Mathematica inbuilt (pre-defined) "functions" (or operations)

Here is a list of some of the most commonly used Mathematica inbuilt "functions" (or operations).

Name	Example Usage	Description
Clear[variable]	Clear[ a ]	Clears any previous definition of the variable
N[expression]	N[Exp[2]] will return 7.38906.	Returns the numerical value of argument to 6 sig.figs
		(Note that Exp[2] alone will return the pure number $e^2$
N[expression, figs]	N[Exp[2],20] returns answer to 20 sig.figs.	Returns the numerical value of argument to figs significant figures
Plot[f[x],{x,xmin,xmax}]	Plot[x^2-1,{x,0,2}]	Plots the function f(x) within the x-limits specified
Integrate[f[x],{x,xmin,xmax}]	Integrate[Sin[x],{x,0,Pi}]	Integrates the function f(x) between the x-limits specified
D[f[x],x]	D[x^2 + x y,x]	Partial derivative of the function f(x) w.r.t. the variable x
	D[g[x,y],x]	Partial derivative of the user-defined function g(x,y) w.r.t. the variable x
D[f[x,y,...],x,y...]	D[6 Exp[x^3] Sin[y], x,y]	Partial derivative of the function f w.r.t. the variables x,y, ...
	= D[D[6 Exp[x^3] Sin[y], x],y]
Solve[lhs==rhs,x]	Solve[x^2-2x+1==0,x]	Solves the equation(s) w.r.t the variable specified
	Solve[{x^2-2y+1==0,x==2y},{x,y}]	Note that if there is more than one equation, then these
		equations must be in a list { lhs1=rhs1, lhs2=rhs2, ...}
DSolve[equation, f[x], x ]	DSolve[f''[x]== -f[x], f[x], x]	Solves the differential equation for the function f[x]
NDSolve[equation(s), f[x], x ]	NDSolve[{f''[x]== -f[x], f'[0]==0, f[0]==1} , f[x], {x,0,4}]	Numerically solves the differential equation for the function f[x]
		in the interval [0,4]
Expand[expression]	Expand[ (a+b)^2 ]	Expands the expression (i.e. gets rid of brackets)
Factor[expression]	Factor[ a^2 + 2a b + b^2 ]	Factors the expression
Simplify[expression]	Simplify[ Cos[t]^2 - Sin[t]^2 ]	Attempts to re-write the expression into a simpler format