Anyway, so also, welcome to everybody else
actually, you guys have noticed the
the board. We have a document camera, but
it's a modern document camera that's meant to look like a board, so when
I write, it looks like I'm writing on the board.
No, I'm kidding. No, it's just fooling around
we're going to be writing on the document camera, so it's basically going to be that,
but bigger. This I just
did for fun, and I did to give you
I wanted to give you guys a nice welcome
so since most of you are new,
welcome to all-new Anteaters
Okay, so what is this course about?
unless you're in the wrong room
you're intended to take calculus
calculus 1. So it's the first quarter in calculus,
many of you guys have probably seen calculus before in school
we're not going to assume that you know
anything about calculus we're going to
assume that you only know
precalc, and we're just going to go from there. So if you already know some calculus,
more power to you, but we're still going to do it again. Okay?
We're going to be using this book, Stewart,
seventh edition, okay?
if you don't have it already, there are several options you have. You can buy the book
you can get the custom edition from UCI,
also, you can also get a DVD version
and any version works as long as it's seventh edition
and as long as its early transcendentals. There's the early transcendentals one
and their other one. So it must say early transcendentals
Some people may have
looked into or got the previous edition
the problem with that edition are that some parts of it are different
like
the problems-- the numbers for the problems are different
so it's a different
book in that sense. Okay?
so I recommend that you try and get the
seventh edition if possible if you
already have the sixth edition
you can come and talk with me too.
alright?
All right. We are going to be recorded
for this course
every single lecture. Which is an interesting program, it's the
UCI OpenCourseWare that has been going
on for some time at UCI
I don't know if you guys know about the MIT
OpenCourseWare
so if I understand right, UCI is right next to MIT on the size of
this program. We have a lot of
a lot of courses recorded, pretty much the whole
chemistry undergrad, or a large fraction of it is
already up online for anybody to see.
Anybody, your parents, anybody can go
there, show up and take a look at the lectures. So we're going to be doing this
for this course
and that means for you guys that if you ever for some reason couldn't come to
class you can always come later
and check it out online. Okay? That's a good thing for the class
Hopefully you'll still come, right?
But it's a very good
service also for the other students who might not have taken calculus 2A before.++++++
you want to see it so
okay today
we're gonna be going over the syllabus
and also mmm
we're gonna be talking some math
but I would first like to start with
some ass and then maybe in half an hour
so we're gonna talk ok about the
syllabus acidosis the lot of
a lot of wrinkles okay so
we will spend some time with the
syllabus 34 let's talk about functions
all rights this is a real screen
K it doesn't look like a port arm
soap what are functions
I guess or two functions with four so
right okay
so what are functions thats that's a
weird question right
I because wonder what a function s
you here but functions all the time okay
so any ideas what do you think raise
your hand to mean
what you think is a function yes okay
1x ones well you only have has one why
why
the other round
your what else a
in general but but also mathematically
okay
so up okay but you say what a function
has a property but what is it what is it
is it a
visit a number is a function a number
it's a relation
actually that's that's a very good
technical term there is actually a
relation
what else process I like that
I like process okay so
yes order part a pop
pardon yes
a program
yes yes exactly that's right a rule
a rule I really like that okay good so
we have different
I think we're narrowing down to some
like black real definition
and I really like your what's in em
Rebecca
is that your real name what's really
okay
Rebecca yeah
I really like your definition so I'm
gonna write that
okay I'm sorry I can practice area named
later but school right now
okay I didn't get it okay so so if
function
is a rule that to every
let's see
element
of a set
Dean assigns
exactly one element
of a set well they said
be UK soul rule
you can think about it as a machine or
process or a program
the idea is that in
you take the number x
you plug it into
machine or ruler program
and
outcomes FX
okay so it's like
a think about it as a factory like a a
number come saying
outcomes a product you know the the the
after processing the the number
okay so there's many different types of
functions
and you can think about you can do about
different types of functions and
in any way you want for example suppose
that
example
this is a set the
and is a said eat supposedly have
a real number: X
and then he could be something like
exquisite
right so to every number x
its quest Inc incomes a number to
Arkansas number for
incomes in a more minus three outcomes a
number not but we don't have to talk
about math necessarily we can talk about
I the students in this room for example
students in this
room what could be a function that we
could assign to every student in his
room
rethink homework
no maybe
now a you that you have to session a
little more yes
year appearance okay
yeah I like that for example what about
like a photo right
so you take a photo it would have to be
a very very specific way of taking the
photo
you stand in a certain way look at the
