivation_from_path_integral

https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_equation#Derivation

https://en.wikipedia.org/wiki/Optical_theorem
https://farside.ph.utexas.edu/teaching/qm/lectures/node87.html

Seismic Wave Equation
http://www.ees.nmt.edu/outside/courses/GEOP523/Docs/waveeq.pdf
tag: PDF

Noether's theorem
https://en.wikipedia.org/wiki/Noether%27s_theorem#Derivations
https://www.youtube.com/watch?v=Rqfj7n5aSwY

https://en.wikipedia.org/wiki/Kalman_filter#Derivations

E=mc2 and F=ma
Ives, Herbert E. (1952), "Derivation of the mass–energy relation", Journal of the Optical Society of America, 42 (8): 540–543, doi:10.1364/JOSA.42.000540 | tag: paywall
On the page http://www.emc2-explained.info/Emc2/Deriving.htm
there's a step which involves https://en.wikipedia.org/wiki/Integration_by_substitution
--> I don't understand the third line of equations. The infinitesimal switches from ds to d(mv), and the integration limit changes.

https://en.wikipedia.org/wiki/Maxwell_relations#Derivation