The notion of pushforward in mathematics is `dual` to the notion of pullback, and can mean a number of different, but closely related things. ...
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http://en.wikipedia.org/wiki/Pushforward
[differential] Suppose that φ : M → N is a smooth map between smooth manifolds; then the differential of φ at a point x is, in some sense, the best linear approximation of φ near x. It can be viewed as a generalization of the total derivative of ordinary calculus. Explicitly, it is a linear map from the tangent space of M at x to the t...
Found on
http://en.wikipedia.org/wiki/Pushforward_(differential)
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