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PROFESSOR: I love teaching this
course, and I tell the

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class that the first day.

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But because of them,
I've learned that

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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--

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many of them took calculus,
differential equations,

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survived it, 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 of

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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 really seeing

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what mathematics brings beyond
just formulas, which is not

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what the subject's about,
but getting answers and

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understanding.

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So one part of the course is
the modeling, getting the

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equations, what's
the structure.

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And the second part of
the course is how do

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you solve the equations?

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Sometimes analytically,
sometimes numerically.

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And that's, of course, the
reality of being a scientist

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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

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how people get answers.

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And also, of course, analytical,
pencil and paper

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homework to see the central
ideas and 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 ?]

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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 able to have

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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 has a

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big step forward
still to take.

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That we, in many situations,
we're doing what we did a

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while ago, and not really
bringing it home, making the

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subject what it can be.

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And part of that has got to be
numerical solution of the

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equations, and also
new applications.

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Well, 18.085 , or really, 18.075
has been an MIT course

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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, and the first step

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was about 20 years
ago with a new

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textbook, a different approach.

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And I have had a wonderful time
teaching classes over

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

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