Note: Here every line in the Mathematica is shown with a $ in the beginning of the line. Capitalize functions and keywords
When given exact input the system doesn't make any approximations. Sqrt[2] Sqrt[2.] $ ? Integrate --> to get help on the keyword Manipulate Manipulate[ Expand[(1+x)^n],{n,0,100}] Manipulate[ Expand[(1+x)^n],{n,0,100,1}] //1 is the step Manipulate[ Plot3D[ Sin[nxy],{x,0,3},{y,0,3}],{n,1,4}] N Numerical precision N[Sqrt[2]] N[Sqrt[2], 100] //100 precision == 1==2 --> False Solve[x^2==9,x] used for a set of equations === X === y False, identity rather than mathematical equality := Funtions are defined using this F[x_] := x //_ is required x=. or Clear[w] Clear the value assigned to x /. Transform a variable (temporary value assignment(not permanent)) (1 + x)^6 /. x -> 3 - a (4 - a)^6 s[t] /. {v -> 0, a -> g} //temporarily assign parameters %, %n or
Out[n] is a global object that is assigned to
be the value produced on the n Expand Expands and expression. NestList Recursive call to a funtion for 0 to n times NestList[Cos, Pi, 4] Pi, Cos[Pi], Cos[Cos[Pi]], Cos[Cos[Cos[Pi]]], Cos[Cos[Cos[Cos[Pi]]]] Last The last element in a list or expr. Last[{a,b,c}] --> c Last[{a,b},{c,d}, {e,f}] --> {e,f} Integrate Integrate[f, x] Integrate[f, {x, xmin, xmax}] Integrate[Sin[xy], {x, 0, 1}, {y, 0, x}] //Multiple integral with x integration outermost D (∂) (Partial Differential) D[f, x]
gives the
partial derivative ![]() D[f, {x, n}] gives the multiple derivative ![]() D[f, x, y, ...] differentiates ![]() ![]() D[f, {{x1, x2, ...}}] for a scalar ![]() ![]() DSolve DSolve[eqn, y, x] solves a differential equation for the function y, with independent variable x. DSolve[{eqn1, eqn2, ...}, {y1, y2, ...}, x] solves a list of differential equations. DSolve[eqn, y, {x1, x2, ...}] solves a partial differential equation. |