I second psyklic's recommendation of Spivak and/or Apostol if you want to "learn calculus the hard way" -- e.g. if you want to learn calculus in a rigorous mann

I second psyklic's recommendation of Spivak and/or Apostol if you want to "learn calculus the hard way" -- e.g. if you want to learn calculus in a rigorous manner that prepares you well to keep going. An informal, brief book on vector calculus is Schey's Div, Grad, Curl and all That. I have not read it personally, but I have heard good things about it. It is probably the quickest way of achieving your immediate goal of understanding Maxwell's equations. Free online copy: ftp://collectivecomputers.org:21212/books/morebooks/Mathematics/Div,%20Grad,%20Curl%20and%20All%20That%20-%20Shey.pdf For single variable calculus, if you want an entertaining and enlightening quick read, I recommend Thompson's Calculus Made Easy: https://www.gutenberg.org/files/33283/33283-pdf.pdf https://www.gutenberg.org/files/33283/33283-pdf.pdf No proofs, but lots of helpful informal explanations.