Why is Calc II required for Linear Algebra?

  • #1
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My university (as well as many others I suspect) require Calculus II before Linear Algebra. I was wondering exactly why that is? I am lead to believe that Linear Algebra does not really require Calc II topics at all. I am taking Calc II through the whole summer, and LA is offered for the second half, so I will essentially take it having been through 1/2 of Calc II. Do you think my department would give this the OK? Or not worth asking?
 

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  • #2
AlephZero
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I guess it depends how far the linear algebra course goes.

If you stick to finite dimensional vector spaces with Rn as a typical example, then you are probalbly right, you don't need much calculus.

On the other hand if you go on to consider infinte dimensional spaces of functions, you definitely need some serious calculus.

I'm not in the US so I don't know what a " typical" Lin Alg course consists of. The contents may be different if the course is meant for mathematicians, physicists, or engineers.
 
  • #3
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I've been told by a math prof that it's because calc I & II are for getting used to university mathematics and that a freshman jumping into a linear algebra course is often overwhelmed by it.

I saw this while in first year engineering because we had to take a linear algebra course in the second semester (so after calc I, but at the same time as calc II). It really isn't like any other math course that we had taken. I think around a third of the class dropped it, a couple more failed, and most students were in the C range. These were students that were getting primarily A's in all their other classes.
 
  • #4
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Yea I think its more for the mathematical maturity at the level of calc 2 rather than knowing calc 2. In fact most upper level math classes at my uni have a prereq of "any class at or above the level of calculus 2" in addition to other prereqs.
 
  • #5
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This is the course I am talking about, it's the intro to linear algebra.
http://www.math.ucf.edu/syllabi/Spring2008/mas3105.L03.pdf [Broken]

The other linear algebra requires a proof-based mathematics course and this one as a prerequisite.
 
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  • #6
fluidistic
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Hmm weird. In my university calculus II and linear algebra are 2nd semester courses and therefore are taken simultaneously. I really have no idea why calculus 2 would be a requirement for an intro to linear algebra...
 
  • #7
Hurkyl
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It helps to have examples, so that the subject doesn't just become a glorified way of solving systems of equations.

Normally when I think "Calculus II", I think one-variable integration and infinite series. But it looks like your course covers "analytic geometry". The plan may be to spend a lot of time on applications of linear algebra to coordinate geometry.

Of course, the best way to get the best answer would be to ask someone at your university. :tongue:
 
  • #8
For me Calc II boosted my mathematical maturity more than Calc I and Calc III combined and its all because of the substitutions. I went through every u, trig, and generalized substitution problem in the book and it significantly increased my ability to move from algebraic expression to algebraic expression easily and seamlessly allowing me to look at the bigger picture.

Looking at the big picture will help a lot in linear algebra as well as any proof based course, especially if you do not have to spend much time and energy on changing algebraic expressions around to suit your needs.

Of course making linear algebra a prerequisite of Calc III would make Calc III a much better course, allowing us to go into higher than 3 dimensional calculus without that much extra effort. Unfortunately that doesn't happen at my university, but there are a few universities that have an honors track that puts linear algebra before multi variable calculus, and I am very sad I didn't get to take those courses.
 
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