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Topology and calculus

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Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

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.

Keywords

  • Vector Field
  • Phase Portrait
  • Smooth Manifold
  • Tangent Plane
  • Jordan Curve

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

“So far as the theories of mathematics are about reality, they are not certain; so far as they are certain, they are not about reality”

Albert Einstein

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  • DOI: 10.1007/978-1-4612-0899-0_11
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© 1993 Springer Science+Business Media New York

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Kinsey, L.C. (1993). Topology and calculus. In: Topology of Surfaces. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0899-0_11

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  • DOI: https://doi.org/10.1007/978-1-4612-0899-0_11

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-6939-7

  • Online ISBN: 978-1-4612-0899-0

  • eBook Packages: Springer Book Archive