How to bridge the gap from a Thomas or Stewart calculus book to this?

[ghostwind]

In my other thread on choosing a precalculus book for review, I went off topic and into calculus books, and how there seem to be these 3 main categories of books universities and high schools use -> the 1000+page ones with tons of examples, very computational, new editions every other year, etc. (Thomas, Stewart, etc.), the "intermediate" ones which seem to balance things somewhat (Simmons, Lang, etc.), and the very theoretical/analysis ones (Apostol, Spivak, etc.).

The idea then was, if a university is using one from the first category (Stewart, Thomas - 1000+page computational ones), you as a student have no choice. You can either use that and stick to it, or choose to supplement it with something. Why would you do the latter? Because later on, you might run into difficulties when taking more advanced courses that use textbooks that are more complex. And the Thomases and Stewarts don't prepare one well for that.

For example, at one school I'm looking at, they use the Stewart calculus book for Calc I & II. There is no honors version track offered - everyone uses the same book for Calc I & II. But they do have an honors version track for Calc III & Linear Algebra, and they use this book:

https://www.amazon.com/dp/0387973885/?tag=pfamazon01-20

For the non-honors they continue with Stewart for Calc III and a more basic/applied book for Linear Algebra.

So the strange thing is that if one decided to to the honors track, they would seem to be at a disadvantage in terms of preparation, unless as I was saying, they supplement Stewart with something.

So the question is, why do universities do this? And what is the best way for a student to bridge that gap? How can one go from a Stewart to the Flanigan book and not be lost somewhat? Professors don't seem to offer any advice on this - I asked! They just say do the work, and you'll be fine. But that doesn't seem logical, or fair, or correct.

So yeah, this is partly for myself, but a question that I'm sure I'm not alone in. Spivak as a supplement may be too much for a student on his own as a supplement. Lang is maybe the book they should have used if they did offered an honors course for Calc I & II, but they don't. The system is strange indeed!

 

[TheAustrian]

This might be a very American thing. When I studied Calculus at uni, we were not tied to any particular textbook. The lecturer taught us based on materials he wrote himself, and had to solve examples made up by the lecturer. (We did not have to buy any textbooks)

 

[verty]

In my other thread on choosing a precalculus book for review, I went off topic and into calculus books, and how there seem to be these 3 main categories of books universities and high schools use -> the 1000+page ones with tons of examples, very computational, new editions every other year, etc. (Thomas, Stewart, etc.), the "intermediate" ones which seem to balance things somewhat (Simmons, Lang, etc.), and the very theoretical/analysis ones (Apostol, Spivak, etc.).

The idea then was, if a university is using one from the first category (Stewart, Thomas - 1000+page computational ones), you as a student have no choice. You can either use that and stick to it, or choose to supplement it with something. Why would you do the latter? Because later on, you might run into difficulties when taking more advanced courses that use textbooks that are more complex. And the Thomases and Stewarts don't prepare one well for that.

For example, at one school I'm looking at, they use the Stewart calculus book for Calc I & II. There is no honors version track offered - everyone uses the same book for Calc I & II. But they do have an honors version track for Calc III & Linear Algebra, and they use this book:

https://www.amazon.com/dp/0387973885/?tag=pfamazon01-20

For the non-honors they continue with Stewart for Calc III and a more basic/applied book for Linear Algebra.

So the strange thing is that if one decided to to the honors track, they would seem to be at a disadvantage in terms of preparation, unless as I was saying, they supplement Stewart with something.

So the question is, why do universities do this? And what is the best way for a student to bridge that gap? How can one go from a Stewart to the Flanigan book and not be lost somewhat? Professors don't seem to offer any advice on this - I asked! They just say do the work, and you'll be fine. But that doesn't seem logical, or fair, or correct.

So yeah, this is partly for myself, but a question that I'm sure I'm not alone in. Spivak as a supplement may be too much for a student on his own as a supplement. Lang is maybe the book they should have used if they did offered an honors course for Calc I & II, but they don't. The system is strange indeed!

I'm not convinced that there is a gap. An n-variable book like the one you mention should cover the case where n = 1 because the formulas and derivations are true when n = 1. And probably a good way to understand them is to start with the one-dimensional case.

 

[ghostwind]

I'm not convinced that there is a gap. An n-variable book like the one you mention should cover the case where n = 1 because the formulas and derivations are true when n = 1. And probably a good way to understand them is to start with the one-dimensional case.

Yes, I didn't mean there is a gap that can be filled between single variable and multivariable calculus. As you say, one follows and builds on the other.

What I'm saying is that there is a gap between the types of books used, and that this can make a difference in how one starts to learn math. The Stewart book, as I was saying, is pretty simplistic in nature, and I feel dumbed down, too computational, etc. And the reason I think (and I could be wrong here) that colleges and universities (in the US at least) use these books, is because the amount of precalculus knowledge high school kids come in with varies so much, so they play to the lowest common denominator unfortunately. Flunking everyone is not an option in most places. In other countries, it seems the high school preparation is better and more uniform, so colleges and universities can use more rigorous books without worrying about the knowledge gap among the students in the class.

I have to believe professors are in a tough bind. But if you have an honors multi calc course, why not prepare those who are going to take it by also offering an honors single variable calc course? It only seems fair. One might say that those motivated and smart enough will have no difficulty going from one to the other, but I've seen it different my first time around in college. And that was at and Ivy school. Learning math also involves reading math if you know what I mean. Being able to read less and think more abstractly. When you are presented with explicit pictures, diagrams, and what not, then you will have a harder time making the transition to a book that is light on that and heavy on content. Make sense?

 

[rezeew]

I can understand your concerns about the gap between different types of calculus books and the potential disadvantage it may pose for students. It is true that universities often use textbooks that may not fully prepare students for more advanced courses. This can be due to various reasons such as tradition, availability, or instructor preference. However, it is important to remember that a textbook is just one resource and there are other ways to bridge the gap between different books.

One way is to supplement the textbook with additional resources such as online lectures, practice problems, or study groups. Another way is to actively engage with the material and seek help from instructors or tutors when needed. Additionally, it is important to focus on the underlying concepts and principles rather than just memorizing formulas and techniques. This will help in developing a strong foundation for future courses.

Furthermore, as a student, it is important to take responsibility for your own learning and seek out resources that can help you bridge the gap. This may include self-study, attending office hours, or forming study groups with classmates. It is also important to remember that every student learns differently and what may work for one student may not work for another. Therefore, it is important to find a method that works best for you.

In terms of your question about the best way to bridge the gap from a Thomas or Stewart calculus book to a more theoretical book like the Flanigan book, my suggestion would be to focus on understanding the underlying concepts and principles rather than just trying to memorize procedures. This will help in developing a deeper understanding of calculus and make it easier to transition to a more theoretical book. Additionally, actively engaging with the material and seeking help when needed can also be beneficial.

In conclusion, while it may seem like a disadvantage to use a certain textbook, there are ways to bridge the gap and succeed in more advanced courses. It is important to take responsibility for your own learning and utilize available resources to supplement your learning. With dedication and hard work, you can overcome any gaps and succeed in your studies.