Calculus and analysis at the same time

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Discussion Overview

The discussion revolves around the challenge of simultaneously learning calculus and analysis, particularly in the context of self-study using specific textbooks. The participant expresses a desire to review calculus while engaging with Zorich's Analysis I, and seeks advice on the best approach to integrate these studies effectively.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested
  • Homework-related

Main Points Raised

  • The original poster (OP) has a background in calculus up to Calculus II but feels they have forgotten much of the material and seeks to learn both calculus and analysis concurrently.
  • Some participants suggest that Zorich's book may not provide sufficient computational methods on its own, implying the need for supplementary resources.
  • Others propose using Piskunov's calculus book alongside Zorich to ensure a comprehensive understanding of both theory and computation.
  • The OP expresses uncertainty about whether learning analysis will adequately cover the computational aspects of calculus.
  • One participant asserts that Zorich alone will not teach computational methods effectively.
  • The OP considers the structure of Zorich's book, noting that it covers differential and integral calculus rigorously, which may help bridge the gap in their understanding.
  • Another participant suggests that if the OP finds Zorich manageable, it could be possible to read it concurrently with a calculus textbook.

Areas of Agreement / Disagreement

There is no consensus on whether Zorich alone is sufficient for learning both computational and theoretical aspects of calculus. Some participants argue for the necessity of using Piskunov alongside Zorich, while others suggest that concurrent study may be feasible if Zorich is not too challenging.

Contextual Notes

The discussion reflects varying opinions on the adequacy of Zorich's book for computational learning and the potential benefits of using additional resources. The OP's prior experience and current understanding of calculus are also factors influencing the recommendations.

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Hello, I dropped out of high school a year ago where I did up to calculus II as it's called in USA. This was done using the computational method so we didn't learn any proof. But I feel like I matured as a mathematician and tried reading Zorich's Analysis I (found online) which I'm not finding too difficult. However downside is that I forgot much of the calculus I learned in high school. I am thinking of the best way to review this. I didn't learn it well at the time and only went to the lessons so I only have a vague recollection of the techniques and methods and can't solve simple calculus problems like finding solid of revolution due to forgetting everything (I could do them at the time though). I am thinking of learning calculus again from scratch to aquaint with the techniques again and learn it in a logically connected exposition in one go, because when I learned it before I only went to lessons and didn't have any good but at the same time I enjoy Zorich's book and want to continue to learn the theory behind the calculus. Is it possible to learn both at the same time? I like the russian style of book so I want to read Piskunov's integral and differential calculus with Zorich and maybe use Demidovich's book (problem in analysis) for problems.

My only worry is that if I don't learn calculus again properly and just learn analysis from Zorich's book I won't be able to solve simple computational calculus problems. But I'm not sure if this is true and would appreciate advice. Will analysis teach my computational methods like calculus, while giving the theory at the same time? Here is Zorich's book so you can see: http://math.univ-lyon1.fr/~okra/2011-MathIV/Zorich1.pdf Given my situation should I just learn Zorich or is it good idea to do Piskunov at the same time? Also I will start university in 2016 as I applied for deferred entry this year because I wanted to learn analysis and revise my high school knowledge this year before starting. I know high school math well except for calculus which I mostly forgot as I said.

Please recommend the best way to proceed. My goals are to learn calculus properly from scratch with all the computations and how to calculate integrals, etc., and at the same time learn analysis because I find it enjoyable from Zorich's book.

Thank you, I hope you understand my question
 
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Try the Coursera online courses called Calculus 1 and Calculus 2 out of Ohio State.

https://www.coursera.org/learn/calculus1
 
Dr. Courtney said:
Try the Coursera online courses called Calculus 1 and Calculus 2 out of Ohio State.

https://www.coursera.org/learn/calculus1
Hello, thanks for your suggestion but I already chose what to study and am looking for advice on how I should study them (Piskunov and Zorich) not what to study. Should I do Piskunov or will Zorich alone teach me computational and theory at the same time by itself

http://math.univ-lyon1.fr/~okra/2011-MathIV/Zorich1.pdf
 
Last edited by a moderator:
letters said:
ill Zorich alone teach me computational and theory at the same time by itself

No.
 
micromass said:
No.
Ok thanks. So I should read them at the same time, or Piskunov first? Or maybe you can advise if it would be ok to carry on with Zorich and then use Piskunov? I mean I doubt I will find calculus hard after analysis, and I can definitely read Zorich now as I've found it fun so far and not too difficult. Btw Zorich isn't like other analysis texts (e.g. Rudin). It assumes you don't know differnetial and integral calculus well and covers it in Volume 1 from a rigorous perspective, as well as multivariable differential calculus. Then it does proper analysis in volume 2 and goes even further than Rudin as I heard. So in that sense it's basically Spivak+an easier version of Rudin (easier to read that is, but definitely more comprehensive than Rudin) bundled up into one. If you read the preface please advise: http://math.univ-lyon1.fr/~okra/2011-MathIV/Zorich1.pdf

It covers many applications to physics as well which I am interested in. It is the best analysis book in my opinion, You can read the good review of it from VI Arnold on the back cover.
 
Last edited by a moderator:
If you don't find Zorich too hard, then you can read it concurrently with a calculus book.
 

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