Should Linear Algebra be a Pre-req for Calc III

[lubuntu]

Hey,

I am going to take either one or the other over the summer. Do you think taking LA first will help in multivariate calc?

 

[Nabeshin]

Hey,

I am going to take either one or the other over the summer. Do you think taking LA first will help in multivariate calc?

Yes.

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.

 

[fluidistic]

Here at my university, in order to subscribe to Calculus III (called mathematical analysis III) you must have succeed in 2 of the 3 tests of Linear Algebra. And to pass the final exam of Calculus III, you need to have passed and succeed in the Linear Algebra one.

 

[Oerg]

for my course, linear algebra and multivariable calculus are in the same module. By the way, how much of linear algebra is covered in a full module? For my half module, we did linear equatins, matrices, determinants, linear transformations, vectors, and vector spaces. How much is it lacking from a full module?

 

[dx]

So, while the two subjects deal with vastly different domains of mathematics, it is nonetheless beneficial to have taken linear algebra.

Linear algebra is intimately related to calculus. Calculus is the mathematics that deals with linear approximations to non-linear things.

 

[Unknot]

I am not sure how you can understand calc III without any linear algebra. You have to get to as far as determinants to be well prepared. Oerg's post (#4) mentions all the things you need.

 

[Nabeshin]

Ok maybe my original statement was too strong. You do need some linear algebra to proceed through calc III as Unknot notes, and the two are tied together, as dx notes. But, in my experience, the concepts from linear algebra used often in calc III, like the determinent, were explained in calc III. If you had taken linear algebra, you understood it that much better, but if not, a little self-study was usually sufficient to grasp the concepts that you missed from linear algebra.

I don't know if this is how most linear algebra classes are, but mine was mostly matrix manipulation, uses to create 3D objects, eigenvalues, and subspaces (And all concepts contained within them). There was quite an emphasis was on proofs, and pretty much none of that knowledge was drawn upon in Calc III.

Just a style of teaching the two courses, maybe?

 

[Oerg]

Ok maybe my original statement was too strong. You do need some linear algebra to proceed through calc III as Unknot notes, and the two are tied together, as dx notes. But, in my experience, the concepts from linear algebra used often in calc III, like the determinent, were explained in calc III. If you had taken linear algebra, you understood it that much better, but if not, a little self-study was usually sufficient to grasp the concepts that you missed from linear algebra.

I don't know if this is how most linear algebra classes are, but mine was mostly matrix manipulation, uses to create 3D objects, eigenvalues, and subspaces (And all concepts contained within them). There was quite an emphasis was on proofs, and pretty much none of that knowledge was drawn upon in Calc III.

Just a style of teaching the two courses, maybe?

oh, so most of the stuff I mentioned were identical to a full module? No wonder linear algebra doesn't feel quite right, I'm almost dying, there's too much to do.

 

[Bourbaki1123]

Nabeshin's class sounds pretty much like mine. We did bases, subspaces, nulspace rank and all of that, and eigenvectors/eigenspaces and a ton of invertible matrix properties so we could tell from any of 20 or so properties if the matrix was invertible(prettty useful because they also answered whether the matrix has the other 19 equivalent properties). We did similar matrices and seperable matricies.
It was a fun course, but we only touched on a few of those topics in multivariable, and we did all of the vector calc and vector geometry in the previous calc class.

 

[physics girl phd]

When I was in college (on semesters), multivariable calculus WAS part of the Calc III description. I think I took linear algebra during the same term as Calc III, and then promptly moved onto Diff EQ (ordinary differential equations... with a partial differential equation/boundary value problem course the next term).

A question for the OP... are you on semesters or quarters? Presumably if no prereq's are formally listed, they won't be needed... but I suspect you could easilty handle linear algebra at this point.

 

[clope023]

When I was in college (on semesters), multivariable calculus WAS part of the Calc III description. I think I took linear algebra during the same term as Calc III, and then promptly moved onto Diff EQ (ordinary differential equations... with a partial differential equation/boundary value problem course the next term).

A question for the OP... are you on semesters or quarters? Presumably if no prereq's are formally listed, they won't be needed... but I suspect you could easilty handle linear algebra at this point.

it still is; calc III = multivariable at least in my school; also at my school calc II is a prereq to linear algebra while LA is a prereq to classes like algebraic structures and things of that nature; again at least in my school classes like calc 3 and differential equations teach basic linear algebra in the context of said classes; I'm doing the pde/bvp course now, the professor is assuming the student knows some linear algebra but the class itself isn't a prereq.

 

[djeitnstine]

I am not sure how you can understand calc III without any linear algebra. You have to get to as far as determinants to be well prepared. Oerg's post (#4) mentions all the things you need.

not necessarily. in my uni linear algebra is completely optional. When doing calc 3 what ever methods we need to use are taught to us during calc 3. That being said, linear alg. is certainly useful and I plan to take it some time.

 

[Unknot]

oh, so most of the stuff I mentioned were identical to a full module? No wonder linear algebra doesn't feel quite right, I'm almost dying, there's too much to do.

It is nowhere near a full module, it's proper one-semester introduction to linear algebra.

 

[Unknot]

not necessarily. in my uni linear algebra is completely optional. When doing calc 3 what ever methods we need to use are taught to us during calc 3. That being said, linear alg. is certainly useful and I plan to take it some time.

Oh I see. Some schools seem to include linear algebra into calc 3; some schools don't. At my school linear algebra starts off with calc 1, and end with calc 2, so the students will have no problem understanding concepts in calc 3.

 

[Oerg]

It is nowhere near a full module, it's proper one-semester introduction to linear algebra.

oh, module as in 'course' for a semester, in that sense, yeh.

 

[lubuntu]

maybe I should be more specific, I am in a typical American university, so I have taken Calc I & II, which only cover topics from those coures, and I don't have much background in linear algebra, I think I'd rather take Calc III first, because it seems more interesting? Am I right?

 

[maze]

maybe I should be more specific, I am in a typical American university, so I have taken Calc I & II, which only cover topics from those coures, and I don't have much background in linear algebra, I think I'd rather take Calc III first, because it seems more interesting? Am I right?

Linear algebra is a truly awesome field and very interesting to learn, I highly recommend it to anyone. Its a field that is deep and elegant mathematically, but also extremely applicable to all sorts of real-world problems. An introductory course will only scratch the surface but I would still recommend it highly.