Calculus Textbook Recommendation (for Chemist/Microbiologist)

[bacte2013]

Thank you, Mr. verty! My plan is to finish Lang's A First Course in Calculus and Spivak's Calculus over this summer. My next mathematics course is a two-semester course called "Multivariable Calculus and Linear Algebra", which requires the second volume of Apostol. I am planning to purchase Lang's Multivariable Calculus and use it as a supplement to the APostol since Spivak only covers the single-variable calculus. I looked at Simmons' Calculus and Analytical Geometry, but I feel like it is not as good as Lang's. Do I need to purchase Apostol's first volume (single-variable) if I already have Spivak? Do I need to complete the first volume of Apostol in order to understand the second volume of his calculus textbook? Does anyone read the book called "How to Prove It" by Daniel Velleman? I am also planning to purchase the linear algebra textbook(s) to supplement the linear algebra portion of my course (I mentioned that the required textbook is Apostol's second volume)...does anyone know a good linear algebra that is easy to read and not rigorous as Apostol? I saw the linear algebra book wrote by Serge Lang, but I do not know if that is a good book..

I sincerely apologize for keep asking many questions regarding to the mathematics textbook, but I want to make sure I bought the right textbooks.

 

[ghostwind]

Also is it okay for me to study calculus and linear algebra simultaneously?

It's perfectly fine as long as you have Calc I-II under your belt. I took Calc III and Linear Algebra honors in the same semester back in 1993, and was no issue. My issue now is finding good books for reviewing all I forgot :)

 

[verty]

Here are four linear algebra books roughly in order of difficulty. Strang is a book focused on computations, how to calculate things. Lay is probably the closest to your request for an elementary book. The last two are what I call typical books, being more advanced. Lang looks possibly more advanced than these so it is probably not any easier than Apostol would be. Shilov is very clear and is the type of book that you could read without doing problems and still learn a lot and it costs about $10. Shilov with Lay or Strang would be a supremely good introduction, I think. Cullen on its own would also work very well, I believe. But I leave choice to you (or to see what others recommend, of course).

https://www.amazon.com/dp/0155510053/?tag=pfamazon01-20
https://www.amazon.com/dp/0201709708/?tag=pfamazon01-20
https://www.amazon.com/dp/0486663280/?tag=pfamazon01-20
https://www.amazon.com/dp/048663518X/?tag=pfamazon01-20

 

[ghostwind]

Thank you, Mr. verty! My plan is to finish Lang's A First Course in Calculus and Spivak's Calculus over this summer. My next mathematics course is a two-semester course called "Multivariable Calculus and Linear Algebra", which requires the second volume of Apostol. I am planning to purchase Lang's Multivariable Calculus and use it as a supplement to the APostol since Spivak only covers the single-variable calculus. I looked at Simmons' Calculus and Analytical Geometry, but I feel like it is not as good as Lang's. Do I need to purchase Apostol's first volume (single-variable) if I already have Spivak? Do I need to complete the first volume of Apostol in order to understand the second volume of his calculus textbook? Does anyone read the book called "How to Prove It" by Daniel Velleman? I am also planning to purchase the linear algebra textbook(s) to supplement the linear algebra portion of my course (I mentioned that the required textbook is Apostol's second volume)...does anyone know a good linear algebra that is easy to read and not rigorous as Apostol? I saw the linear algebra book wrote by Serge Lang, but I do not know if that is a good book..

I sincerely apologize for keep asking many questions regarding to the mathematics textbook, but I want to make sure I bought the right textbooks.

Whew! One busy summer! So let me try to summarize at least what I understand so far, and what I would do in your situation given I understand it correctly:

1. You have taken Calculus I & II using Stewart's book, which you were fine with, but felt it/the course wasn't as rigorous or in-depth as you'd like and think you will need for further studies.

2. You are looking for a good book to self-study/review Calc I & II from over the summer in a more in-depth/proof-based way than you did in school with Stewart.

3. You looked at Spivak and were surprised to see how tough it was.

4. You decided to use Lang's "A First Course in Calculus" then, but also got Spivak even though you admitted it will take you over 2 months to just read the book, never mind do the problems.

