Book Recommendation Advanced Calculus?

In summary: Analysis is fairly different from standard computational courses in calculus. I would think the best way to prepare for your analysis class would be to get a head start reading the textbook that the course will be using.Several introductions to analysis will have an opening section on prerequisites. Your class may go over this section quickly or not at all, but if your book has such a section it may benefit you to read all of it before the class begins.Alternatively, you may want to pick up the calculus books by Apostol. As calculus books, these are high-powered; as analysis books, they are low-powered. So they should be a great warm-up for your advanced calculus class.In summary, the person is asking for a recommendation for a good book to
  • #1
Integral8850
15
0
Could someone recommend a good book to review Calculus leading up to Advanced Calculus. I have Advanced Calculus next semester and want to get a jump on it. It has been a couple of years since I had Calc II. and I am reviewing the Stewart Book. I am looking for something a little more concise. Thanks!
 
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  • #2
Integral8850 said:
Could someone recommend a good book to review Calculus leading up to Advanced Calculus. I have Advanced Calculus next semester and want to get a jump on it. It has been a couple of years since I had Calc II. and I am reviewing the Stewart Book. I am looking for something a little more concise. Thanks!

More concise than James Stewart? I found the Stewart book quite concise, I'm not sure there is one more concise.

I always recommend Stewart.

CS
 
  • #3
Analysis is fairly different from standard computational courses in calculus. I would think the best way to prepare for your analysis class would be to get a head start reading the textbook that the course will be using.

Several introductions to analysis will have an opening section on prerequisites. Your class may go over this section quickly or not at all, but if your book has such a section it may benefit you to read all of it before the class begins.

Alternatively, you may want to pick up the calculus books by Apostol. As calculus books, these are high-powered; as analysis books, they are low-powered. So they should be a great warm-up for your advanced calculus class.
 
  • #4
Do you have any experience doing proofs? If not, then I suggest that you get some! I recommend "analysis, with an introduction to proof" by Lay. I worked through a used copy of the second edition and thought that I learned a lot. The first two chapters will get you somewhat up to speed, teaching you logic, quantifiers, methods of proof, set theory, etc. I expect that there are better books out there for this, but Lay is what I am familiar with.

Good luck,

jason
 
  • #5
Together with jasonRF's suggestion, I would recommend David Brannan, An Introduction to Mathematical Analysis
 
  • #6
I second the nomination of Analysis by Steven Lay. It's a great introduction to proof techniques and analysis, and it isn't that long of a book, which makes it great for a preparation book. If you could give a little more detail on the topics of your course, that would help. Different courses can mean different things by advanced calculus.

The calculus books by Richard Courant or Tom Apostol are excellent and rigorous presentations of calculus and basic analysis, but probably aren't texts you can go through over the Christmas break. Probably the best rigorous calculus book is by Michael Spivak, but again is something you wouldn't want to rush through. I've also heard good things about Understanding Analysis by Stephen Abbott, which would be aimed closer to what your course will probably be like, like the Lay book.
stewartcs said:
More concise than James Stewart? I found the Stewart book quite concise, I'm not sure there is one more concise.

I always recommend Stewart.

This is a joke right? I'm sorry, but Stewart has to be the worst recommendation as preparation for an analysis course ever.
 
  • #7
What exactly does this "Advanced Calculus" course contain?

out university offers a course of same title and it is a continuation of Calculus III (multivariable). AC course contains stuff like Div, Grid, Curl and more throughout detail of topics taught in multivariable Calculus. Here, this course does *NOT* require Analysis background (or any proof background whatsoever)..although it helps if we do.

If that is the type of course you are taking then use Springer Vector Calculus book

https://www.amazon.com/dp/3540761802/?tag=pfamazon01-20

If this is Analysis type couse then get a good hold of Analysis first

here's an Analysis book from Spirnger

https://www.amazon.com/dp/1852333146/?tag=pfamazon01-20

both listed Springer books are easy to follow and were written to be a guide for student as well as a formal text.if you need an introductory book for proofs, this is a good one

https://www.amazon.com/dp/0521597188/?tag=pfamazon01-20

pretty neat for self-study
 
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  • #8
n!kofeyn said:
I second the nomination of Analysis by Steven Lay. It's a great introduction to proof techniques and analysis, and it isn't that long of a book, which makes it great for a preparation book. If you could give a little more detail on the topics of your course, that would help. Different courses can mean different things by advanced calculus.

The calculus books by Richard Courant or Tom Apostol are excellent and rigorous presentations of calculus and basic analysis, but probably aren't texts you can go through over the Christmas break. Probably the best rigorous calculus book is by Michael Spivak, but again is something you wouldn't want to rush through. I've also heard good things about Understanding Analysis by Stephen Abbott, which would be aimed closer to what your course will probably be like, like the Lay book.


This is a joke right? I'm sorry, but Stewart has to be the worst recommendation as preparation for an analysis course ever.

Who said anything about analysis and proofs?? The OP asked about advanced calculus books and stated that it had been a while since they had Calc II. If anything they are implying that they are taking Calc III next, which is typically multivariable calc. Hence, my recommendation.

CS
 

Related to Book Recommendation Advanced Calculus?

1. What is Advanced Calculus?

Advanced Calculus is a branch of mathematics that deals with the study of functions, limits, derivatives, integrals, and infinite series in multiple dimensions. It is considered to be a more rigorous and abstract approach to traditional Calculus.

2. Why is Advanced Calculus important?

Advanced Calculus is important because it provides a deeper understanding of the fundamental principles of calculus and their applications in various fields such as physics, engineering, and economics. It also serves as a foundation for more advanced mathematical topics such as real analysis and differential geometry.

3. Who should read a book on Advanced Calculus?

A book on Advanced Calculus is typically recommended for undergraduate and graduate students majoring in mathematics, physics, engineering, or other quantitative fields. It can also be useful for anyone with a strong background in calculus who wants to deepen their understanding of the subject.

4. What are some good books on Advanced Calculus?

Some popular books on Advanced Calculus include "Advanced Calculus" by Patrick M. Fitzpatrick, "Advanced Calculus: A Transition to Analysis" by Thomas P. Dence and Joseph B. Dence, and "Advanced Calculus: A Geometric View" by James J. Callahan. It is important to choose a book that aligns with your level of understanding and learning style.

5. What is the best way to study Advanced Calculus?

The best way to study Advanced Calculus is to first have a solid foundation in single variable calculus and then work through a comprehensive textbook or take a course that covers the topics in depth. It is also helpful to practice solving problems and work through proofs to gain a deeper understanding of the concepts. Seeking help from a tutor or study group can also aid in the learning process.

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