Chapter 1. Introduction to differentiable functions
Chapter 2. Level seats and tangent spaces
Chapter 3. Lagange multiplers
Chapter 4. Maximum and minima on open sets
Chapter 5. Curves in Rn
Chapter 6. Line integrals
Chapter 7. The frenet-serrent equations
Chapter 8. Geometry of curves in R3
Chapter 9. Double integration
Chapter 10. Parametrized surfaces in R3
Chapter 11. Surface area
Chapter 12. Surface integrals
Chapter 13. Stokes theorem
Chapter 14. Triple integrals
Chapter 15. The divergence theorem
Chapter 16. Geometry curvature
Chapter17. Gaussian curvature
Chapter 18. Geodesic curvature

Aimed primarily at higher level undergraduates in the mathematical sciences, the author provides the reader with a deep understanding of the uses and limitations of multivariate calculus by the integrated use of geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. On reading this book the student will acquire the confidence and techniques necessary to tackle new problems. In this revised edition, which includes additional exercises and expanded solutions, Seán Dineen gives a solid description of the basic concepts, via simple familiar examples which are then tested in technically demanding situations. The author recognises the varied backgrounds students bring to the subject and only assumes the minimal prerequisite knowledge necessary for a comprehensive and unified understanding of the Differential, Integral and Geometric Calculus of Several Variables.---Summary provided by publisher