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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 https://en.wikipedia.org/wiki/Lorentz_transformation and 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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