Solve[x^2 + b x + c == 0, x]
x^2 + b x + c /. First[%]
Together[%]
Integrate[x^2 Exp[x],x]
D[%,x]
Simplify[%]
 N[ Pi ,50]

Plot[Sin[x],{x,0, 2 Pi}]

Plot[Tanh[y]-1/(2/y-1),{y, , }]
FindRoot[Tanh[y]==1/(2/y-1),{y,.8}]
Tanh[y]-1/(2/y-1) /. First[%]

Series[Cos[x],{x,0,6}]

list={Normal[Series[Cos[x],{x,0,2}]],
Normal[Series[Cos[x],{x,0,4}]],
Normal[Series[Cos[x],{x,0,6}]],
Normal[Series[Cos[x],{x,0,8}]],
Normal[Series[Cos[x],{x,0,10}]],
Cos[x]}
list /. x->Pi
N[%]

Plot[Evaluate[list],{x,0,Pi}]

myfun[x_]=Re[Exp[I x]]
Plot[myfun[x],{x,0,Pi}]

m={{a,b},{c,d}}
Det[m]
minv=Inverse[m]
minv.m
Simplify[%]

DSolve[y'[x]+y[x]==0, y, x]

lorenz chaos...
r=24
solution=NDSolve[
{x'[t]==10(y[t]-x[t]),
y'[t]==-x[t] z[t]+r x[t]-y[t],
z'[t]==x[t] y[t]-(8/3)z[t],
x[0]==.1,
y[0]==0,
z[0]==0},{x,y,z},{t,0,30},MaxSteps->10000]

Plot[Evaluate[{x[t],y[t],z[t]}/.First[solution]],{t,0,30},PlotRange->All,
PlotStyle->{{RGBColor[1,0,0]},{RGBColor[0,1,0]},{RGBColor[0,0,1]}}]


Plot3D[Sin[x + Sin[y]], {x,-6,3}, {y,-9,9}, Lighting->True, Mesh->False, 
PlotRange->All, PlotPoints->90]

Needs["Graphics`Animation`"]
<<Graphics/Polyhedra.m
<<Graphics`Shapes`
theta = .3; irat = .3; phidot = 1; psidot = (irat  - 1) Cos[theta]
ShowAnimation[Table[RotateShape[AffineShape[Polyhedron[Cube],{1,1,irat}],
-psidot t,-theta,-phidot t],{t,0,4 Pi,.1 Pi}]]

