Curves in two and three dimensions, Curvature and torsion for space curves, Existence theorem for space curves, Serret-Frenet formula for space curves, Jacobian theorem, Surfaces in R 3 as 2-dimensional manifolds, Tangent spaces and derivatives of maps between manifolds, Geodesics, First fundamental form, Orientation of a surface, Second fundamental form and the Gauss map, Mean curvature, Gaussian Curvature, Differential forms, Integration on surfaces, Stokes formula, Gauss-Bonnet theorem.
- M. P. Do Carmo, “Differential Geometry of Curves and Surfaces”, Prentice Hall, 1976.
- Andrew Pressley, “Elementary Differential Geometry”, Springer, 2010.
- M. P. Do Carmo, “Differential Forms and Applications”, Springer, 1994.
- J. A. Thorpe, “Elementary Topics in Differential Geometry”, Undergraduate texts in mathematics, Springer, 2011.