MAT 237 Y

MULTIVARIABLE CALCULUS

COURSE 2005-2006

 

COURSE DESCRIPTION

MAT 237Y is a multivariable calculus course.

This year, the course will present material with more mathematical rigour than before, developing topics from basic principles and generalizing many subjects.

Together with standard applications, the course will now include more proofs.

The material of MAT 137Y will be extended to any number of dimensions, with varying degrees of difficulty, resulting in very powerful theorems.

The topics covered include parametric equations and polar coordinates, vectors and vector functions, basic topology (limits in n dimensions, compact sets, and sets of measure zero), derivatives of functions of several variables (these will be done starting with the limit definition), inverse and implicit functions, multiple integrals (starting at upper and lower sums), and vector calculus (this will be covered in a very general setting called k-cubes, where integrals of functions with n variables will be taken over surfaces of k dimensions).

 

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