Tricks and Shortcuts

Head[37]

Head[3/7]

Head[3.71]

Head[ 3 + 4 I ]

Head[ "Hello" ]

Head[ x ]

Head[a+b]

Plus[a+b]

r = {1,2,3,4,5,6,7,8,9,10}

Head[%]

Apply[Plus,r]

Plus @@ r

Plus @@ r / Length[r]  // N

cube = Function[x, x^3]

Function[x, x^3] [2]

cube[3]

#^3 &

#^3 & [a]

Function[{x,y}, Sin[x] Cos[y^2]]

%[a,b]

Sin[ #1 ] Cos[ #2^2 ] &

%[a,b]

Map[ #^2 &, {1,2,3,4,5} ]

vars = {a, x^2, 1.3, Cos[y] }

Map[ f, vars]

Map[ Sin, vars ]

Sin /@ vars

Applications

eq = a^2 Sin[ f[t] ] +  t b Cos[ f[t] ] == 0

Map[ #/a^2 &, % ]

Apart /@ Map[ #/a^2 &, eq]

neweq = %

Series[ #, {f[t],0,2} ] & /@ neweq

newesteq = Normal[%]

sol = Solve[%, f[t] ]

f[t] /. sol[[1]]