# Calc II needed for Linear Algebra?

• bob1182006
In summary, the conversation discussed the topic of whether or not Calculus II is needed in order to learn Linear Algebra. Some argued that it is necessary, while others believed it is not needed at all. It was also mentioned that Linear Algebra covers topics such as vector spaces, linear transformations, and matrix transformations. The conversation also touched on the idea that Calculus III and Linear Algebra have some similarities, but are ultimately different courses. It was concluded that while some basic knowledge of calculus may be helpful in understanding certain concepts in Linear Algebra, it is not a prerequisite for learning the subject.

#### bob1182006

At my university (UNLV) in order to take Linear Algebra Calc II is required.

I'm thinking of taking Calc II + Linear Algebra over the summer, so I can take Calc III this Fall, but both of these courses are only offered during the same 5-week session, I might be able to talk to my advisor/math department and get into Linear Algebra without completing Calc II.

So is Calc II really needed in order to learn Linear Algebra?

I would say yes and m any cases I'd suggest Calc III before Linear Algebra also.

Really? I've heard so much about Linear Algebra being fundamental for Calc III

ok I guess I'll take Linear Algebra this Fall and go from there

You don't need anything.

I first took Linear Algebra while take Calculus I. I don't see how not knowing Calculus will hinder someone from understanding what vector spaces are and linear transformations.

How much of linear algebra are matrix transforms? I read on ratemyprofessor.com about the teacher that's teaching this coming fall and most of his ratings for Linear algebra just said like
"all he does is mainly matrix transforms"

bob1182006 said:
How much of linear algebra are matrix transforms? I read on ratemyprofessor.com about the teacher that's teaching this coming fall and most of his ratings for Linear algebra just said like
"all he does is mainly matrix transforms"

Well, that is the heart of linear algebra, so it is expect to be mainly matrix transformations, which is linear transformations, like I pointed out.

You don't need Calculus at all to do. None whatsoever. I'd be surprised if I've ever seen a textbook saying Calculus is a pre-requisite in the preface of the textbook.

Ok thanks I thought maybe the teacher was skipping out on important things in his class.

I think I'll wait and take linear algebra over the summer since I've never had summer school and Calc II + LA + work might be too much for me :/

bob1182006 said:
Ok thanks I thought maybe the teacher was skipping out on important things in his class.

I think I'll wait and take linear algebra over the summer since I've never had summer school and Calc II + LA + work might be too much for me :/

You might be able to handle it. I found Calculus I harder than Linear Algebra. So if you found Calculus I alright, then Linear Algebra might be alright too.

I don't see any need for Calculus 2 either. Our calculus 3 and linear algebra class had a similar first week, but after that were almost completely different. I would say go for it.

Thanks for all the advice

I just "re-did" my finances which were the only things nudging me away from doing it, but now I think I'll be able to with little problems

Same, i took linear algebra after calc 1! I don't think I needed calc 1 even, they just taught you chunks of what you needed.

logically it is the other way around, linear algebra is needed to understand advanced calc, maybe calc 3. but calc 2 is is used as a sort of maturity test for taking any kind of abstract math, like linear algebra.

so no, it is not needed, but yes it is useful experience.

Interesting the only thing from matrices I've used so far in calc III is when applying parametric/substitution and you have to take the determinant with partial derivatives but that's all so far, maybe there was other times and I just didn't realize it.

I found linear algebra incredibly difficult-- as did the rest of the class with a class average of 30s on the midterm. However, we never ever needed any sort of calculus. But, you might get more out of the topic of eigen vectors/values/functions and their applications to differential equations if you've studied a bit of Diff EQ.

I am about to finish Linear Algebra for the spring semester. I would again state that Calc 2 is not needed at all. No amount of Calc is needed for Linear Algebra, however it may help on a few small problems. We talked very briefly about how to show that differentiation and integration of polynomial functions can be shown to be a Linear Transformation and did one problem involving finding the matrix that corresponded to that transform. As stated in an above post, Calc 3 was similar to Linear in the first week or so, in the vector subjects but that's about it. The similar topics were dot and cross products and projections of vectors to lines or planes.

I agree. I was thinking about this the other day.

mgiddy911 said:
talked very briefly about how to show that differentiation and integration of polynomial functions can be shown to be a Linear Transformation

Not knowing this will not hinder your knowledge of Linear Algebra. In fact, not knowing that does not say anything about whether or not you know Linear Algebra. So, the fact above is irrelevant when learning Linear Algebra. Of course, I'm talking about the abstract sense.

If you get Linear Algebra down, and then learn Calculus I (you don't need Calculus II to know the above), and then someone told you about the fact above, you should be no doubt capable of figuring it out without much trouble.

JasonRox said:
If you get Linear Algebra down, and then learn Calculus I (you don't need Calculus II to know the above), and then someone told you about the fact above, you should be no doubt capable of figuring it out without much trouble.

Not to mention that most calculus books point that fact out.

radou said:
Not to mention that most calculus books point that fact out.

