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PROFESSOR: I love
teaching this course,

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and I tell the class
that the first day.

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Partly because of
them, I've learned

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that they are really serious.

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And I have something
that I hope they get,

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which is the idea--
many of them took

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calculus, differential
equations, survived it,

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didn't especially enjoy it.

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And I'm always hoping that
they see what math is about,

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and how it looks for the
pattern in a whole lot

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of different applications.

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Often engineering,
but many others too.

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Science, economics,
biology, wherever.

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And if they see the
pattern, then they're

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really seeing what
mathematics brings

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beyond just formulas, which is
not what the subject's about,

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but getting answers
and understanding.

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So one part of the
course is the modeling,

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getting the equations,
what's the structure.

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And the second
part of the course

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is how do you solve
the equations?

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Sometimes analytically,
sometimes numerically.

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And that's, of
course, the reality

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of being a scientist
or engineer now.

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So this course is
three times a week.

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Very typical hour's lecture.

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And a fair amount of homework,
including some MATLAB

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homework, because that's the
reality of how people get

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answers.

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And also, of course,
analytical, pencil and paper

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homework to see the
central ideas in use.

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And office hours from TAs.

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Because a lot of people
haven't had linear algebra.

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They haven't had 18.06
when they take this course.

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And so they ask, do I have
to know linear algebra?

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And I say, well, maybe
not, but you soon will.

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Well, I think it's
so fantastic to be

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able to have OpenCourseWare and
try to do something beyond MIT.

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And so, what am I trying to do?

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I guess, I think that the
teaching of applied math

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has a big step
forward still to take.

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That we, in many
situations, we're

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doing what we did a
while ago, and not

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really bringing it home, making
the subject what it can be.

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And part of that has got
to be numerical solution

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of the equations, and
also new applications.

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Well, 18.085, or
really 18.075, has been

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an MIT course for a long time.

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And Professor Hildebrand's
textbooks were used.

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He was an exceptionally
good teacher.

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But computing wasn't
part of it, really.

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And it has become part of what
all users do to get answers.

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So the course had
to move forward,

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and the first step
was about 20 years ago

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with a new textbook,
a different approach.

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And I have had a wonderful
time teaching classes

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over those years, and now it's
ready for the next generation.

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