Exit[];, Quit[];
◇ 도움말:
간략사용법:  ?Solve
명령어찾기:  ?Sol*
자세한설명:  ??Solve

◇ 함수정의: f[x_, y_]:=x^2+y^2, 변수: [x_]
             Infinity, Pi, Degree

근사값:      N[수식,k 자리수], 수식//N
반복계산:    Table[expr, {i,min,max}]
절대값:      Abs[x]
제곱근:      Sqrt[x]
삼각함수:    Sin[x], Cos[x], Tan[x], Csc[x], Sec[x], Cot[x]
로그함수:    Log[x], Log[a,x]
지수함수:    Exp[x]
가우스함수:  Floor[x]

도함수:      D[f[x],x], f`[x]
n계 도함수:  D[f[x],{x,n}]
편미분:      D[f[x1,x2,...],x1,x2,...]

부정적분:    Integrate[f[x],x]
정적분:      Integrate[f[x],{x,xmin,xmax}]

극한:        Limit[f[x]], Limit[f[x],x->x0,Direction->1 (*Direction->-1*)] , Limit[f{x],x->infinity] 

합:          Sum[f[i],{i,a,b}]

풀이:        Solve[좌변==우변,x], Sol=Solve[a x == b, x], x /. Sol[[1]]

소수확인:    PrimeQ[.]

             x_Integer, Real, Complex, List
             x_/;조건


벡터:        v={a,b,c}
행렬:        A={{a,b},{c,d}}
행렬형태:    MatrixForm[행렬], 행렬//MatrixForm
역행렬:      Inverse[A]
전치행렬:    Transpose[M]
|A|:         Det[A]

	     
◇ 파일저장 
   exp >> File, Put[exp,"File"]
   exp >>> File, PutAppend[exp."File"]
   Save["File",symbol]
   !! File
   << File

   FullDefinition[symbol]

   SetDirectory["a:"]
   Directory[]
   Import["filename"]
   Show[%]>>aaa.txt
   !!aaa.txt
 
◇ 주석:   (* 주석 *)

◇ 바로앞 결과 출력 이용: %, Eliminate[1,1,2], k번째: %%%... or %k, Out[k]
◇ Part[Out[n],1] == Out[n][[1]]: k={1, 2, 3};Part[k,2];

수식전개:    Expand[수식]
인수분해:    Factor[수식]
유리수통분:  Togather[유리식]
간략화:      Simplify[수식]
변수명정리:  Collect[수식,변수명]
생략:        수식//short, short[수식]

◇ 함수명령어
   If[조건문,참 명령어, 거짓 명령어]
   While[조건문, 명령어]
   For[i=0(초기값),i<=12(조건문),i=i+1(증감),s=s+i;(명령어)]
   Which[조건1,명령1,조건2,명령2,....,조건(n-1),명령(n-1),True,명령어]
   Switch[Expr,값1,명령어,값2,명령어,....]
   Break[];
   Continue[];
   Return[expr];
   Goto[Label[a]]; Label[a];
   Do[명령문,{i,imin,imax,d}]
 

◇ 그래픽: FullForm[Out[10]]
   Plot[f[x],{x,xmin,xmax}] or Plot[{f1[x],f2[x],...},{x,xmin,xmax},선택사항]
   ListPlot[{y1,y2,y3,...},선택사항] or  ListPlot[{{x1,y1},{x2,y2},{x3,y3},...},선택사항]
   ContourPlot[ , {x..},{y..}]
   Plot3D[f[x,y],{x,xmin,xmax},{y,ymin,ymax},선택사항]
   Show[Graphics3D[{EdgeForm[],Polygon[]}]]
   ParametricPlot[{x(t),y(t)},{t,t1,t2}]
   ParametricPlot3D[{x(t,u),y(t,u),z(t,u)},{t,t1,t2},{u,u1,u2}]
   PolarPlot[f[t],{t,tmin,tmax}]
   Show[]; GraphicsArray[{{},{},{}}];
   선택사항: Hue[h], RGBColor[r,g,b], PointSize[r], AbsolutePointSize[d]
   Options[Plot]: Thinckness[r], AbsoluteThickness[d], Dashing[{r1,r2,...}], AbsoluteDashing[{d1,d2,..}]
         AspectRatio->Automatic, AxesLabel->None or {" "," "," "}, PlotPoints->n, PlotLabel->" "

