Curves and Surfaces

Basic information

Workload: 

60 hours

Prerequisite: 

Ordinary Differential Equations and Introduction to Computation

Syllabus: 

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.

 

Teaching Plan

Bibliography

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