Welcome

This website is to keep me (Oliver) organized and in order not to You can reach me always by email knill@math.harvard.edu. Our section meets 9-10:15 am in Northwest B108. Course assistants are Brandon and Eman.


Here is a simpler Taylor graphing applet. You can also just copy paste the following lines. The code should be self-explanatory.
Taylor[f_,c_,n_]:=Function[x,Sum[D[f[y],{y,k}](x-c)^k/k! /. y->c, {k,0,n}]];
f = Function[x, Sin[x] + Cos[3 x]]; g = Taylor[f, 0, 5]; g[x]
Manipulate[Plot[{f[x],Taylor[f,c,n][x]}, {x,-10, 10},PlotRange -> {-11,11}], 
  {n,1,40,1}, {c,-9,9}]
Mathematica has Taylor already built in. But it is nice to do things yourself. Anyway, here is a command which allows to compute finite sum expressions like in problem 1 of HW 11. Change the function, the center of the expansion and the point x0 where we evaluate the function:
f[x_]:=x^2+Cos[x]+Exp[x]; x0=9.0; c=0; 
S[n_]:=Series[f[x],{x,c,n}]; 
Normal[S[10]] 
Table[(Normal[S[k]] /. x->x0) -f[x0],{k,1,50}]
See also the Desmos Taylor Series.

Slides

Summaries



Location

Reminders



  • Problem set 0 is due 9/3/2021
  • QRD Iceberg due 9/10/2021
  • Integration techniques 9/15/2021