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To the math people: which text would you recommend, and why?

 

We have Stewart, and I am not thrilled with his single variable book. Compared to AoPS, I find it too applied and too little depth.

I heard great things about Apostol: is that too theoretical?

 

FWIW, we would be able to teach by direct instruction, but prefer a text that lends itself to self-study with occasional support.

THanks.

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I myself own both Stewart and Thomas Calculus textbooks (The ones that cover all 3 semesters). Have you looked into Thomas at all. I will have to compare the two texts side by side, to highlight any differences. I am learning multivariable calculus from Thomas. I took Differential and Integral Calculus from Stewart. I think that Thomas Stewart may be a little nicer to read through.

 

I think that both texts are geared a little more to the engineering crowd, rather than the math crowd, though both Thomas and Stewart can be sufficient for a math-for-the-sake-of-math type of person. They are kind and gentle and get you up and running with Calculus.

 

I have heard that Apostol, Courant and Spivak are like the gold standard of Calculus texts, though I don't own any of them. I plan to eventually read through and work through all 3 though. What are you looking for in a text? Where are you trying to get your student to go?

Edited because dear God, I prefer Stewart to Thomas and that was a nasty Typo.

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What are you looking for in a text? Where are you trying to get your student to go?

 

 

My student is somewhat unsual: she is highly gifted, at age 15 excelling in calc based physics at a STEM university and volunteering in the Physics tutoring center of the university as a tutor for engineering physics. She may want to major in physics (or English literature, LOL). So far, she has used and loved Art of Problem Solving for all math since algebra; it is the perfect fit.

For her, we are not looking for "kind and gentle" or for a text with lots of examples for engineering applications. I am looking for a text that focuses on a thorough conceptual understanding of vector calculus and will help to develop a deep appreciation of its application in Maxwell's theory of electromagnetism. If only AoPS has a multivariable calc text...that would be perfect. Basically, I am looking for a text that makes you go "wow, that's so cool!".

We are also planning for her to retake the calculus sequence at the university; so this should be a good conceptual introduction, but I do not worry about developing proficiency in execution.

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My favorite for those advanced learners who are interested in theory & applications to physics is Marsden and Tromba's Vector Calculus. It's on Amazon with a student study guide offered, but we just used the text alone along with an online publisher's website. There are lots of almost free copies on Alibris. [Marsden is a prof at Caltech who worked with my phd adviser in continuum mechanics, which is math applied to the mechanics of continuous bodies]

 

It's nothing like Stewart or Thomas, though. Very good & theoretical explanations that don't sidestep what's going on mathematically. Lots and lots of relating the math to examples from physics. Like AoPS, there are fewer problems, but of a much more challenging variety.

 

I also like Apostol and have also heard terrific things about Spivak and Courant. You wouldn't go wrong with them, either. But for a physicist's family, Marsden & Tromba would probably be a natural choice.

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My favorite for those advanced learners who are interested in theory & applications to physics is Marsden and Tromba's Vector Calculus. It's on Amazon with a student study guide offered, but we just used the text alone along with an online publisher's website. There are lots of almost free copies on Alibris. [Marsden is a prof at Caltech who worked with my phd adviser in continuum mechanics, which is math applied to the mechanics of continuous bodies]

 

It's nothing like Stewart or Thomas, though. Very good & theoretical explanations that don't sidestep what's going on mathematically. Lots and lots of relating the math to examples from physics. Like AoPS, there are fewer problems, but of a much more challenging variety.

 

I also like Apostol and have also heard terrific things about Spivak and Courant. You wouldn't go wrong with them, either. But for a physicist's family, Marsden & Tromba would probably be a natural choice.

 

Thanks, Kathy, that is very helpful.

I'll see if they have those in our library, so I can compare.

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Have you looked at MIT's OCW courses in "calculus with theory" (18.012 and 18.022). They use Apostle's book, which is very heavy with theory and proofs. Unless she has a lot of experience with mathematical proofs, she may need to start at the beginning of this book (i.e. single-variable calculus). I used Thomas's book in college and thoroughly enjoyed it. Although, I would say it was more applications based than theory based.

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For something on the theoretical side, take a look at Protter and Morrey's Modern Mathematical Analysis. (Do not be mislead by the title!)

51v2WZPbX9L._SL500_SY300_.jpg

 

Kathy, have you seen this book? Amazon has it for 67 cents!

 

This is one of those classic 1960's texts designed for use after a year of Calculus, back in the days when people did proofs in Calculus. While I did not attend college in the '60's, this was the book that my mentor undergraduate professor chose for her Multivariable class.

 

I still think it is a great book but not a choice for an engineering oriented student.

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For something on the theoretical side, take a look at Protter and Morrey's Modern Mathematical Analysis. (Do not be mislead by the title!)

51v2WZPbX9L._SL500_SY300_.jpg

 

Kathy, have you seen this book? Amazon has it for 67 cents!

 

This is one of those classic 1960's texts designed for use after a year of Calculus, back in the days when people did proofs in Calculus. While I did not attend college in the '60's, this was the book that my mentor undergraduate professor chose for her Multivariable class.

 

I still think it is a great book but not a choice for an engineering oriented student.

 

Hi Jane, yes I own Protter and Morrey! Love that one, too - I taught a multivariable calculus out of it once upon a time. Yes, it's very nice for mathematicians :-) Just forgot about this one in my earlier post (i'm not home to check out my bookshelf before I type today, lol.

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When I was looking for a good multivariable calculus text, I looked at what the top universities used for their honors classes.

 

One that I haven't seen mentioned yet is Hubbard and Hubbard's Vector Calculus, Linear Algebra, and Differential Forms. Cornell uses this for their Theoretical Linear Algebra and Calculus course.

 

BTW, I totally agree about Stewart.

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Just as an FYI, my son's high school uses the Stewart book (9780495011637).

 

http://www.alibris.c...n/9780495011637

 

I am thinking he might not like it, so I will have to check out the others mentioned here as well. Ds is not going to need it until his senior year, though, a few years from now.

 

 

MBM, your son's high school offers multivariable calc?

 

Wow!

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And they use Rogowski, which I detest and refuse to use in my classroom except to pull problem sets, and Salas, Hille, and Etgen for the dual enrolled class.

 

The high schools around here offer multivariable calc. Some offer it via a local university and some offer it in-house.

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