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Taylor - UNSA MI 2001
power series expansion and Taylor formula.
90 2001
3
U1
analysis, calculus
taylor expansion, order, infinitesimal, convergence, limit, series, polynomial, continuity, derivative


This is the translation of
a sheet designed for first year students of mathematics and computer
science at Université de Nice - Sophia Antipolis, of year 2000-2001. 
Each student has had 1h30 to work on this sheet.

:U1/analysis/taylor.en
types=combin&center=0&order=3
10
0.5
Taylor level 1
linear combination.
:U1/analysis/taylor.en
types=combin&center=1&order=3
10
0.7
Taylor level 2
linear combination again.
:U1/analysis/taylor.en
types=derivsum&types=deriv&types=sumwderiv&center=1&order=3
10
1
Taylor level 3
derivative and linear combination.
:U1/analysis/taylor.en
types=compo&types=division&types=reciproc&center=1&order=3
10
1.5
Taylor level 4
inverse function and division.
:U1/analysis/coincdev.en
Degree=2&range=3
20
0.5
Coincidence-Dev level 1
graphically find the Taylor expansion of a function.
:U1/analysis/coincdev.en
Degree=3&range=5
20
1
Coincidence-Dev level 2
graphically find the Taylor expansion of a function.
:U1/analysis/joint.en
order=2&fundif=3&tolerance=0.001
10
0.7
Joint level 1
parametrize a function to make it differentiable to a required order.
:U1/analysis/joint2.en
order=4&fundif=1&tolerance=0.001
10
1
Joint II
parametrize a function to make it continue or differentiable on 2 points.