True. As well as other things like the Wronskian.

Many introductory linear algebra books use examples from calculus. For instance the book I teach from explains that $D=d/dx$ is a linear map $D: P_n(x) \rightarrow P_{n-1}(x)$. You would need some basic calculus for that, but certainly not Calc II.

Tom Mattson said:
Many introductory linear algebra books use examples from calculus. For instance the book I teach from explains that $D=d/dx$ is a linear map $D: P_n(x) \rightarrow P_{n-1}(x)$. You would need some basic calculus for that, but certainly not Calc II.

But not knowing this example doesn't say anything about whether or not you know linear algebra. It's only a linear transformation that you have yet to understand more than linear algebra to understand. Yet, you still know what a linear transformation is. If someone said you need to understand the above to understand linear algebra, than you can throw in an example that requires like knowledge of abstract algebra to understand the linear transformation, so does that mean you need to know abstract algebra to learn linear algebra? Certainly not.

I know all of that, Jason. But obviously, if an instructor wants to feel free to use examples of the type I mentioned, then he'll have to insist that calculus be a prerequisite, won't he?

Tom Mattson said:
I know all of that, Jason. But obviously, if an instructor wants to feel free to use examples of the type I mentioned, then he'll have to insist that calculus be a prerequisite, won't he?

Not really because he can just show you how it works, and then it's done. Of course, you will have no depth regarding that example, but you can get by for sure with no Calculus. The example doesn't require a whole term of Calculus to understand.

It seems clear enough to me that the examples from calculus that appear in a linear algebra book aren't placed there simply as an exercise in formal manipulations. The whole point of examples such as the one I described is to show the student that he has already been exposed to linear maps on finite dimensional vector spaces, without being told so. That point would be completely lost on the student if he hadn't been previously exposed to them.

Tom Mattson said:
It seems clear enough to me that the examples from calculus that appear in a linear algebra book aren't placed there simply as an exercise in formal manipulations. The whole point of examples such as the one I described is to show the student that he has already been exposed to linear maps on finite dimensional vector spaces, without being told so. That point would be completely lost on the student if he hadn't been previously exposed to them.

That still doesn't mean it should be a pre-requisite.

In the Linear Algebra at our school, the subject was even used to solve Differential Equations and Calculus itself wasn't even a pre-requisite. No one seemed to have much trouble because of it.

I would agree that calculus is not needed, however there are a number of useful things in linear algebra that add depth to calculus and intern depth to linear algebra.

for instance is the integral of a function a linear transform? how bout a definate integral? or a derivative?

also is theeigenvector related to matrices or linear transforms?

Thanks al for the advice, I talked with my math department suposedly they made calc II a pre-req because they wanted people to have "practice in math" before getting into Linear Algebra

That makes sense. You don't really need calculus before taking linear algebra, abstract algebra, or even analysis. Each of those subjects is taught from first principles. But in typical introductions to those subjects, there is an admixture of computations and proofs. Most calculus courses only require you to do the computations.

## 1. What is the connection between Calculus II and Linear Algebra?

Calculus II and Linear Algebra are both branches of mathematics that are closely related. Calculus II deals with the study of continuous change and its applications, while Linear Algebra focuses on the study of linear transformations and their properties. Many concepts in Linear Algebra, such as vector spaces, matrices, and determinants, involve techniques and principles from Calculus II. Therefore, a strong foundation in Calculus II is essential for understanding and applying concepts in Linear Algebra.

## 2. Can I skip Calculus II and still take Linear Algebra?

While it is not recommended, it is possible to take Linear Algebra without completing Calculus II. However, you may struggle to understand certain concepts and applications in Linear Algebra without a strong understanding of Calculus II. It is highly recommended to have a solid understanding of Calculus II before taking Linear Algebra.

## 3. What specific topics from Calculus II are necessary for Linear Algebra?

Some of the key topics from Calculus II that are necessary for Linear Algebra include derivatives, integrals, limits, and series. These concepts are used in Linear Algebra to understand and manipulate functions, vectors, and matrices. Additionally, knowledge of multivariable calculus, including partial derivatives and double integrals, is important for certain applications in Linear Algebra.

## 4. Is there a particular order in which I should take Calculus II and Linear Algebra?

It is generally recommended to take Calculus II before Linear Algebra. This is because Calculus II builds upon the concepts learned in Calculus I, and many of these concepts are necessary for understanding Linear Algebra. Additionally, some universities require Calculus II as a prerequisite for Linear Algebra.

## 5. How can I prepare for Linear Algebra if I have not taken Calculus II yet?

If you have not taken Calculus II yet, you can still prepare for Linear Algebra by reviewing basic concepts from Calculus I, such as derivatives, integrals, and limits. You can also familiarize yourself with vector operations and basic matrix algebra. There are also many online resources available that provide introductions to Linear Algebra and its applications. However, it is highly recommended to have a strong understanding of Calculus II before taking Linear Algebra to ensure success in the course.