Ryan/Female/18/The PNW/Almost dead account/angsty musings/music

To kill or not to kill (the purp?)

To kill or not to kill (the purp?)

halfstoned:

So I got this little dude today and I absolutely love how it turned out, fucking awesome and worth all the pain. My artist Joshua Smith was equally as awesome, check his work out! Any artist that puts on Star Wars for the entire session is fantastic in my book. (I wonder what thefrontbottoms thinks of it, though?)

halfstoned:

So I got this little dude today and I absolutely love how it turned out, fucking awesome and worth all the pain. My artist Joshua Smith was equally as awesome, check his work out! Any artist that puts on Star Wars for the entire session is fantastic in my book. (I wonder what thefrontbottoms thinks of it, though?)

fouriestseries:

Taylor Series Approximations
A Taylor series is a way to represent a function in terms of polynomials. Since polynomials are usually much easier to work with than complicated functions, Taylor series have numerous applications in both math and physics.
There are many equations in physics — like the one describing the motion of a pendulum — that are impossible to solve in terms of elementary functions. “Approximations using the first few terms of a Taylor series can make [these] otherwise unsolvable problems” solvable for a restricted area of interest [1].
The GIF above shows the five-term Taylor series approximation of a sine wave about x=0.
Mathematica code:
f[x_] := Sin[x]
ts[x_, a_, nmax_] := 
    Sum[(Derivative[n][f][a]/n!)*(x - a)^n, {n, 0, nmax}]
Manipulate[Plot[{f[x], ts[x, 0, nmax]}, {x, -2*Pi, 2*Pi}, 
    PlotRange -> {-1.45, 1.45}, 
    PlotStyle -> {{Thick, Cyan}, {Thick, Dotted, Yellow}}, 
    AxesStyle -> LightGray, Background -> Darker[Gray, 0.8]], 
    {nmax, 1, 30, 1}]

Sitting in the library staring at this rather than try to derive Virial theorem for my problem set. Its ok because we talked about binomial expansion in lecture today so its relevant. Also math is so pretty I need to figure out this major thing but ugggg 

fouriestseries:

Taylor Series Approximations

A Taylor series is a way to represent a function in terms of polynomialsSince polynomials are usually much easier to work with than complicated functions, Taylor series have numerous applications in both math and physics.

There are many equations in physics — like the one describing the motion of a pendulum — that are impossible to solve in terms of elementary functions. “Approximations using the first few terms of a Taylor series can make [these] otherwise unsolvable problems” solvable for a restricted area of interest [1].

The GIF above shows the five-term Taylor series approximation of a sine wave about x=0.

Mathematica code:

f[x_] := Sin[x]
ts[x_, a_, nmax_] := 
    Sum[(Derivative[n][f][a]/n!)*(x - a)^n, {n, 0, nmax}]
Manipulate[Plot[{f[x], ts[x, 0, nmax]}, {x, -2*Pi, 2*Pi}, 
    PlotRange -> {-1.45, 1.45}, 
    PlotStyle -> {{Thick, Cyan}, {Thick, Dotted, Yellow}}, 
    AxesStyle -> LightGray, Background -> Darker[Gray, 0.8]], 
    {nmax, 1, 30, 1}]

Sitting in the library staring at this rather than try to derive Virial theorem for my problem set. Its ok because we talked about binomial expansion in lecture today so its relevant. Also math is so pretty I need to figure out this major thing but ugggg 

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