camera and out comes the photo
but is assigned to every student right
service and that's a different photo
but I like that they're yes use in many
wonderful
I really like that that has all the
properties we want okay
for sample could soon have to sue 90s
know right is really just one that comes
out
once in ninety the service in house in
ninety yes right
okay I really like the example let me
write it down student ID
okay
what it what other function can we
assigned to the citizen is room
a key
for what for for the apartment
yes yes
I like that assuming you don't have two
apartments
feeling just in one place that's good
let me right there i read it if you i
think you may be a little bit confusing
okay but let's let's try that the key so
apartment key I
what about the heights okay
each state has its own Heights hurt
their own Heights right
can to students have their same the same
height
is OK actually I it's okay
yet this is gonna the same night look
for simple the function Eq square
minus Eagles 2-3 goes to nine 30 29 and
its okay
right it doesn't the only thing that it
says is that to every element that
assigns
exactly one element all the other set it
doesn't say that
two elements can have the same the same
a the same assignment
too good what's up gender
yes yes I like that gender so
the said he would be the center for the
students and the said he would be the
set
of the two genders male and female right
okay
will we might also get more tricky but
you know what would be just gonna be
there but up
let's see for sample
if you have the items
in a store for example items in Walmart
and outcomes the price each item has a
price
okay so you
I want to point out who very important
properties that are actually written in
the in the definition of the function
but you may not have noticed explicitly
so this order to properties that you're
looking for notice
the two things
one of them is that no element
of d is left
without function value
another one
is that
no element
Indy
can have more than one value
okay that's what we mean by exactly one
when I say exactly one
that's really what I mean that it cannot
be too
anything to be easier it's all contain
exactly one
the values the number every every other
man has exactly one value not
to values Nazir Ali is exactly what
about okay
but it is OK to have
for two
different elements to huff
the same value okay
Saudi means weight with the recent
example the key
worst an interesting example is is it
okay for people to share an apartment
10 people share an apartment
yes that means that two different people
can have the same key
that's still a function right but if
somebody had two apartments
they would have two keys that's not a
function anymore okay
so there you go that's the idea
you can come up with all kinds of
examples and every time you can wonder
is its a function or not now we're gonna
be especially interested in functions
that have mathematical me
so for simple the function with the
gender is fine but
it's not you know if it doesn't involve
number his order is under read more into
said
is that we cannot really handle it
mathematically is easily
so went we're gonna start narrowing it
down to functions that have numbers in
them
okay numbers in number south for the
most part okay it's gonna get more
complicated later and other courses
in this course is mostly gonna be real
number seem real numbers out
okay I now the question is
and this is the next thing we're going
to be talking about
is how
we represent functions
how to represent a function okay if you
don't see more or less what I'm running
is in more or less clear more or less
okay I'm gonna try n
insane right as clearly as I can: okay
now we're gonna be talking about how to
represent the function but let me ask
you first
one last time the US this is a good to
you guys aren't going to be clear to
everybody
what a function is okay was it the
sample with the key was that
was an understandable every person has
their own key hopefully all we have some
took some place to stay so that means
that they were put every person has a
cute assigned to them
right but you cannot have two piece that
would not be a function
but two people can have the same here
that's right okay
genders the same thing two people can
have the same gender
okay or for simple the height two people
can have the same height
that's okay alright hmm
another type of question for example
suppose that
let's all make you more calm more
complicated to say that heights are just
Pena any interest okay so five of the
5 feet 9 inches or 5p five-feet
ten-inches' nothing between
does a function have to cover every
single Heights
to be a function doesn't have to be in
the room somebody for every single
possible hike
not right though he kinda part right
to have somebody with a resync per for
every single height okay
so another thing they're not writing
their is not not every single possible
value of the campaign is is this i
really there
not every single possible key the
is belongs to somebody right if you
dream up a key
and it's okay if if nobody has that key
okay you okay so
the first way to represent the function
he so we call
and arrow diagram
what is an RO diagram well
it's the following you take the set
the and take the said easy
and put all the elements in a bag
suppose that the said the consists of
five
7 and two K
and we're gonna put the sim the Irma so
the said he and another back for sample
7 9
for 3
you and now we're going to have
and iro that's what's called an arrow
diagram right
though so arrow that assigns to
every element Indy an element any
its
mmm
okay
well there you go
look at the situation the said
ds3 elements their does any
