/wolfram-commands

my cheatsheet for wolfram commands

Wolfram Commands CheatSheet

Basic Algebra

Partial Fractions

Apart[(x^2-4)/(x^4-x)]

Simplify

Simplify[1/6 n (19 + 15 n + 2 n^2)]

Basic Calculus

Limit and Domain

Limit[sin(2t)/t, t -> 0]
FunctionDomain[sqrt(9-x^2-y^2)]

Derivatives

D[2x]
D[2x, x]
D[2xy, y]
D[2x^2y, x, y]

Indefinite Integrals

Integrate[2x]
Integrate[2x, x]
Integrate[2xy, y]
Integrate[2x^2y, x, y]

Definite Integrals

Integrate[2x,{x,0,5}]
Integrate[2yx,{y,0,5}]
Integrate[Integrate[2yx,{y,0,5}], {x, 5, 4}]

Extrema

LocalExtrema[(x^2/3)+y^2+1/5+xy-(x/2)-(2y/3)]

Linear Algebra

Dot Product

Dot[{1, 2}, {3, 4}]
Dot[{t, t^2}, {2t, 1}]

Determinant

Det[{1, 2}, {3, 4}]
Det[{t, t^2}, {2t, 1}]

Norm

Norm[{1,2}]
Norm[{t^3,5t}]

Extras

Curl[-y/(x^2+y^2), -x/(x^2+y^2), z]

Differential Equation

Check if a function is a solution of the equation, if the result is 0 that means is a solution

Simplify (D[#, x] + 3# - e^(2x))& @ (e^(2x)/5)

e^(2x)/5 = function to test
D[#, x] + 3# - e^(2x) = differential equation

Find potential function

Dsolve[{D[u[x, y], x],D[u[x, y], y]} == {f(x,y),g(x,y)}, u[x,y], {x,y}]
vectorial field = F(f(x,y), g(x,y))