Fall 2010 - Calculus III or Linear Algebra

[Cod]

I am a computer science major with a minor in mathematical sciences. I just finished up Calculus I this semester (with a 97%, yay!) and scheduled to take Calculus II this summer. The list of available fall classes was just released and I'd like to take either Calculus III or Linear Algbera. I could possibly take them both; however, as a full-time worker with two children and a wife, is it wise to try taking them both at the same time? I planned on taking one with another computer science course or my last general education science course. I know universities are different when it comes to what is taught in Calculus III and Linear Algebra, so I've pulled each description from my university's catalog:

Calculus III: An introduction to multivariable calculus. Exposition covers vectors and vectorvalued functions; partial derivatives and applications of partial derivatives (such as tangent planes and Lagrangian multipliers); multiple integrals; volume; surface area; and the classical theorems of Green, Stokes, and Gauss.

Linear Algebra: An explanation of the basic concepts of linear algebra. Topics include vector spaces, applications to line and plane geometry, linear equations, and matrices, as well as linear transformations, changes of basis, diagonalization, similar matrices, Jordan canonical forms, eigenvalues, determinants, and quadratic forms.

So, long post short, which class do y'all recommend I take first? Or should I just bite the bullet and take both courses Fall semester and work on major/final general education course later?

Any help is greatly appreciated.

 

[The Chaz]

Take Calculus III first. Linear algebra moves into abstraction, which you should try to delay as long as possible!

 

[jwxie]

To me it's so odd that school actually allows you to take linear algebra before Calc3 is done.
Like Chaz, you should complete all three calculus sequence.
In our school (well I am a physics and computer engineering major), linear is spring sophomore year, which is after all three calc 3 sequence.

 

[Klockan3]

To me it's so odd that school actually allows you to take linear algebra before Calc3 is done.

Why? I feel that it is strange that you are allowed to do it the other way around. A lot of stuff in multivariable calculus really comes from nowhere if you haven't studied linear algebra.

 

[Jack21222]

Why? I feel that it is strange that you are allowed to do it the other way around. A lot of stuff in multivariable calculus really comes from nowhere if you haven't studied linear algebra.

The only thing that "came from nowhere" when I took calc 3 that linear algebra would have helped me with is the determinant method of solving a cross product.

 

[Sankaku]

I did LA before Calc III and was very glad I did. Many LA courses are more proof based, which comes as a bit of a shock to people used to straight Calc computation. Klockan is right, it is worth doing - there is a lot of Multivariable Calc that is built on LA foundations.

It does depend a lot on what kind of LA course it is, though. An engineering type matrix-cruching course won't do much for your understanding of the underlying concepts.

 

[The Chaz]

Why? I feel that it is strange that you are allowed to do it the other way around. A lot of stuff in multivariable calculus really comes from nowhere if you haven't studied linear algebra.

That's a bit of a stretch... the cross product of a matrix with operators as entries? THAT comes from nowhere!

The only other thing I can think of is Jacobian determinants, but if we weren't just force-fed the formula, few students could actually justify their use. Recently (which is funny, given how long I've been doing calculus!) I was shown how to keep an account of the area distortion when using Reimmann integration... the determinant makes a WHOLE lot of sense now. Memorizing a1a4-a2a3 isn't hard - who says you need a whole class on matrices first?!?

 

[Klockan3]

That's a bit of a stretch... the cross product of a matrix with operators as entries? THAT comes from nowhere!

The only other thing I can think of is Jacobian determinants, but if we weren't just force-fed the formula, few students could actually justify their use. Recently (which is funny, given how long I've been doing calculus!) I was shown how to keep an account of the area distortion when using Reimmann integration... the determinant makes a WHOLE lot of sense now. Memorizing a1a4-a2a3 isn't hard - who says you need a whole class on matrices first?!?

I thought that the jacobian determinants role was obvious when I took multivariable calc after having taken linear algebra, since it defines the area/volume change at each point. Also other things are quadratic forms, the whole deal with vector operations, projections etc. The deal is that nothing from multivariable is used in linear algebra while a lot of things from linear algebra is used in multivariable so I don't understand why anyone would think that you should take multivariable first.

Memorizing a1a4-a2a3 isn't hard

No, but is that what you want to get out of your maths classes?

 

[soleil]

I took linear algebra before multivariable. I actually found my multivariable professor relating things to linear more than the other way around.