the main thing to get a sense for today
the first thing really is the goals of
the course and there's really three of
them and they align nicely with the
questions people answered in the online
quiz as to what they hope to get out of
it
what they saw challenging the first is
what I would call put those finishing
touches on your math you've had you know
roughly six quarters of math through the
math department depending what you
placed out of what you placed into how
many of you have taken previously
whether you're doing stuff concurrently
it's been siloed into fixed courses you
haven't had to deal with it sort of all
at once in an integrated fashion there
may be things that you found easy things
you found hard not all math topics you
had are relevant to your physics so this
is kind of to go through that and and
what I would call clean that up and
write in that is really to provide a
framework for why the math you learned
we're going to use in physics I try very
hard so in this regard there will be a
big difference most of the time a pretty
big difference between what I am doing
in lecture and what is in the bow as
reading
the bow as is about doing the math so
the reading will be very specific give
you the you know how you do it the
details of that I will be doing how you
do the math to to a large extent but
everything I would do will be focused
and aimed at why would we use this in
physics where would we use this in
physics why do physicists care about
that that tends to be my focus and
priority
there we hopefully won't show that again
and then the third one really is this
Mathematica issue to give you the basic
skills in Mathematica and it's very
useful in a lot of our upper division
courses it depends who you have you will
use more or less Mathematica in your
classical mechanics ENM quantum
mechanics courses so I'm used a lot some
use less you should always check but in
fact most faculty if you get really good
at typing solutions in Mathematica even
if they're handed in paper ones if you
format it nicely and print it that is
much more fun to read than handwritten
solutions and once you get good at
Mathematica you'll find you can do those
solutions quite quickly and and you know
a happy grader is one who is likely to
give you more points but one of the
things about Mathematica and I want to
go back to the Dropbox here briefly
whoops is there are lots of ways to
often do things and I really want to
encourage you to use this shared student
files I'll be showing you one way or how
to do things I find the students
particularly ones who are very computer
inclined quickly find cooler formatting
better ways to prepare the text
shortcuts to things keyboard shortcuts
you find anything interesting or cool
post it for your fellow students keep in
mind there's no curve in this class you
can all get A's so it really is a class
where you can share this information and
knowledge with each other and with
Mathematica that's particularly helpful
so I do encourage people to use this
shared student file to share with each
other good ways or tricks if you find
for doing stuff that in this class is
not considered cheating so feel free to
share any Mathematica ideas with each
other
now the other issue that I like to go
over is given that these are the goals
the real question is how to achieve
these and when students first look at my
courses typically at the websites and as
some of you said this they're like oh my
god there's so much stuff to keep track
of that's the hard challenge how am I
going to do all this I've done this
hopefully long enough and well enough it
actually is all designed with a purpose
so the lecture the lecture and the
readings that's really about giving you
the key information that you need for
the course the stuff you know the
details of how to do things why we're
doing it all of that the pre assignments
that's critical for both of us
where
to figure out where we are in the class
okay I need to know what it is you know
and don't know so I already know for
instance by asking you to find the
magnitude of 3 plus 4i that pretty much
all of you can do that we don't have to
spend a lot of time in that particular
problem that hasn't been true every year
I taught the course a lot depends on you
know where the math class is put in
there complex analysis and if you know I
decide oh most of the class got
something right and we're not going to
do much on it and you got it wrong you
need to know okay did I just make a
careless error there but I really know
how to do that or is that something I
actually don't know how to do professor
Denton's assuming I know how to do it so
I better meet with him his office hours
I better find the TA I better figure out
how to know that stuff talk to somebody
else in the class so in these pre
assignments keep in mind that most of
them my assumption is you all know how
to do everything in the pre assignments
whether it's the homework problems or a
quiz I happen to post except of course
the Mathematica stuff that the reason
it's a pre assignment is I think it's
easy enough to learn on your own by
going through the tutorial so that's
both a check for you and a check for me
the problem solving sessions are key
because this is the one place you get
and I get real-time feedback that's
where we're doing the challenging
problems in the course trying to push a
little bit farther than we might
otherwise but doing it an environment
where I can see immediately what
mistakes you're making you can see
immediately what mistakes you're making
and there could be that real-time
feedback and that's critical and that
really prepares you for the harder
problems on the homework and for the
exam problems obviously the exams are
key I find the only things I really
remember are the things I got wrong on
exams and there's a reason I give you
four exams before the final the four
exams in class are really a chance to
make sure and double-check do I really
know all this stuff because until you do
it under time conditions on your own
you're just not going to know if you
really know it yet or not well and the
final exam is also a great place to
learn stuff but hopefully by then you've
learned it all in the four exams so
there's four in-class exams plus a final
so it's four plus one what it means is
you'll have had an exam on every topic
that's going to show up on the final so
that's a useful thing going into the
final and then a lot of students often
complain about stuff that they declare
to be busy work but it's just it's math
you just have to practice a lot of stuff
you just have to drill in practice and
so there are a lot of things that you
know if you're doing it and you've got
it mastered you're doing more of it may
not help you and so those are things you
can probably spend less time on and
ignore but until you actually have it
mastered you really need to do it so
that's the design of the course but any
questions on that
I just like to be upfront with why I put
each piece in the course where I put it
in how we're doing it the other thing
just to give you an overview the topics
we'll be doing we're going to start with
series and complex numbers we're then
going to go into matrices and the first
thing we'll do is just review the
mechanics you know how to use matrices
determinates multiply add subtract all
those good things with complex numbers
we're going to focus and series why we
um in physics because there's a lot of
math machinery that you learned that
doesn't necessarily get used a lot in
the physics class right after doing
matrices we're going to go into linear
vector spaces this will be an
interesting place because I know the
math curriculum has reorganized in the
past half the students typically had not
really done a lot with linear vector
spaces so this is where the pre-quiz
will become key I'm going to have to get
a sense where this class is they've
reorganized this um and you may know
more than past classes have and will
adjust for that but this is a central
for so much of physics and it really
uses the matrices a lot then we're going
to go into Fourier techniques just out
of curiosity how many have already done
Fourier series if you've done for a
series raise your hand
okay this is a great example of linear
vector spaces so we're going to do it
from the physics point of view of this
being a linear vector space
not necessarily the math class point of
view which I think really will help and
are something that you'll use a lot we
spend a little bit of time reviewing
differential equations and partial
differential equations the reason there
is you've all had or are taking
concurrently the math differential
equation course right yes say yes no but
you did the differential equation yeah
and so we just highlight a few things
from that class that you use a lot in
physics and there's just one or two
things that you will use a lot going
forward some of these topics like the
partial differential equation a lot of
topics you don't really learn until the
second or third time you saw them so
some things in this class like
differential equations or a review I
expect you to have seen it we're going
to review it and so on or you might be
taking it concurrently partial
differential equations this will be
first time you see it I don't
necessarily expect you to master it in
this class but when you see it again
next year in your E&M class you'll be
prepared to then understand it the
second time you see it so there are
things that I actually don't expect you
to understand the first time and then we
close by reviewing vector calculus and
integration just because of how much
they're used and really the unifying
theme for the whole thing is how to
physicists use all these topics so these
are the topics we're going through