Curves and Surfaces

Introduction to Topology of Rn: open and closed sets, homeomorphisms, related sets. Curves in the plane and in space: parametric and implicit representations. Tangent and normal vectors. Arc length, areas, curvature, torsion. Surfaces: parametric and implicit representations. Tangent plane and normal vector. Average and Gaussian curves. Visualization of parametric and implicit curves. Visualization of surfaces.

Basic Information

Workload
60 hours
Requirements
Ordinary Differential Equations and Introduction to Computation

Mandatory: 

  • BLOCH, Ethan D. A first course in geometric topology and differential geometry. Springer Science & Business Media, 1997.
  • Pressley, Andrew N. Elementary differential geometry. Springer Science & Business Media, 2010.
  • Manfredo do Carmo. “Differential Geometry of Curves and Surfaces”, SBM; 2012
     

Complementary: 

  • Jorge Picado. “Notes of Differential Geometry”, Dep. Of Mathematics, University of Coimbra, 2006.
  • Tenenblat, K., 2008. Introduction to differential geometry. Blucher Publisher.
  • Elsa Abbena, Simon Salamon, Alfred Gray, "Modern Differential Geometry of Curves and Surfaces with Mathematica", Third Edition, CRC Press; 2017
  • Vladmir Rovenski, “Modeling of Curves and Surfaces with MATLAB”, Springer; 2010
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