Which Should You Study First: Linear Algebra or Multivariate Calculus?

[Aciexz]

Do you need one before the other or does the order not matter?

 

[qntty]

There was a discussion about this before. Some people prefer doing LA first, but it doesn't really matter in most cases. Nabeshin summed it up nicely

Linear Algebra gives you a little more intimate knowledge of vectors, which play a key role in multivariable calc. So, while the two subjects deal with vastly different domains of mathematics, it is nonetheless beneficial to have taken linear algebra.

That said, LA is by no means a prerequisite. It helps, but not significantly enough to be a pre or even co requisite. You shouldn't worry about going into multivar having not taken calc III, as the classes are about 95% independent of each other.

 

[Aciexz]

Thanks, and now for the real point of this post, after getting someone to confirm what I wanted to hear, I need a suggestion for a first LA book. ^_^ I'm not really into applications, lots of rigor and proofs is what I want, as long as it's plausible considering I've had nothing past Calc. II. This will be for self-study.

So basically I want the most rigorous LA I book. Thanks a bunch. :]

 

[fluidistic]

Try Linear Algebra by Hoffman and Kunze. Very rigorous and good book on the subject.

 

[qntty]

Hoffman and Kunze was written for 3rd year math majors at MIT so it definitely fits your description of rigorous but be warned.

Alternatives include Introduction to Linear Algebra by Strang and linear algebra by Shilov.

 

[Aciexz]

Hoffman & Kunze looks great, but is the latest version from '71? Would that matter?

And what about Friedrich? It also seems highly praised, and has a 2002 edition.

 

[qntty]

Hoffman & Kunze looks great, but is the latest version from '71? Would that matter?

And what about Friedrich? It also seems highly praised, and has a 2002 edition.

If you can handle Hoffman & Kunze then it's a good textbook regardless.

 

[Aciexz]

This is pretty much my exact situation(also from physicsforums):

Yowhatsupt
Mar2-07, 12:36 AM
I'm planning on teaching myself linear algebra over the summer and was wondering what text to grab.

Thoughts, suggestions, recommendations etc are all appreciated.

morphism
Mar6-07, 02:13 AM
Hoffman-Kunze or Friedberg are the way to go. (I personally lean towards Friedberg because of the amount of material covered in that book, as well as the plethora of exercises.)

But I've also read that Friedberg is for a second course. If that's the case does it matter?
(like how it wouldn't matter what calculus book you get because all calc II books are calc I-II books)

What are everyone's thoughts about Friedberg?

 

[owlpride]

It seems like the OP has already made up his mind, but I would like to mention that sometimes the order in which the classes are taken does matter. My college has two versions of multivariable calculus, one with and one without a linear algebra prerequisite. I would have not wanted to take the more rigorous version without a strong background in linear algebra and solid proof-writing skills.

But I guess it is safe to say that the order does not matter as long as neither is a prerequisite for the other.

 

[Nick M]

We used "Linear Algebra and It's Applications", by David C. Lay.

For Multivariate (Calculus III) we finished the mega-text "Calculus", by McCallum, Hughes-Hallett, and Gleason.
We also used this text for Calculus I & II (it's over 1000 pages).

I'm now reading "div grad curl and all that" to cement those topics, and the electromagnetics examples are great since I'm doing EE.

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And just to round it out, I'm finishing up in the Math department this semester with "Differential Equations" by Blanchard, Devaney, and Hall. It's turning out to be a pretty good text.