# Calculus on Curved Spaces

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In Calculus and PDE, people study rather complicated functions, equations on

relatively simple spaces (real line or n-dim Euclidean spaces). On the other hand,

in topology, people study complicated spaces with relatively simple function theory

on them. We are going to introduce a kind of calculus that takes the underlying

topological space into account. Thus we can see how topology interacts with calculus

naturally. The kind of new Calculus is called differential geometry. From this point

of view, Calculus and topology are finally unitfied into differential geometry.