查看“《超越学科的认知基础》2015张世超学习报告第六周”的源代码


== 关键词 ==
'''Mathematica'''[https://en.wikipedia.org/wiki/Mathematica]

== 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算符计算程序（Symbolic computing program),也叫做计算机代数程序（computer algebra program).其强大的功能不仅可以处理2D空间的算符、向量、代数问题，还可以进行3D图像的合成。这个软件本身就是一个隐喻的转换器，通过各种数字符号的输入从而导出各种我们认知领域内的图像、数字结果。

===Mathematica 指令表[https://www.teambition.com/project/55e87360f31d7ebb58c0c24a/files/55e87360f31d7ebb58c0c250/work/5615d75952f8ca117801b40e]===

{| class="wikitable"
!colspan="8"|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}] 
|-
!colspan="8"|complex numbers                      
|-
|absolute value
|Abs[z]
|-
|Argument value
|Arg[z]
|-
|Complex conjugate
|Conjugate[z]
|-
|Imaginary 
|Im[z]
|-
|real component
|Re[z]
|-
!colspan="8"|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
|A[[1]]//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]
|-
!colspan="8"|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}
|-
!colspan="8"|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]
|-
!colspan="8"|Calculus
|-
|Solving the differential equations
|Dsolve[ ]
|-
|Derivatives 
|D[sin[x],x]
|-
|Take the indefinite integral
|Integrate[sin[x],x]
|-
!colspan="8"|Sums
|-
|Add up number i² from 0≤i≤n
|Sum[i²,{i,1,n}]
|-
!colspan="8"|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]
|}
===隐喻===
#隐喻性概念的系统化