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Calculus 3 -- should I take linear algebra before or can I take it after?

  1. Jun 22, 2014 #1
    I will start calculus 2 in the fall. I am comfortable with the integration techniques. I did not quite get Taylor series an d the like during self study. I can learn this from the professor swing that I have somewhat completed the cal 2 portion and the semester is 2 months away.

    now my question is for calculus 3? I am allowed to take linear algebra together with calculus 2 at the same time, but I opted. Instead I will be taking cal 2, physics intro, computer science intro, and a spanish class.

    Can calculus 3 be done without knowing introduction linear algebra? The only pre rec for calculus 3 is calculus 2.

    Would I also have to learn proof writing when I take linear algebra? I do not know anything of proof writing besides proof by induction and a few proofs of calculus 1, trig, and algebra I have seen in my college textbooks.

    I will be purchasing a copy of "How to solve it" to learn basic proof reasoning.

    If I need to self study linear algebra to do well in calculus 3, what would be a great introduction to linear algebra? I prefer one where the language is clear and not to hard, like say Spivak Calculus, but will allow me to grasp the material.
  2. jcsd
  3. Jun 22, 2014 #2


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    You can do either, what would I personally suggest? Do Linear beforehand.
  4. Jun 22, 2014 #3

    Simon Bridge

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    Yes it can.
    You should seek advise from someone who knows your work better though - you may benefit from the algebra course anyway. I cannot tell from here :)

    ... yes. Don't worry, you'll catch on.
    The main tool you need for proofs is reasoning.

    ... probably overkill.
  5. Jun 23, 2014 #4
    Thanks. Any intro linear algebra books I should look like. Not looking for a heavy theory book at the moment. One that strikea a balance between computation n theory.
  6. Jun 23, 2014 #5


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    Two possible distinct viewpoints fit this question.

    One view is that after a year of Calc 1&2, you have enough mathematical sense to begin learning linear algebra, and doing so will be practical for at least SOMETHING that you'll study and maybe also useful outside of academic courses. Linear algebra will make some things found in Calculus 3 a little more comfortable when you study them.

    The other view is that you want to continue learning Calculus, moving from Calc 2 to calc 3 without interrupting, so that you maintain skills and knowledge better about Calculus. You would then choose to study Linear Algebra after finishing Calc 3.

    Do you have room for still another point of view: Doing Calculus 3 and Linear Algebra in the same term?
  7. Jun 23, 2014 #6

    Won't have time to do both. The problem is that in the community college district I am at, the teacher that teaches calculus 3 there is very bright. She has extremely good lecture. Although, after calculus 3 their is only one professor that teaches both linear algebra and differential equations and he is horrible. Rambles about his country being number 1 and just tells joke during the lecture. So I would have to go to a sister college in the same district to receive a good education with a Proffesor whose lecture is just like the female calculus 3 teacher. I do not drive, I am rather poor so going to 2 different schools on the same day is time wasted from studying. Also there would be a conflict of schedule with a physics class I need that meets every semester at the same time for the last 3 yes as I recall.

    What does learning leaner algebra first benefit me in calculus 3?
  8. Jun 23, 2014 #7


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    If you have seen determinants before, that could help with calculating areas or the cross product of two vectors. But it isn't a big deal, what you need will be taught anyway. Really I would say you should only do it if you are interested in learning linear algebra.

    Continuing, if you just want to have a look at determinants, there is a free book online by Jim Hefferon, look at chapter 4 if you like. If you want a proper book to learn more about linear algebra, you have said you don't want a heavy book, this one looks good for being clear but not difficult:

    Last edited by a moderator: May 6, 2017
  9. Jun 23, 2014 #8


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    I would agree that you don't need linear algebra for calc III.

    Actually, I thought calc III was easier than Calc I and II.

    Why? Because once you pass calc II, you already know all the rules. Calc III simply introduces the "z" axis.

    All the rules you used for the x and y axis are identical for the "z" axis.

    Piece of cake, enjoy.
  10. Jun 23, 2014 #9
    Taking calculus 3 without linear algebra is totally fine. If you have a solid understanding of calc 1 and 2 then calc 3 should be doable. The only issue for me was trying to visualize everything in my head; it can be abstract and weird at first. I hope you have have fun with it.

    It would be helpful for you to get any elementary linear algebra textbook and learn the very basic stuff like solving systems of linear equations and matrices/determinants. It's very quick to learn if you don't already know it.
  11. Jun 24, 2014 #10
    I remember systems of equations using up to the gauss an elimination method. There was an interesting problem I once did to solve for median of a triangle to find the lengths of something in the figure. The trick was to remember to use similar triangles to find the relationship. Easy as pie. Instead I broke it up into 2 triangles and used elimination. I had to use gauss an method for a tetrahedron.

    Matrix I don't remember them all. Last time I used them was in intermediate algebra and that was 5 math classes agp.

    I downloaded the linear algebra book somebody posted the link too. Thanks alot. Will study linear algebra on my own after I finish reviewing my calculus 1.

    Maybe I am over thinking mathematics in general. This B I received in Cal 1 left a sorrow taste in my mouth. My dream is to transfer to UCLA because it is near my home. The problem is I cannot be getting B's.

    How hard is it to get into UCLA as a community college transfer student in mathematics in either applied or pure. I will most likely have a 3.6 gpa after all my classes are done. I am Mexican American, low income, first to attend college in my family, and no criminal history.
  12. Jun 24, 2014 #11


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    I understand your wish to attend your dream college, but B's in math can be just fine. I got B's in math all the way thru....until calc 3 I finally got an A. I'm a very succesful engineer who went to a decent school, graduating with a 3.1 cumlative.

    Getting A's in college engineering can be tough. Very little room for error.

    When you finally do land your job and get acclamated to work, no one cares where you went to school or what your GPA is. They only thing they care about is what you can do at work and how much money you can make them.
  13. Jun 24, 2014 #12


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    My two cents: I took linear algebra after Calc III and did fine in each. If I could go back in time, I would have rather taken Linear Algebra first, for reasons others have given above. I don't think it matters very much. The quality of your professor indeed may matter much more than the order of these classes.
  14. Jun 29, 2015 #13
    You don't need Linear algebra to do Calculus III. They are very different courses. In fact, I think Linear Algebra is considerably more difficult than vector calculus. The key in linear algebra is not merely to learn how to do matrix operations, but to learn the concepts of vector spaces, linear independence, span, basis functions, orthogonality, linear operators, eigenvectors / eigenvalues, etc. Learn these concepts in the abstract. Don't settle for just working through algebraic operations.

    Linear algebra became alive to me in graduate school when I had to use linear algebra to numerically solve differential equations.
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