Derivation list: Physics Derivation Graph

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name	abstract	number of steps	reference
angle of maximum distance for projectile motion		23
coefficient of isothermal compressibility using the equation of state for an ideal gas		9	https://hj.hi.is/EE2/HD1lausn.pdf
coefficient of thermal expansion using the equation of state for an ideal gas		9	https://hj.hi.is/EE2/HD1lausn.pdf
Compton's equation for scattering		8
curl curl identity		9
derivation of Schrodinger Equation		39
double intensity when phase is coherent (optics)		33
electric field wave equation: from time dependent to time independent		11
equation of motion for a spring		15
equations of motion in 1D with constant acceleration - SUVAT (algebra)		31	https://en.wikipedia.org/wiki/Equations_of_motion
equations of motion in 2D (calculus)		40
escape velocity		23
Euler equation proof		12
Euler equation to exp(i pi) + 1 = 0		6
Euler equation: trig square root		16
Euler equation: trigonometric relations		12
Euler's equation from MacLaurin series		4	https://fermatslasttheorem.blogspot.com/2006/02/eulers-formula.html
first law of thermodynamics	https://www.youtube.com/watch?v=QTiqF-HtkS0 and https://www.youtube.com/watch?v=3Yls-t3B49U	12
frequency and period	subset of the frequency relation derivation. Intended for display on the homepage	4
frequency relations		11
hyperbolic trigonometric identities		28	http://www.physics.miami.edu/~nearing/mathmethods/mathematical_methods-one.pdf
identity sin(2 x) = 2 sin(x) cos(x) using Euler's equation		9
integration by parts		5
Kepler's Third Law: period squared propto distance cubed		20	https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion#Third_law
Langmuir Adsorption	from https://arxiv.org/pdf/2210.12150.pdf	20
Lorentz transformation	source: \cite{1999_Tipler_Llewellyn}, page 21; see also \url{https://en.wikipedia.org/wiki/Lorentz\_transformation} and \url{https://en.wikipedia.org/wiki/Derivations\_of\_the\_Lorentz\_transformations}	30
mass of the Earth		12
Maxwell equations to electric field wave equation		12
Newton's Law of Gravitation	from https://www.youtube.com/watch?v=fJYdFIZlD8k	19
Newton's Second Law of Motion: vector to scalar	convert vector representation to scalar	6
optics: Law of refraction to Brewster's angle	\cite{2001_HRW}; see figure 34-27 on page 824	15
particle in a 1D box		39
projectile path in 2D is parabolic	Using the 2D equations of motion, show that projectile path is second order polynomial of the form $y = a x^2 + b x + c$	5
quadratic equation derivation		15	https://en.wikipedia.org/wiki/Quadratic_formula#Derivations_of_the_formula
quantum basics Hermitian operators have realvalued observables		7
quantum basics orthogonality		9
radius for satellite in geostationary orbit		16	https://en.wikipedia.org/wiki/Geostationary_orbit#Derivation_of_geostationary_altitude
Schwarzschild radius for non-rotating black hole		4	https://en.wikipedia.org/wiki/Derivation_of_the_Schwarzschild_solution
speed of Earth around Sun	from \cite{1999_Tipler_Llewellyn}, page 9	13
time invariant force conserves energy		32
total electrical resistance for circuit with two resistors in parallel		10	http://www.dfcd.net/articles/derivations/resistors.html
total electrical resistance for circuit with two resistors in series		8	http://www.dfcd.net/articles/derivations/resistors.html
upper limit on velocity in condensed matter		20	https://arxiv.org/pdf/2004.04818.pdf
variance relation		6
velocity at distance r of object dropped from infinity	https://www.youtube.com/watch?v=5F1XcTjpJs4 - Derivation of Gravitational Potential Energy by Rhett Allain	26
work and force and energy		9

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