This subject unifies linear algebra and vector calculus from second year into the sort of calculus used in differential geometry and analysis. The central objects of study are curves and surfaces in the space and differentiable maps. Topics include: the implicit and inverse function theorems, tangent space and tangent map, curvature and torsion for curves, intrinsic and extrinsic curvature for surfaces, and the Theorema Egregium of Gauss.
