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getting-started-mathematica-commands

getting-started-mathematica-commands - ChE132a Analytical...

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ChE132a: Analytical Methods of Chemical Engineering Professor Mike Gordon, Fall 2011 Getting Started Mathematica Commands f=5 define f to be 5 f:= some expression define f to represent some expression f[x_]:=some function of x define a function f(x) f[x_,y_,z_]:= some function of x,y,z define a function f(x,y,z) D[f,x] derivative of f wrt x D[f,{x,n}] n-th derivative of f wrt x Integrate[f,x] indefinite integral of f wrt x Integrate[f,{x,a,b}] definite integral of f wrt x from a to b NIntegrate[Sin[x]/x^2,{x,1,7}] numerically integrate a function over a defined limit DSolve[{f’[x]==f[x]-x^2,x[0]==1},f[x],x] analytically solve the ODE DSolve[{a’[t]==a[t]-b[t],b’[t]==3*a[t]-2*b[t],a[0]==1,b[2]==1},{a[t],b[t]},t] analytically solve the ODE system NDSolve[{w’[x]==w[x]*y[x],y’[x]==3*w[x]-x,w[0]==2,y[0]==1},{w[x],y[x]},{x,0,0.5}] numerically solve ODE system Table[g[i], {i,1,10}] make list of g(i) for i=[1...10] with step 1 Table[g[i], {i,1,10,2}] make list of g(i) for i=[1...10] with step 2 Table[{f[i],g[i]}, {i,1,10}] make a list of ordered pairs {f(i),g(i)} for i=[1...10] with step 1 Simplify[]
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