Ebook: Multivariate calculus and geometry Seán Dineen

1. Introduction to differentiable functions -- 2. Level sets and tangents spaces -- 3. Lagrange multipliers -- 4. Maxima and minima on open sets -- 5. Curves in Rn -- 6. Line lengths -- 7. The frenet-serret equations -- 8. Geometry of curves in R3 -- 9. Double integration -- 10. Parametrized surfaces in R3 -- 11. Surface area -- 12. Surface integrals -- 13. Stokes' theorem -- 14. Triple integrals -- 15. The divergence theorem -- 16. Geometry of surfaces in R3 -- 17. Gaussian curvature -- 18. Geodesic curvature.