“《超越学科的认知基础》2015张世超学习报告第六周”版本间的差异
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== 学习报告 == | == 学习报告 == | ||
| + | ===Mathematica简介=== | ||
| + | Mathematica是一款由!!Stephen Wolfram[https://en.wikipedia.org/wiki/Stephen_Wolfram]和他的团队共同研发的计算软件。 | ||
===Mathematica 指令表[https://www.teambition.com/project/55e87360f31d7ebb58c0c24a/files/55e87360f31d7ebb58c0c250/work/5615d75952f8ca117801b40e]=== | ===Mathematica 指令表[https://www.teambition.com/project/55e87360f31d7ebb58c0c24a/files/55e87360f31d7ebb58c0c250/work/5615d75952f8ca117801b40e]=== | ||
2015年10月27日 (二) 10:41的版本
关键词
Mathematica[1]
学习报告
Mathematica简介
Mathematica是一款由!!Stephen Wolfram[2]和他的团队共同研发的计算软件。
Mathematica 指令表[3]
| 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 =) | 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] | ||||||
