I'm an undergraduate student of physics. I have an upcoming course on Advanced Calculus but I do not know which book to follow. So, recommend me an undergraduate level book on Advanced Calculus.

Edit: The syllabus has 1. Multiple integration, 2. Partial Derivatives and 3. Applications of Partial Derivatives. (It has one more block, it's something basic though)

Edit 2: I just looked up on quora to know what Advanced Calculus actually is. They are saying it includes things like Green's theorem, Stokes' theorem, line integrals, linear algebra ( I've a separate course on this), Fourier analysis, Taylor series, $$\mathbb{R}^n$$ and $$\mathbb{R}$$ (infinity) etc. My course includes all of these and even more( I listed them just for an idea)

• This is essentially what you want to look at Jun 15 '19 at 15:14
• What do you mean by "Advanced Calculus"? Jun 15 '19 at 15:14
• @user10354138 I don't know about the syllabus as this is an upcoming course. Jun 15 '19 at 15:15
• Setting aside what you're looking for, there's a really good, albeit said to be hard, book called Advanced calculus by Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University. There's an available online copy (legal) math.harvard.edu/~shlomo/docs/Advanced_Calculus.pdf This book is based on an honors course in advanced calculus that the authors gave in the 1960's.
– Luyw
Jun 15 '19 at 17:50
• @Luyw Thanks for your recommendation Jun 17 '19 at 0:30

Advanced Calculus by John Srdjan Petrovic

• The book sucks.
– rash
Jun 16 '19 at 11:32
• Thanks, I'll look into it Jun 17 '19 at 0:31
• @rash Haven't read that book. In what way it sucks? Jun 17 '19 at 7:04
• +1 I haven't really read this book, but some passages look nice. On p.441: "The definition of the area of a surface is very different from the definition of the length of a curve. Namely, the length of a curve is defined as the limit of the lengths of inscribed polygonal lines. Initially, an analogous definition was stated for the area, with inscribed polyhedral surfaces playing the role of polygonal lines. (A polyhedral surface consists of polygons so that just two faces join along any common edge.) For example, such a definition can be found in a 1880 calculus textbook by Joseph Serret.... Jun 17 '19 at 18:42
• ... However, in 1880 Schwarz showed that the formula is inconsistent, even for simple surfaces such as a cylinder. Namely, he demonstrated that it is possible to get different limits, by selecting different sequences of inscribed polyhedral surfaces. (See [109] for the details.) In 1882, Peano independently showed that the surface area cannot be defined using inscribed polyhedral surfaces. Formula (15.13) is nowadays a standard way of defining the area of a surface. It was developed by W.H. Young in a 1920 article [108]." Jun 17 '19 at 18:43