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.