Ordinary Differential Equations and Introduction to Computation
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.
• 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
• 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