**Math 12 - Calculus Plus - Fall 2010**

*Dartmouth College*

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Multivariable calculus is the branch of calculus that studies functions of more than one variable.
Partial derivatives and multiple integrals are the generalizations of derivative and integral
that are used. An important theorem in multivariable calculus is Green's theorem, which is a
generalization of the first fundamental theorem of calculus to two dimensions. Another important
theorem is Stokes's theorem that relates surface integrals to line integras.

Multivariable calculus is used in many fields of natural and social science and engineering to
model and study high-dimensional systems that exhibit deterministic behavior.

This course can be viewed as equivalent to Mathematics 13, but is designed especially for first-year
students who have successfully completed a BC calculus curriculum in secondary school. In particular,
as part of its syllabus it includes most of the multivariable calculus material present in Mathematics 8.

This version of Mathematics 11 is designed for students who are curious about the broader role of
calculus within mathematics and the sciences. Non-routine problems and examples will be discussed,
and side topics explored. Some of the more routine calculus skills will be left to students to learn
on their own or in groups.