5. You want to ensure you are getting the best book(s) and not missing out on anything.

6. You will be taking a 2 semester course on Linear Algebra & Multivariable Calculus in the fall, which will use Apostol's 2nd volume.

7. You also want to get a head start on linear algebra this summer as well.

This is a summary of what I got out of your posts thus far - the facts as it were.

If these "facts" are true, then what I would say (and actually do myself if in your shoes), is get Apostol Vol. 1, and use that to review and go more in-depth for Calc I & II and to get an intro to linear algebra (the last 4 chapters are linear algebra in Vol. 1). Why complicate things with Lang, Spivak, etc.? You may like those, and they are good books, but if you are going into a course that will be using Apostol Vol. 2 for more linear algebra and multivariable calculus, then why not get familiar with Apostol by reviewing single-variable calculus and intro linear algebra with Apostol Vol. 1? For me, it makes perfect sense to go this route and just stick with Apostol Vol. 1 over the next few months. It will certainly take you pretty in-depth on Calc I & II and introduce you to linear algebra. And you will be perfectly lined up to start your course that uses Vol. 2!

You don't want to go nuts with 5 books over one summer! It would be better I think to get the most out of Apostol Vol. 1 instead of using 5 books. Just my 2 cents and what I would do.

 

[verty]

You don't want to go nuts with 5 books over one summer! It would be better I think to get the most out of Apostol Vol. 1 instead of using 5 books. Just my 2 cents and what I would do.

Don't you think Apostol 1 is too dry for him? It's like HAL explaining calculus. He has backed off the super rigorous books to some degree, I think he has made good choices so far.

 

[ghostwind]

Don't you think Apostol 1 is too dry for him? It's like HAL explaining calculus. He has backed off the super rigorous books to some degree, I think he has made good choices so far.

Only he can say if he likes Apostol's style or not. I do see this criticism of Apostol (i.e. that he's dry, etc.), but I think he's OK. Clearly there is a contrast to Spivak who's more verbose and "fun" in a good way, but both cover ground, though Spivak is all theory and no applications at all from what I've seen. Apostol is more "scholarly" for lack of a better word, and covers everything without missing a beat it seems. But mainly I just think if he's to be using Apostol in 2.5 months time for a course designed to use that book (Vol. 2), it would behoove him to get used to Apostol via Vol. 1. This will accomplish his goals of wanting to go deeper, and also allow to connect with Apostol's style which he'll have no choice but to use come fall. And those courses that he'll be taking that are using Apostol Vol. 2, have Apostol Vol. 1 courses as prerequisites most likely.

The linear algebra books you listed are fine, and I could add the one I used, but I think taking on that as well in 2.5 months time max is a lot to swallow. Spend the time in a quality way, in a productive way, instead of being too ambitious. Again, this is just my advice, but exactly what I would do. The whole story changed when he said he'll be taking a course that uses Apostol Vol. 2 next year. For me it became a no-brainer to recommend Apostol. If he can get through that in 2.5 months, he'd be in a very good position and have a bit of linear algebra too.

 

[bacte2013]

Thank you very much all of your helps! I actually have been reading the Volume 1 of Apostol. I actually like it better than Spivak in terms of writing style and contents (I think Apostol covers more than Spivak). I also think that the problem sets in Apostol is much doable than Spivak, which is filled with all hellish problems on every chapter. I also recently bought the book called "Essential Calculus with Applications" by Richard A. Silverman (Dover) to learn more about the applications of calculus. My chemistry research mentor also studied from Apostol, and he said that book helped him to understand the higher-division chemistry courses like quantum mechanics and statistical mechanics. I also love those books more than my Stewart, which I donated to my high school.

Once again, thank you very much for all of your advice! This forum is incredibly helpful!

 

[ghostwind]

Wow. I'm shocked by this information. I assumed that Calculus was unilaterally a standard thing everywhere in the last (two) year(s) of high school. Actually I'm confused as hell about US maths education. What topics do they cover in HS?

Here's a very good read on the history of math education in the US over the last 100 years, and why we are where we are today.

http://www.maa.org/sites/default/files/pdf/CUPM/pdf/MAAUndergradHistory.pdf