+,-,,/,^ Mathematica 2Pi + 2; (Enter) Maple + 2 (Shift+Enter) Mathematica 3 Maple abs(x) Mathematica Abs[x] : % %+ : ^ , / +, - 23^42 + 4/2; (Mat

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1 Maple Mathematica Maple Mathematica ( 3, 7). Maple classical maple worksheet 3 : Maple quit; Mathematica Quit Maple : Maple Windows Maple Maple5. Linux xmaple. (Display) (Input display) (Maple Notation). Maple. Maple.. :Maple?sin Mathematica? Integrate : Maple > Enter Mathematica In[]:= Shift+Enter

2 +,-,*,/,^ Mathematica 2Pi * + 2; (Enter) Maple + 2 (Shift+Enter) Mathematica 3 Maple abs(x) Mathematica Abs[x] : % %+ : ^ *, / +, - 23^4*2 + 4/2; (Mathematica ; Shift+Enter) (23) ( ) : := eq:= x+y; eq:= x+y Maple Mathematica eq x+y x=,y=2 eq eq(,2) subs(x=,eq); subs(x=,y=2,eq); Maple eq /. x-> eq /. {x->,y->2} Mathematica eq:= x-> x^2; eq:= (x,y) -> x+y; Maple eq[x_,y_]:= x+y Mathematica eq(,2); eq[,2] Maple Mathematica Maple f:= x-> x^2 f:= x-> x^3 Mathematica Clear[f] 2

3 : with(linalg); Maple << Calculus VectorAnalysis Mathematica Mathematica Calculus VectorAnalysis 3

4 Maple ( ) +,-,*,/,^,abs(x) evalf( ) evalf(, ) Pi I infinity binomial(n,r) ( ) f:= x -> x^2+ () f:= (x,y) -> x^2*y+ sin(x) cos(x) tan(x) arcsin(x) exp(x) 2^x log(x) log[](x) value(limit(f(x),x= )) value(limit(f(x),x=,left)) () solve({x+y=,x^2+y^2=2},{x,y}) () fsolve({x+sin(y)=,x-y=},{x,y}) ( ) diff(f(x),x) diff(f(x,y),x$,y$ ) int(f(x),x) () int(f(x),x=..) () evalf(int(f(x),x=..)) convert(f(x),parfrac,x) series(f(x),x=, ) jacobian([x^2,x*y],[x,y]) 4

5 Maple ( ) 2 plot(x^3+,x=-5..5) 3 plot3d(x^2-y^2,x=..5,y=..5) ( ) plot([x,x^2,x=..5]) (2 ) plot3d([x*y,x^2,x+y],x=..5,y=..5) polarplot(f(t),t=..2*pi) pointplot([[,2],[3,]]) pointplot3d([[,2,3],[2,3,4]],symbol=circle) 2 implicitplot(x^2+y^3=,x=-2..2,y=-2..2) 3 implicitplot3d(x^2+y^2+z^3=,(x,y,z )) () contourplot(x*y,x=-5..5,y=-5..5) () contourplot3d(x*y,x=-5..5,y=-5..5) Maple ( ) matrix(2,2,[,2,3,4]) evalm(a+b),evalm(a-b),evalm(a^(-3)) evalm(c * A), evalm(a &* B) transpose(a) rref(a) det(a) vector([,2,3]), ( 3 ) dotprod(v,w), crossprod(v,w) norm(v,2) eigenvects(a) jordan(a, P ); evalm(p); 5

6 Mathematica ( ) +,-,*,/,^,Abs[x] N[ ] N[, ] Pi I Infinity Binomial[n,r] ( ) f[x_]:= x^2+ () f[x_,y_]:= x^2*y+ Sin[x] Cos[x] Tan[x] ArcSin[x] Exp[x] 2^x Log[x] Log[,x] Limit[f[x],x->] Limit[f[x],x->,Direction->] ( -) () Solve[{x^2-2==,y^2==3},{x,y}] () (Mathematica) ( ) D[f[x],x] D[f[x,y],{x, },{y, }] Integrate[f[x],x] () Integrate[f[x],{x,,}] () NIntegrate[f[x],{x,,}] Apart[f[x]] Series[f[x],{x,, }] (Mathematica) 6