does every other men have a value and
assign value any yes right
does it have exactly one bug assigned
any yes
that's all you protect everything else
is is this service
is gravy in this case for example is it
okay for two elements to go to the same
value
yes is it okay that the number three
there is missing
not with nobody nobody going there yes
so it's a fun
or if you had to our is coming under the
same day they'll be a problem
right hmm but right now this is OK
alright
so the US economy
looking at some other ira diagrams this
homework cliff
I'm going to do this
so that you can see still see what we
had before
a second way
hmm a second which represented I
a a function what do you guys think any
ideas on how else you can represent the
function
was it at
tart like a table yes I like that
for a graph or what else
formula expression
yes I like that okay first let's talk
about one
let's talk about the chart so the second
one is
a chart or a table hmm
so for example if we're talking about
the function
that to every student the science their
a student ID for example let the worst
somebody was you're suggesting I think
right so
me so name
and then the student ID
so here for some police Peter
and the student ID is that in a 745
the 32 okay that's a soon idea I mean I
know it's longer but let's just make it
like that
the Mary has a silly the one
37 for 9
and salsa for to make a list of
as many students as you want in their
corresponding city
mmm that's a little bit more systematic
than having to draw or
things into a bubble enjoying our its
okay but it's basically the same thing
and you'll be seeing that in the course
they're the first one is a little more
more like
like up primary school X you're getting
more into like
middle school okay I so
you can see for every person for every
element in do you can see their assigned
bout
and implicitly the chart is the fact
that you cannot have more than one
any kind of have see you you have to
have one so they're not very convenient
hmm but what's the problem with that
actually with both of those well what do
you think it's a problem with both of
those things we've talked about so far
yes well
actually okay good good point good point
dozer if there's a systematic way to do
it
that's fine but the definition of the
function does not call for a systematic
way
you could be completely arbitrary
effective August another example
you know when you send a letter to the
post office
the they make the the person at the
close of business is that not exactly
how much it will cost to ship
right is there a simple like for me not
to write to toughen up
is really a table it's a start if the
wait say what if the wait is less then
so so much
air then this does the price go the way
the Sun so much then that's the price
okay
it doesn't have to be a a procedure to
do it is just a table
right or how much tax you pay okay
there's a table saying OK fits
between this and these you pay so much
so so forth the
doesn't have to be a form okay but
what is a problem with this particular
table the to every single
I'm and assigns a value yes I
excellent excellent what if there's
infinitely many I'm in Sandy
okay so then you would know if it is
running the table
right you would never learn calculus
yes San cert
good yes we could talk about limits it
limits involving infinity to in this
case is just a practical problem you
would never be done
okay so what do we do with
with with with infinite sets the okay
so problem as you well pointed out
what about
infinite sets
the
okay
so now we get into one of the more
efficient you really one of the more
efficient ways
to display a function and you guys also
brought it up a ready
and that is that if a graph okay so
a gruff a graph
works as follows: and I know you guys
have probably seen it before
but I'm still gonna tell you you put
here
the X values for example
12 three
and so on so forth any put here the y
values Ron
to 3 we're going by ex-wives and why
will you as well tell you in a moment
n you draw graph
okay how do you interpret that gruff
well for example the point three if you
take the points when you follow it
vertically
it goes to the point to okay
so 3 come up to
can be interpreted in the following way:
it means that the function the machine
takes a number three
and spit other number took okay that's
what it means
hmm
so it means
X comma F of X and
from this pair you can read the value
the input and the value of the output
so if you take any value for the input
anyone know the value of the output is
followed vertical
okay what is the offensive that over a
table
well as you can see in just one stroke
just by drawing and once in a moment I
already do infinitely many
function vice amazing right
those very efficient you would have
taken me forever I would have never
finished because it's infinitely many
real numbers
there's you anything too many numbers
between 0 and five the ones that I drew
over there
you see the advantage right
great awesome so now
doesn't have to be a formula again for
for the folks in the Red Room
10 is just it's just like ne9 that I
drew
you know it doesn't even have to be a
line you know but
let's not get at me for something I
could have a line is broken into two
right there would still be a function if
you do it right but that's just so for
the moment talk about lights okay
for every point on the x-axis there's
one point on the y-axis that's about you
hmm
now how do you know
if a given graph is actually a function
or not yes
that's right we just heard about the
vertical line test
well some of you may have heard about it
the idea is that the graph
what what is a vertical line test to
exactly if you draw a vertical line
