Topology and calculus

  • L. Christine Kinsey
Part of the Undergraduate Texts in Mathematics book series (UTM)


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.


Vector Field Phase Portrait Smooth Manifold Tangent Plane Jordan Curve 
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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • L. Christine Kinsey
    • 1
  1. 1.Department of MathematicsCanisius CollegeBuffaloUSA

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