7 Mathematica ( ) 2 Plot[Sin[x],{x,-Pi,Pi} 3 Plot3D[x*y,{x,,},{y,,}] ( ) ParametricPlot[{x,x^2},{x,,}] (2 ) ParametricPlot3D[{x,y,x*y},{x,,5},{y,,5}] PolarPlot[+Cos[x],{x,,2Pi}] 2 ContourPlot[x^3-x*y+y^3==2,{x,-5,5},*] 3 ContourPlot3D[,{x,,},{y,,},{z,,},*] Graphics[{PointSize[.5],Point[{,2}]}] Graphics3D[{PointSize[.5],Point[{,2,3}]}] ( ) 2 * Contours->{,2,3} (2 ) 3 * Contours->{,2,3} Mathematica ( ) {{,2},{3,4}} A+B, A-B, MatrixPower[A,n] c A, A. B Transpose[A] RowReduce[A] Det[A] {,2,3}, ( 3 ) v. w, Cross[v,w] Norm[v] Eigenvalues[A], Eigenvectors[A] JordanDecomposition[A] 7

8 (Maple) Maple simplify() expand() evalf(cos()) evalf evalf(cos(),2) solve(x^2-2*x+2=,x) () fsolve(x^3-x-=,x) () fsolve(x^3-x-=,x=..2) ( ) {x+y=,x-y=2} { } Digits:= ; fsolve() {x=..2,y=-5..5} Maple Mathematica Mathematica 3 x+ x dx Maple 3, Mathematica 7 evalf(int(f(x),x=..)) int(int(x^2+y^2,y=..x^2),x=..); jacobian() with(linalg); jacobian() [x] with(plots); with(plots); p:= pointplot([,2],[3,-]); p2:= plot(x^3+,x=..5); display(p,p2); f:= x-> diff(x^2,x); f(); x 2 2x x = f(x) x = Maple Mathematica 8

9 f:= diff(x^2,x); subs(x=,f); f:x-> diff(x^2,x); subs(x=,f(x)); f(x) subs( ) (Mathematica) Mathematica Simplify[ ] Expand[ ] N[ ] N[Cos[],5] 5 Direction->- Solve[x^2-2==,x] NSolve[x^2-2==,x] Maple FindRoot[x-Sin[x]-==,{x,,2}], 2 [, 2] 2 Maple Calculus VectorAnalysis JacobianMatrix 3 D[ ] Maple shift ) Graphics Graphics Graphics ImplicitPlot Graphics ParametricPlot3D Graphics ContourPlot3D Graphics Graphics3D PolarPlot 2 (ContourPlot ) ParametricPlot3D, SphericalPlot3D 3 3 Mathematica g = Graphics[{PointSize[.5],Point[{,2}],Point[{2,3}]}] g2 = Plot[x^2,{x,,2}] Show[g,g2] (g ) Mathematica Maple f:= D[x^2,x] (Shift+Enter) f /. x-> f[x_]:= D[x^2,x] (Shift+Enter) f[x] /. x-> f(x) x = (Maple, Mathematica) 9

10 Maple evalm( ) A,B A+B; A+B inverse(a) A^(-) eigenvects(a) A. Maple Mathematica Mathematica //MatrixForm Inverse[A]. y = x 3 +x 2 x+ x = y = 4x x 5 plot({x^3+x^2-x+,4*x-2},x=-2..2,*); Plot[{x^3+x^2-x+,4*x-2},{x,-2,2},*] Maple Mathematica * Maple, Mathematica display, show Maple thickness=2,resolution=3,color=blue macro(color=rgb(,,.5)); color=color. RGB Mathematica PlotPoints->5,PlotStyle->{Thickness[.],RGBColor[,,]}

11 2. y = sin(x) + cos(x) + 2 cos(2.2x). 3 2 x Maple Mathematica f:= sin(x)+cos(x)+2*cos(2.2*x); plot(f,x=..6); g:= diff(f,x); a:= fsolve(g=,x=..); evalf(subs(x=%,f)); ( ) a5:= fsolve(g=,x=5..6); evalf(subs(x=%,f)); 3. x(t) = sin(t)+exp( t), y(t) = cos(2t)+sin(t) (t [, 2])... f:= Sin[x]+Cos[x]+2*Cos[2.2*x] Plot[f,{x,,6}] g:= D[f,x] FindRoot[g==,{x,,}] f /. % ( ) FindRoot[g==,{x,5,6}] f /. % Maple Mathematica x:= sin(t)+exp(-t); y:= cos(2*t)+sin(t); F:= diff(x,t)^2+diff(y,t)^2 evalf(int(f^(/2),t=..2)); x:= Sin[t]+Exp[-t] y:= Cos[2*t]+Sin[t] F:= D[x,t]^2+D[y,t]^2 NIntegrate[F^(/2),{t,,2}] 4. with(plots);(maple) << Graphics ContourPlot3D (Mathematica) Mathematica 7