anywhere then what you should not touch
two points that's right
you could draw any vertical line issued
only touched a graph
once because if it s it twice it means
that
the same makes would have twice right
exactly
so we have to satisfy the vertical line
test
hmm each vertical-align:
over
the set
d you
can only
intersect in conflict
also the graph
once
we're running out of time to talk about
the center will someone be
meant I finished quick hmm alright
so for example if it's something like if
you went there
and then back like this the new
intersected twice right this is a
vertical line I'm not plug on a droid 26
not to mess up the graph
but pp for example
this kind of graph
woods what do you think is it OK or
is OK right the present anyway okay
right it's not okay this is it is not a
function
but
this one like this is OK
it doesn't matter where you draw the
line
hmm this only one intersection
okay now we can talk about the fourth
the fourth way to
describe the function and you guys have
already mentioned it what is it
the question
formula question
let's right formula okay
little
that is probably the most efficient way
to do it
if there is one I mean you there's a
formula for it it's a very efficient way
to describe it for example
if you write from if your idea question
F of X equals takes squared
what does that mean min
yes yes
with and that values what was were
rights that's right
so very good point what's in here
this X right here is
the input and
who input Indy
okay that's that's seen put in this
thing here
is the value okay
so what does that mean right in just one
for me not just one line that i right
there
I can hurry say okay -2 goeth before
three ghosts tonight forgot to 16 I can
plug in the number x
in outcomes expert okay it's more
efficient than a table
is more efficient an arrow diagram any
salsa more efficient than a graph
in the sense that what if I try to draw
a graph for to function X squared
what would happen in that case for
it's a problem yes but could I told the
whole thing
I cannot go the whole thing I would
rather bored right
at some point I cannot continue to draw
because they run abort
this formula does not have a problem you
see
you never run a report no matter how
large X
I can tell you what is the value expert
okay
so very efficient it doesn't always work
of course for example for the case of
the postal worker
there may or may not be a natural
formula you may need to make do with the
with the graph with with with the table
okay
I mmm know whether it's a formula it's a
very efficient way to describe a
function
okay do you guys have any questions no
questions
okay I'm not sorry one last thing and
then we're gonna move over to the
syllabus
the syllabus okay link
and nother we're talking about function
someone to tell you but
a special to function which is called a
piecewise the find
function peace
piecewise the find
function
mmm
I sometimes
you almost a formula but you don't quite
how come you don't almost yourself from
your but not quite for example suppose
that
we go back to the sample with the taxes
okay
no two people have exactly the same
income I mean principle this
such a wide range well okay thanks to
people can have the same income time yes
but there's there's not exactly a table
is more like a formula right
that for every yet grab the income you
multiply by soon so much chocolate so so
much percent that's the out that's how
much to tax you have to pay
buddy the incumbents in a certain range
it's one formula
if the Commission another certain range
is a different formula okay
are not I mean if you guys have done
your own taxes so Mary F
the show is the best example ok ima not
that wasn't a question
I'm hmm but the point is sometimes
there's more than one formula in the
same function depending on the Rights
so for example you could have a function
that has the formula X squared
for X bigger equal than 0
and the value 1
for X less
than 0 that is also function
rights once again for every work for
every input X
you know exactly you have one output and
you only have one output exactly what
because the number is either be really
put us here or on this issue it cannot
be both at the same time
what will be the graph for this
function:
you be a funny drunk but it's okay
here so this is
X this is why how would that work
well for XP curriculum 0
you'll be a parable that something like
this actually nevermind its
little different but let me remind their
mind to detail so that all the love that
so values but
for Expedia 0 it's a problem yeah
I well let's see so
here I got I got on yep
alright so this this
one
in this is one okay
and this is one half and so on so forth
so is a problem okay
but what happens with X is less than 0
the function as always value
one right which is right here okay
what do we do at zero well
we're getting there but what episode 0
ih0 lesson zero
now its bureaucrats the right
so ever issue is what it was your is
0 US agree
the resolute yes it's zero so
how do we specify in this graph that the
value at 2.00
because if you just look at the graphic
cannot see it up
okay so you drove circles you Joe
a an empty circle over here saying that
is 111 11 but not a zero
any DRO a full circle here indicating
that the function has value 0 ALG 0 for
luv
okay great
now we can talk about the syllabus of
the one more thing
the which I forgot them to say up the
the
the sets d any actually half names what
are the names of those are those
okay
especially the set the the CDS as an
important name
was a call domain that's right
okay the sets
easy what about the
well okay they were you can get a little
bit tricky but
ok of sort hmm
you can talk about the range or you can
