Topology and calculus
Henri Poincaré was studying the behavior of solutions of differential equations when he developed the fundamental group and so started the active and growing fields of geometric and algebraic topology. In this chapter we indicate some of the connections between topology and calculus, as examples of sort of unexpected relationships and applications between seemingly unrelated fields of mathematics. Students too often see mathematics as compartmentalized.
KeywordsVector Field Phase Portrait Smooth Manifold Tangent Plane Jordan Curve
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