Hello, I am a physics major currently finished with my second year and I am trying to teach myself vector calculus since the Calculus III class at my university did not include it and I am taking upper level electromagnetic physics courses at another univeristy this coming up fall semester. So far I have completed Calculus I, II, and III, Ordinary Differential Equations, and Linear Algebra all with A's. I am pretty avid at mathematics and have been able to teach myself most of what the teachers could not with fair success. The book I am using for vector calculus is Thomas' Calculus 11th edition, which includes a chapter dedicated to Vector Analysis. In order to make sure I am understanding everything right and can solve some problems I would like to have a supplementary book on vector analysis but I don't know what to pick, what is your advice? The Thomas book leaves off a lot of proofs by stating "in more advanced texts..." which is a pain most of the time. I would not like to buy a separate calculus textbook but rather a specialized book on vector analysis that will help me as a physicist and a mathematician. The topics covered in the Thomas book are: 1. Line Integrals 2. Vector Fields, Work, Circulation, and Flux 3. Path Independence, Potential Functions, and Conservative Fields 4. Green's Theorem in the Plane 5. Surface Area and Surface Integrals 6. Parametrized Surfaces 7. Stoke's Theorem 8. The Divergence Theorem and a Unified Theorem Advice please! Thank you.