talk about the call domain
actually the the term coda mainly cell
is more precise
something was sometimes we use range and
hmm it depends and we're not gonna talk
about it now because it says something
more technical are so
instead I'm gonna ask if you have any
other questions
okay remember we're not done yet was
just 10 more minutes right so we're
going to talk about the syllabus
its
of you know what let me know let me know
give you two different names let's just
this stick with with go to main okay
we'll talk about the rain say okay hmm
alright so
up
okays who s already downloaded and look
%uh the syllabus
first chance okay not so many be alright
so we're gonna go over it
maybe a miss reform would have time to
read the whole thing but
I mmm-hmm I'm gonna read the premise so
mmm this course you learn the most basic
concept is fresh so calculus
which will find useful in almost any
scientific carrier
whether you're an engineer an economist
even a social scientist for
or even in him well in the humanity some
nicer but
you know like if you're a political
scientist any kind of scientific
the and never you're probably going to
find companies very useful
biology okay the main idea
is that if a derivative you guys we have
heard the rudest before that's gonna be
the central concept of the course
derivatives okay once a derivative
well three but if to spoil
to to spoil their the surprise the
derivative
is a function that describes how another
function is changing
okay rights right surprising not
a area that probably doesn't make any
sense right now we're going to talk
about that in detail
yes it has to do with the soap that's
right
graphical Lisa slope right I'll
that's gonna be the central concept for
the course now around the course
first we have to explain a few things to
understand what we need to know
work for understanding the concept and
then we're going to use the concept
we're going to a plot okay so we first
we'll talk about various special
functions such a sine cosine
exponential functions and the concept of
a limit which somebody already broke up
and the ruling elite up to dramatise
then
we will use derivatives in various
applications okay
in that includes Mali exponential growth
estimating
errors in function sometimes you don't
know exactly the value of up X
but you know the function you wanna find
out that affects you can use relatives
and optimizing function sometimes you
want to know the maximum a function for
the minimum
okay in that can be very important to
for example optimize productivity in a
fuckin a factor in
if you have a factory of tears you wanna
know how many churches should be making
to optimize your profit you can use
calculus mmm-hmm
okay there's gonna be to make some exams
when there's no be Christmas every week
and there will be a final exam there's
also something called web work
you guys have not been a UCI before you
probably haven't heard Weber to force
what works is something like a homework
like a graded homework up but its own
way by human
is rated by a computer what it means is
this personalized
they are you looking to up to a computer
pates it tells you a particular set of
problems that are specially designed for
you the numbers are only for you
if this heat index next seats gonna get
a different set of numbers
and you're supposed to figure out how to
call it works and give the answer
you can try as many times as you want to
solve it okay
if it takes you 10 tries that's okay as
long as you get it right at some point
idea you shouldn't just but guess around
but you should know the answer
and then right that's it does that's the
plan up
there's gonna be one every week starting
in the second or third week
okay not not right now so don't worry
about it for now and the lowest grade
will be dropped
now there's also a number of places
and we also have dropped the lowest quiz
so if for some reason during the quarter
up somebody you family got for bits pass
away
or you have a problem or you know you
really couldn't make it
that's okay that big tits up that means
you're not
handicapped in any way with respect to
your a
classmates okay hmm so
I quiz assignments oh and this is the
percentage is right Chris I'm is this
going to be a quiz every week
on Tuesday okay and the quiz on Tuesday
covers material from the previous week
so for example
hmm I suppose this had been a normal
lecture
week you know Monday Wednesday Friday
this week we I know it's not we just
started today
suppose we have had lecture Mon the 16
right this Cummings Tuesday
there will be a quiz covering the
lectures form this week
money was a fight okay
so those are the the lectures are
covered in the quiz
hmm
a there's gonna be a quiz pretty much
every week except right before the exam
or I ready for the final exam
you might wanna spend some time some
additional time talking about the exam
hmm okay homework
up you guys may have been really good in
math in
in high school I'll but you will find
the discourse in college most a lot
faster than it did in high school
okay like they found that out you know i
i I experience that is a sitting very
much
I you have to up you have to really
raise your level study
to the keep up in college okay and the
the way that I find not only me but in
general the students learn the best
is by doing so just coming to class and
and and and trying to pay attention is
not
is really not enough for this kind of
things that were going to do re the best
thing to do what I recommend you to do
is to sit down with the book enough to
do problems
okay so those problems because we're
going to have the WebWork
those problems that are assigned are
just assigned for you
