Calculus and analysis at the same time

In summary: However, if you find that you are struggling with the computational aspects of calculus while reading Zorich, it may be beneficial to review calculus first before diving into analysis. Ultimately, the best way to proceed will depend on your personal learning style and goals. You may also want to consult with a math professor or tutor for personalized advice.
  • #1
letters
3
0
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
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
Try the Coursera online courses called Calculus 1 and Calculus 2 out of Ohio State.

https://www.coursera.org/learn/calculus1
 
  • #3
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:
  • #4
letters said:
ill Zorich alone teach me computational and theory at the same time by itself

No.
 
  • #5
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:
  • #6
If you don't find Zorich too hard, then you can read it concurrently with a calculus book.
 

Related to Calculus and analysis at the same time

1. What is the difference between calculus and analysis?

Calculus is a branch of mathematics that deals with the study of continuous change and motion, while analysis is a more general branch that focuses on the rigorous study of functions, sequences, and limits. Essentially, calculus is a part of analysis, but analysis also includes other topics such as topology and measure theory.

2. Can calculus and analysis be studied at the same time?

Yes, it is possible to study both calculus and analysis at the same time, as they build upon similar concepts and can complement each other. However, it is recommended to have a solid foundation in calculus before delving into analysis, as it can be more abstract and rigorous.

3. How can calculus be applied in real life?

Calculus has numerous real-life applications, such as in engineering, physics, economics, and even medicine. It is used to model and analyze various natural phenomena, from the motion of objects to the growth of populations. Many modern technologies, such as GPS and MRI machines, also rely on calculus.

4. Is calculus necessary for understanding analysis?

While a basic understanding of calculus is helpful, it is not necessary for understanding analysis. Analysis introduces new concepts and techniques, and can be studied independently of calculus. However, a strong foundation in calculus can make it easier to grasp the more advanced ideas in analysis.

5. What are some common challenges when studying calculus and analysis at the same time?

One of the main challenges is the transition from the more computational approach of calculus to the more theoretical and abstract approach of analysis. It can also be overwhelming to learn new concepts and techniques in both subjects simultaneously. Time management and practice are key to successfully studying both calculus and analysis at the same time.

Similar threads

Is this a good self-study program?
    • STEM Academic Advising
Replies
16
Views
506
Need resources for self study of tensor analysis and other Physics topics
    • STEM Academic Advising
Replies
11
Views
551
Studying Should I first study the math or math and physics at the same time?
    • STEM Academic Advising
Replies
9
Views
2K
Studying Am I Challenging Myself Too Much in Math Learning?
    • STEM Academic Advising
Replies
14
Views
1K
Help me use my library of textbooks to form a study plan
    • STEM Academic Advising
Replies
3
Views
971
Self-Studying: Theoretical Calculus vs Analysis
    • STEM Academic Advising
Replies
2
Views
2K
Analysis Study plan for Functional Analysis - Recommendations and critique
    • Science and Math Textbooks
Replies
13
Views
2K
Studying Specific guidance suggestions?
    • STEM Academic Advising
Replies
14
Views
756
Studying What to do in a gap year to prepare for a Physics + Math degree
    • STEM Academic Advising
Replies
15
Views
2K
Studying Should I start with a basic physics book without calculus?
    • STEM Academic Advising
2
Replies
45
Views
5K

Hot Threads

Recent Insights

Back
Top