52 Week 1: Discrete Charge and the Electrostatic Field
- Two pieces ofmaththat we will use repeatedly in this part of the course are theTaylor Series
Expansion of a functionin terms of its derivatives:
f(a+ ∆a) =f(a) +df(a)
dx∆a+1
2!
d^2 f(a)
dx^2∆a^2 +1
3!
d^3 f(a)
dx^3∆a^3 +...which converges for small ∆a(used in problems 3, 5, 6, 11) and the Taylor series of a particular
functional form, theBinomial Expansion:(1 +z)n= 1 +nz+n(n−1)
2!z^2 +n(n−1)(n−2)
3!z^3 +...which only converges unconditionally if|z|<1 (used in problems 2, 3, 5, 6, 11).Note well the similarity between this concepts summaryneeded for the homeworkand the con-
cepts summary that started the chapter. This is no accident; thechapter summary is there at the
start for a reason! However, there may be additions or deletions –don’t just copy the summary, and
be sure to cross-reference the problems. The latter step is what will really help you when you
are studying for a quiz or exam. What are the most important ideas,the ones youmustknow for
the exam? Your concept review will (eventually) let you see at a glance...
Also, I included more concepts than are strictly needed by the problems –don’t hesitateto add
important concepts to your list (including concepts from Introductory Physics 1 in this series) even
if none of the problems seem to need them! Some concepts areideasand underlie problems even
when they aren’t actually/obviously used in an algebraic way in the solution! Remember, anything
that you needed to know to solve the problems should (in the end) bein this list along with a list
of the problems where it is needed.