Geometric differentiation: for the intelligence of curves and surfaces

Plane curves 2. Some elementary geometry 3. Plane kinetics 4. The derivatives of a map 5. Curves on the unit sphere 6. Space curves 7. k-times linear forms 8. Probes 9. Contact 10. Surfaces in R3 11. Ridges and ribs 12. Umbilics 13. The parabolic line 14. Involutes of geodesic foliations 15. The circles of a surface 16. Examples of surfaces 17. Flexicords of surfaces 18. Duality.