PROFESSOR: I love
teaching this course,
and I tell the class
that the first day.
Partly because of
them, I've learned
that they are really serious.
And I have something
that I hope they get,
which is the idea--
many of them took
calculus, differential
equations, survived it,
didn't especially enjoy it.
And I'm always hoping that
they see what math is about,
and how it looks for the
pattern in a whole lot
of different applications.
Often engineering,
but many others too.
Science, economics,
biology, wherever.
And if they see the
pattern, then they're
really seeing what
mathematics brings
beyond just formulas, which is
not what the subject's about,
but getting answers
and understanding.
So one part of the
course is the modeling,
getting the equations,
what's the structure.
And the second
part of the course
is how do you solve
the equations?
Sometimes analytically,
sometimes numerically.
And that's, of
course, the reality
of being a scientist
or engineer now.
So this course is
three times a week.
Very typical hour's lecture.
And a fair amount of homework,
including some MATLAB
homework, because that's the
reality of how people get
answers.
And also, of course,
analytical, pencil and paper
homework to see the
central ideas in use.
And office hours from TAs.
Because a lot of people
haven't had linear algebra.
They haven't had 18.06
when they take this course.
And so they ask, do I have
to know linear algebra?
And I say, well, maybe
not, but you soon will.
Well, I think it's
so fantastic to be
able to have OpenCourseWare and
try to do something beyond MIT.
And so, what am I trying to do?
I guess, I think that the
teaching of applied math
has a big step
forward still to take.
That we, in many
situations, we're
doing what we did a
while ago, and not
really bringing it home, making
the subject what it can be.
And part of that has got
to be numerical solution
of the equations, and
also new applications.
Well, 18.085, or
really 18.075, has been
an MIT course for a long time.
And Professor Hildebrand's
textbooks were used.
He was an exceptionally
good teacher.
But computing wasn't
part of it, really.
And it has become part of what
all users do to get answers.
So the course had
to move forward,
and the first step
was about 20 years ago
with a new textbook,
a different approach.
And I have had a wonderful
time teaching classes
over those years, and now it's
ready for the next generation.
