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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)

N. F. Taussig
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Sourav Bhattacharya
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    This is essentially what you want to look at – Clayton Jun 15 '19 at 15:14
  • What do you mean by "Advanced Calculus"? – user10354138 Jun 15 '19 at 15:14
  • @user10354138 I don't know about the syllabus as this is an upcoming course. – Sourav Bhattacharya Jun 15 '19 at 15:15
  • @Clayton it's not real analysis anyways. Thanks though – Sourav Bhattacharya Jun 15 '19 at 15:28
  • Advanced Calculus - Fitzpatrick. I don’t know if this is what you’re looking for as “advanced calculus” could be exactly what this book states, or if your university means you are taking a lower division calculus course as honors (which is why this is a comment). I will make it an answer if it indeed is what you need. (Note that this is not the real analysis you are not interested in). – Compact Jun 15 '19 at 15:29
  • @SouravBhattacharya: I suspect it is real analysis in disguise. Likely an introduction to proofs type of course where your focus will be on sets, real numbers, the archimedean principle, $\varepsilon-\delta$ proofs, continuity, etc. If you try looking at the information from the course catalog, you can see what topics are taught in the course. – Clayton Jun 15 '19 at 15:33
  • @Clayton Ok thanks. I'll look into it – Sourav Bhattacharya Jun 15 '19 at 15:34
  • @SouravBhattacharya: I just saw your updated post with the information regarding the syllabus. It sounds more like a multivariable calculus class than an advanced calculus class. You might try looking for introductory calculus texts, then (Stewart has a reasonable, widely-used textbook simply called Calculus... while not my favorite textbook, it is certainly a common standard). – Clayton Jun 15 '19 at 15:37
  • Griffiths's electromagnetism book has a good intuitive explanation of vector calculus. I also like Div Grad Curl and All That. – littleO Jun 15 '19 at 15:45
  • Additionally to the very interesting recommendations above, I would encourage you to check open courses platforms from renowned universities. I'm quite familiar with Oxford's excellent material available for free, and I've stumbled upon more than once with quite nice MIT course notes. I'm sure good materials can be found left, right, and centre, and it's quite nice that these universities offer it for free to anyone interested. – Sam Skywalker Jun 15 '19 at 15:46
  • Talking specific books, we have the more basic Marsden-Tromba and Apostol's books, and the more advanced and rigorous Spivak's Calculus on Manifolds and Marsden-Hoffman. Any of them is quite a good read, depending on the stage you are right now. – Sam Skywalker Jun 15 '19 at 15:47
  • @Compact I saw the index of Fitzpatrick, it has many things that my course has like line and surface integrals, partial derivatives, Euclidean space R^n etc but doesn't cover some topics like multiple integrals and things related to it. It's a nice recommendation, thanks. Though it has some topics that has already been covered in my current course on Calculus. – Sourav Bhattacharya Jun 15 '19 at 16:05
  • @littleO Thanks I've a separate course on that under the course name "Mathematical Physics". – Sourav Bhattacharya Jun 15 '19 at 16:10
  • I have only studied basic calculus, but I know Professor Leonard on YouTube has a good course which covers many of the subjects listed (although not a book, it might be useful anyway?) – Jamminermit Jun 15 '19 at 16:20
  • @Jamminermit thanks – Sourav Bhattacharya Jun 15 '19 at 16:52
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    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) http://www.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. – GDGDJKJ Jun 15 '19 at 17:50
  • Advanced Calculus of Several Variables by C.H. Edwards can be of interest (it is discussed in this post). – Pedro Jun 16 '19 at 22:09
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    @Luyw Thanks for your recommendation – Sourav Bhattacharya Jun 17 '19 at 00:30
  • @Pedro ok thank you – Sourav Bhattacharya Jun 17 '19 at 00:31
  • You are welcome. – GDGDJKJ Jun 17 '19 at 00:58
  • Does this answer your question? References for multivariable calculus –  May 21 '23 at 20:55

1 Answers1

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Advanced Calculus by John Srdjan Petrovic

xrfxlp
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V_kim
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    The book sucks. – rash Jun 16 '19 at 11:32
  • Thanks, I'll look into it – Sourav Bhattacharya Jun 17 '19 at 00:31
  • @rash Haven't read that book. In what way it sucks? – user1551 Jun 17 '19 at 07:04
  • +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.... – user1551 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]." – user1551 Jun 17 '19 at 18:43
  • I think this passage summarises the historical development of the geometric definition of area of surface very well. It also clarifies why surface area isn't defined in a way parallel to the definition of length of curve. But admittedly, this book has its drawbacks: it is very expensive and the author doesn't seem to write fluently. – user1551 Jun 17 '19 at 18:48