《超越学科的认知基础》2015张世超学习报告第六周
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Mathematica[1]
学习报告
Mathematica 指令表
| Mathematica 指令表 | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| 操作 | 指令 | ||||||||
| enter i | type esc-ii-esc | ||||||||
| enter square root | control -2 | ||||||||
| enter "e" | esc-ee-esc | ||||||||
| power | control-6 | ||||||||
| fraction | control-forwardslash | ||||||||
| evaluate | shift-return | ||||||||
| new line | return | ||||||||
| alias for the last output expression | % | ||||||||
| make substitution | /. | ||||||||
| Expand | Expand[ ] | ||||||||
| Simplify x²+(2x²+sin(x)) | Simplify[x²+(2x²+sin[x])] | ||||||||
| Factorise | Factor[x²-1] | ||||||||
| Evaluate πto decimal places | N[π，100] | ||||||||
| poly=1+3x+5x³+6sin[x] | poly=1+3x+5x³+6sin[x] | ||||||||
| extract the coefficient | Coefficient[poly,x²] | ||||||||
| Solve the equation z=x²+1 for x (remember to use == not =)eeeeeeeeeeeeeeeeeee | z==x²+1 | ||||||||
| Solve the system of equations:x+y+z=1 x-y=2 | Solve[x+y+z==1&&x-y==2,{x,y,z}] | ||||||||
| complex numbers | |||||||||
| absolute value | Abs[z] | ||||||||
| Argument value | Arg[z] | ||||||||
| Complex conjugate | Conjugate[z] | ||||||||
| Imaginary | Im[z] | ||||||||
| real component | Re[z] | ||||||||
| Linear algebra | Define a 2*2 matrix A with elements 1,2,3,4 and a 2 element vector v with element v1 and v2. | A={[1,2],[3,4]} v={v1,v2} A//MatrixForm | |||||||
| Determinant | Det[A] | ||||||||
| Mutiply the matrix A by the Vector v. | A.v %//MatrixForm | ||||||||
| Inverse | Inverse[A]//MatrixForm | ||||||||
| MatrixPower | [A,2]//MatrixForm or A²//MatrixForm | ||||||||
| Transpose | Transpose[A]//MatrixForm | ||||||||
| Extract | A1//MatrixForm | ||||||||
| Make a 10×10 matrix and automatically populate if with a formula. | M=Table[i*j+sin[i+j},{i,1,10},{j,1,10}];M//MatrixForm | ||||||||
| data={1,2,3,4,5} | av2[v_]:=Total[v]/Length[v];av2[data] | ||||||||
| Function | |||||||||
| Define a function;f[x_]:=cos[x]+sin[x];g[x_]:=cos[x]-2; | Evaluate+for x =1;N[f[1],500] | ||||||||
| Average:Write a function av(v) | evaluate it for {1,2,3,4,5} | ||||||||
| Plotting | |||||||||
| Plot the function sin(x) in the range 0<x<5 | Plot [sin[x],{x,0,5}] | ||||||||
| Superimpose the plots of sin(x) and cos(x) | Plot[{sin[x],cos[x]},{x,0,10}] | ||||||||
| Make a 3D plot of sin(x)cosxy over the range 0<x<5,0<y<5 | Plot 3D[sin[x]Cos[y],{x,0,5},{y,0,5}] | ||||||||
| Change the font size and disale the mesh | Plot3D[sin[x]cos[y],{x,0,5},{y,0,5}] BaseStyle→{FontSize→14} | ||||||||
| Make a density plot | DensityPlot[sin[x]cos[y],{x,0,5}] | ||||||||
| Make a parametric plot in 3D x=cos(t), y=sin(t) z=t {t,0,4π}] | ParametricPlot3D[{cos[t],sin[t],t] | ||||||||
| Calculus | |||||||||
| Solving the differential equations | Dsolve[ ] | ||||||||
| Derivatives | D[sin[x],x] | ||||||||
| Take the indefinite integral | Integrate[sin[x],x] | ||||||||
| Sums | |||||||||
| Add up number i² from 0≤i≤n | Sum[i²,{i,1,n}] | ||||||||
| Flow control | |||||||||
| Step function,if x>0, +1,if x<0 -1,if x=0 ,1 | d[x_]:=If[x>0,1,0] d[1],d[-1] | ||||||||