12 ContourPlot3D. z = x 3 x y + y 2 y, z = x 3 3 x 2 y + y x x y y.5.5 x.5. Maple Mathematica plot3d(x^3-x*y+y^2-y,x=-...5,y=...5,*); plot3d(x^3-3*x^2*y+y^3+3*x^2,x=-..,y=-..,*); * axes=frame,grid=[2,2],color=x Plot3D[x^3-x*y+y^2-y,{x,-,.5},{y,,.5},*] Plot3D[x^3-3*x^2*y+y^3+3*x^2,{x,-,},{y,,},*] * PlotPoints->5,ColorFunction->Hue Maple export eps. Mathematica Export["C:\Home\gazou.eps",%] y 5 4xy(y 2 x 2 ) + 2x 5 =.. y x.5 Maple, Mathematica implicitplot(y^5-4*x*y*(y^2-x^2)+2*x^5=,x=-.8..,y=-..2,*); ContourPlot[y^5-4*x*y*(y^2-x^2)+2*x^5==,{x,-.8,},{y,-,2},*] * grid=[,], PlotPoints->{2,2}. 2

13 x 3 +y 4 z 2 =, xy + xz + yz = Maple : p:=implicitplot3d(x^3+y^4-z^2=,x=..2,y=..2,z=..2,*): p2:=implicitplot3d(x*y+x*z+y*z=3,x=..2,y=..2,z=..2,*); display(p,p2); * color=red, color=blue. Mathematica : p=contourplot3d[x^3+y^4-z^2-,{x,,2},{y,,2},{z,,2}] p2=contourplot3d[x*y+x*z+y*z-3,{x,,2},{y,,2},{z,,2}] Show[p,p2] Contours->{.}, PlotPoints-{2,2,2}. Mathematica. Maple : with(linalg); A:= matrix(3,5,[,2,3,4,5,2,5,3,4,,,-2,4,3,7]); rref(a);

14 . with(linalg); A:= matrix(3,3,[,2,3,4,5,6,7,8,9]); B:= diag(2,5,3); evalm(a^2 &* transpose(b)); det(a); A 2t B, det A. A. eigenvects(a) A.. Maple with(linalg); A:= matrix(3,3,[,2,3,4,5,6,7,8,9]); jordan(a, P ); evalm(p); A J A = P JP P. Mathematica :. A= {{,2,3,4,5},{2,5,3,4,},{,-2,4,3,7}} RowReduce[A]//MatrixForm A= {{,2,3},{4,5,6},{7,8,9}} B= DiagonalMatrix[{2,5,3}] A^2. Transpose[B]//MatrixForm Det[A] A= {{.,2,3},{4,5,6},{7,8,9}} 4

15 Eigenvalues[A] Eigenvectors[A] A= {{,2,3},{4,5,6},{7,8,9}} JordanDecomposition[A]. y + y =, y() = c, y () = 2 c. Maple eq:= diff(y(x),x$2)+y(x) = ; sol:= dsolve({eq,y()=c,d(y)()=2},y(x)); with(plots); f:= unapply(rhs(sol),x,c); plot({f(x,c) $ c=..5},x=..6); plot({seq(f(x,c),c=[,3,4])},x=..6);. Mathematica eq= y [x]+y[x]== DSolve[{eq,y[]==c,y []==2},y,x] Last[Last[Last[Last[%]]]] f[x_,c_]= % Plot[Table[f[x,c],{c,,5,}],{x,,6}] Plot[Table[f[x,c],{c,{,3,4}}],{x,,6}]. 5

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sin x Mathematica 1998 7, 2001 3 Mathematica Mathematica 1 Mathematica 2 2 Mathematica 3 3 4 4 7 5 8 6 10 7 13 8 17 9 18 10 20 11 21 12 23 1 13 23 13.1............................ 24 13.2..........................