Calculus Who's familiar with all: Piskunov, Fichtenhols, and Smirnov?

  • Thread starter Thread starter Humanlimits
  • Start date Start date
  • Tags Tags
    calculus
AI Thread Summary
The discussion centers on the appeal of the Russian mathematical approach, particularly its blend of rigor and practical examples from physics and engineering. The texts in focus are "Differential and Integral Calculus" by N.S. Piskunov, "Fundamentals of Mathematical Analysis" by G.M. Fichtenholz, and "Course of Higher Mathematics" by V.I. Smirnov. The conversation highlights the historical significance of these texts, noting their widespread translation and use among physicists and engineers. While the texts share similarities, there are nuanced differences in their presentation and depth. Piskunov is recognized for its accessibility and problem sets, Fichtenholz is considered the most challenging, and Smirnov is noted for its comprehensive coverage and advanced material. Ultimately, all three texts offer valuable insights, making them worthwhile for anyone seeking a solid mathematical foundation.
Humanlimits
Messages
6
Reaction score
5
I am very interested in the "russian" type of math approach, a mix of rigor with lots of examples from physics and engineering mixed in with the calculus/analysis pedagogy. It also fascinates me that the same texts were studied by both physicists and engineers of the time period; so lauded after, they were translated into many languages and spread outside the eastern bloc. I'm not looking for suggestions but would be happy to hear from anyone who is familiar with the following texts:

Differential and Integral Calculus - NS Piskunov
Fundamentals of Mathematical Analysis - GM Fichtenholz
Course of Higher Mathematics - VI Smirnov (vol 1&2 on calculus)

I would like to know if the texts are in any way markedly different enough to select one over the other. As far as I can tell from the prefaces and tables of contents, it is hard to find a stark contrast between the books; the authors occasionally gave each other suggestions even!

I am especially interested on reading Smirnov because I like the idea of finishing all five volumes as a good mathematical foundation while reading supplementary/specialized content. Thanks in advance for any relevant thoughts.
 
  • Like
Likes madscientist_93
Physics news on Phys.org
I used the Piskunov volumes in my undergrad math curriculum at the Indian Institute of Technology (IIT) in the early 80s. Good books with lots of problems, but a bit dry. I still have my copies on my bookshelf.
 
  • Like
Likes madscientist_93
Fikhtengol'ts is roughly regarded as the best and hardest of the three at the topics it does, but Piskunov sometimes does things in a nicer way and does more on a few things, while Smirnov will skip smaller topics but still do crazy things in Fikhtengol'ts and overall cover way more and sometimes do more advanced versions of the material the others cover, so you can't go wrong with any choice, or choosing them all.
 
  • Like
Likes madscientist_93
TL;DR Summary: Book after Sakurai Modern Quantum Physics I am doing a comprehensive reading of sakurai and I have solved every problem from chapters I finished on my own, I will finish the book within 2 weeks and I want to delve into qft and other particle physics related topics, not from summaries but comprehensive books, I will start a graduate program related to cern in 3 months, I alreadily knew some qft but now I want to do it, hence do a good book with good problems in it first...
TLDR: is Blennow "Mathematical Methods for Physics and Engineering" a good follow-up to Altland "Mathematics for physicists"? Hello everybody, returning to physics after 30-something years, I felt the need to brush up my maths first. It took me 6 months and I'm currently more than half way through the Altland "Mathematics for physicists" book, covering the math for undergraduate studies at the right level of sophystication, most of which I howewer already knew (being an aerospace engineer)...
Back
Top