◇ 확장:
   Needs["~~~'~~~'"]
   < PolarPlot[ ,{,,}];
   < ImplicitPlot[A==B,{x,x1,x2}]
   < Show[Graphics3D[Torus[], MoebiusStrip[3,1,100]]
   < MovieParametricPlot[{,},{,,},{,,},Frames->io, 
   속성{Boxed->False, Axes->False, AspectRatio->Automatic, DisplayFunction->Identity}]
   SpinShow[g,Frames->io,SpinRange->{0,180}];
   ShowAnimation[{a,b,c}];
 

◇ 매개변수표현
1) 삼각함수: x=Cos[q], y=Sin[q]
2) 원(Circle): x=a Cos[q], y=a Sin[q]
3) 타원: x=a Cos[q], y=b Sin[q]
4) 쌍곡선: x=a Sec[q], y=b Tan[q]
5) 포물선: x=2 a t, y=a t^2
6) 파선(Cycloid): x=a (t-Sin[t]), y=a(1-Cos[t])
7) 바퀴안파선(HypoCycloid): x=(a-b) Cos[t]+b Cos[(a-b)/a t], y=(a-b) Sin[t]-b Sin[(a-b)/a t]
8) 바퀴위파선(EnCycloid): x=(a+b) Cos[t]-b Cos[(a+b)/b t], y=(a+b) Sin[t]-b Sin[(a+b)/b t]
9) 성망형(Astroid): x=Cos[t]^3, y=Sin[t]^3
10) 심장형(Cardioid): x=2b Cos[t]-b Cos[2t], y=2b Sin[t]-b Sin[2t]
11) 데카리스엽선(Descartes Lenf): t!=-1, x=3t/(1+t^3), y=3t^2/(1+t^3)
12) 아르키메데스의나선(Spiral): x=q Cos[q], y=q Sin[q]
13) 연주형(Comliscate): x=±Cos[q] Cos[q], y=±Cos[2q] Sin[q]

◇ 공간도형
1) 구: x=a Sin[u]Sin[v], y=a Sin[u]Cos[v], z=a Cos[u]
2) 나팔곡면(Pseudo Sphere): x=a Sin[u]Cos[v], y=a Sin[u]Sin[v], z=a(Cos[u]+Log[Tan[u/2]])
3) 상나선(Circular Helix): x=a Cos[t], y=a Sin[t], z=b t(a>0, b!=0)
4) 나선면(Helicoid): x=v Cos[u], y=v Sin[u], z=b u
5) 현수면(Catenoid): x=a Cosh[v]Cos[u], y=a Cosh[v], z=a v
6) 윤활면(Torus): x=(a+b Cos[u])Cos[v], y=(a+b Cos[u])Sin[v], z=b Sin[u] (a>b)
7) 원주면(Circulorcylinder): x=a Sin[u], y=a Cos[u], z=v
8) 타원면(Eilisoid): x=a Cosh[u]Cos[v], y=a Cosh[u]Sin[v], z=b Sinh[u]
9) 일엽쌍곡선(One Sheet Hyperboloid): x=a Cosh[u]Cos[v], y=b Cosh[u]Sin[v], z=c Sinh[u]
10) 이엽쌍곡선(Two Sheet Hyperboloid): x=a Sinh[u]Sin[v], y=b Sinh[u]Sin[v], z=c Cosh[u]
11) 타원포물면(Elliptic Paraboloid): x=a u Cos[v], y=b u Sin[v], z=u^2
12) 쌍곡포물면(Hyperboloid Paraboloid): x=a u Sec[v], y=b u Tan[v], z=u^2
13) 뫼비우스띠(Moobius Band): x=(a-vSin[u/2])Cos[u], y=(a-vSin[u/2])Sin[u], z=v Cos[u/2]
14) 원숭이안장곡면(Monkey Saddle): x=u, y=v, z=u^3-3u v^2

data = {{471, 30}, {406, 40}, {355, 50}, {312, 60}, {278, 70}, {247, 80}, {224, 90}, {207, 100}};
fdata = FindFit[data, a/(x + b) + c, {a, b, c}, x];
a/(x + b) + c /. fdata

plotdata = ListPlot[data, PlotStyle -> PointSize[0.02], DisplayFundataion -> Identity];
linedata = Plot[a/(x + b) + c /. fdata, {x, 600, 100}, DisplayFundataion -> Identity];
Sdata = Show[plotdata, linedata, DisplayFundataion -> $DisplayFundataion];

표현 형식 출력
FullForm[]

#JavaView 3D
http://www.javaview.de/download/data/javaviewWin_setup.exe

brainmath@gmail.com

<< JavaView`JLink`
viewer = InstallJavaView[]
G=Graphics3D[];
JavaView[G]