wouldn't we don't integrate them for you
I as an incentive for you to actually do
the homework
the quickness will have usually two
questions every week
and one of the two questions will be
basically from the home
okay so if you do the homework problems
is gonna be easy because you've already
done it
once you've done before math problem you
always remember
just the way to get hmm okay
so that's an incentive to do the
homework problems but really it should
be a preparation for you to drill
for the something to really understand
the material
I my more practical yes another
incentive
if you don't understand the material
because we didn't do enough practice
you gonna have a hard time in the
midterm okay
so I'll hmm
which one final exams you should bring
your ID they have the exam
you may not use any calculators cell
phones
iPhones or anything that beeps
upgrades have exams are expected to line
the C range
been so if if everybody does really
badly
an exceptional case that everybody does
really badly we can race everybody's
wait a little bit that so in the US we
call a car
okay I I wanna hear a lot about curves
this quarter
more than I would prefer to I the
ideally the 71 but
if if people did really badly for what
for some reason will
will will make sure that not everybody
has a has a bad break
but in general this should not be a
great occur there should not be a need
for a car
okay we're gonna have the standard a way
to determine the
the greats which you can see here a
table there you go
this is a function right the function
that's where a great
assigns a letter either a ABC or so so
forth
okay a the midterm great the meeting
dates are here
by the way be careful if you downloaded
the syllables
three or four days ago or before %uh
because the dates have been changed it
used to be November
13th now it's over 15 ok
suck or
a
I'm okay we're almost done so mmm-hmm
alright great the first question
assignments
is special it's not a normal quests
that's going to be the quiz for two for
Tuesday night sweet because we didn't
have any lectures
million principal we could do a quiz
about today but when I'm gonna do that
instead and when I ask you for a special
procedure
I am the first part of the procedure
roughly the same parts
and when you do all three parts their
city service informs
when you do them although see things
will constitute a great for your first
quiz
okay that chris is gonna be worth maybe
three percent of your grade so it's not
that big a deal
for the whole course but it is it is a
question I mean it would lower your
grade if you don't do it i mean it's
it's it's a it's a it's a course for you
to do
the first part is something that I would
like to do so find out more about you
okay it's a it's an easy form to to fail
at basically contains certain
arrests in bio information your name
what
what you like about mathematics a what
you're expecting from the course
and a photo I would like to be able to
see a photo view so that I can remember
you
%uh later if you show up I the office
hour or
yes the question i mean is going to be a
lot of student but I'm gonna try to run
a few names if I can
I so long to have your photo if you
don't mind
I just okay fine
yeah okay fine for are so I'll
okay that's the first part you need to
turn in by Tuesday
you can turn into any time in the next
few weeks before the first midterm which
is i think
October 23rd so anytime between on
October 23rd
you come to my office hour and you turn
into me why to my office hour
%uh so you could argue well why don't
just do to me now or
you between the end of class another
purpose I love this serb love this
summer
love this assignment is for you to find
out where my office is
believe it or not why because a lot of
times people don't go to office hours
because
they don't know where the office Rs
right so I would like us to find out
about my office
so the next time when you actually have
a question about math you can come and
ask me direct
okay are so that's the first part the
second part is just a survey that you
receive an IEEE
on on Tripoli up by email you fill out
the survey about practice is a fav how
your
learn cock is what you expect from the
course and you turn it
also like that's part of a a fight
instructional
program that is served miss kallins
research and we're doing
to learn how students are learning okay
where we already talked about
I OpenCourseWare is what we just
mentioned before
this that everything electoral the
recorder I am
okay and now there's also hmm
something called lock its at
is a program that's a sign to give you
special personalized
assistance so if you fall behind if
you're feeling that you're struggling in
the course
you can go to our I think it takes place
but twice a week anything gets lessons
there
now the lessons there are not free you
have to pay but it's very cheap
if you consider what you can get what
you get is I think it's
a hundred dollars for the whole quarter
right because you you pay by the quarter
you should think it now if you're
interested in it because in that way
through
you sign up early you get more out of it
okay so
it may be worth investing in it this
also something else
in the math government has a tutoring
center and the service sector what the
differences between the
between the two probably more respect
the tutoring center to center spree
so you can sew up to the math department
at a given time and ask questions about
the class
that's also available there's something
to that in the website and that's it
actually this is the the actual sections
were gonna cover everything every every
day
from the book the services just homework
problems
okay and that's it that's the syllabus
