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Linear Algebra or Calculus III

  1. Aug 5, 2009 #1
    I need some advice...

    I have the option to take Linear Algebra from an excellent professor, but the course isn't required for my physics major and would only count as an elective for my math minor.

    Alternatively, I could take Calculus III from a mediocre (at best) lecturer. This course is required for both my physics major and math minor.

    I'm tempted to take the Calculus class if for no other reason than that Calculus II is still moderately fresh in my mind, but in the spring semester it will be less so. On the other hand, I have heard horror stories about the instructor and so am hesitant to take his course.

    Your input is much appreciated.
  2. jcsd
  3. Aug 5, 2009 #2


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    Linear Algebra not required for Physics??
  4. Aug 5, 2009 #3
    No, the only math classes required are:
    Calculus I
    Calculus II
    Calculus III
    Differential Equations
  5. Aug 5, 2009 #4
    If you have the chance, definitely take Linear Algebra. I am a little surprised it is not required for your physics degree, but every school is different. If Calc III is multivariable calc, you can probably put it off for a semester because it is not terribly more difficult than your previous calc in my opinion. If Calc III is vector calc, you will need that ASAP to really keep up with your physics.

    Hope this helps.
  6. Aug 5, 2009 #5
    I am a math major so I am not too sure about physics but, isn't linear algebra very important in areas of quantum mechanics?. I would personally take linear algebra from a great professor then take calculus from a bad lecturer. Im sure you won't forget your calculus even after the term =P
  7. Aug 5, 2009 #6


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    It is used heavily in physics though, so I suggest you don't skip it.
  8. Aug 5, 2009 #7
    Thank you all for the advice.

    I guess it'll be Linear Algebra in the fall and Calculus III in the spring.
  9. Aug 5, 2009 #8


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    Try doing the other way around. You have or would have Calculus II fresh in your mind just before studying Calculus III. That is a safe way to plan your Math courses. Not everyone finds calculus III to be so easy. It will probably deal with vectors, among other things. You can and should still take the linear algebra course when you are done (or in the following term). If you are concerned about the quality of your Calculus III teacher, begin studying the course on your own, well in advance of the term in which you enroll for it. In this way, you might learn some of the material well, before doing it for credit.
  10. Aug 9, 2009 #9
    Hi mvantuyl,

    my university does not require Linear Algebra either and the maths course requirement are same as yours (Calc I, II, III, and DE) however i took Linear Algebra nevertheless. I didn't like the course at all the course but it is indeed useful in physics, math (obviously) and engineering.

    Your university, among many other, might offer multiple Linear Algebra course. One is normally for engineering students and another is for math majors. If you are not planning on double major in maths then take engineering one...it is more of application (it's harder as well btw).

    another thing your university might offer is a physics course with sole purpose of introducing mathematics techniques to physicist. In that case, you might not want to take Linear Algebra at all...as most likely they'll teach you stuff you need in that course.

    oh and Calc III does not have much stuff from Calc II. Most likely upto first exam you'll just be doing vectors which has little to no relevance with derivatives and integrals. In latter part of the course you'll be doing polar, spherical, and cylindrical coordinates along with double and triple integrals and few more stuff. The integration involved in those are pretty much of calc I, by that i mean you won't be using the most of the integration techniques you learned in calc II. If i remember correctly, all you'll need is derivative (and integrals of course) of sine, cosine, and tangent along with u-subustitution for most part in calc III....i'm sure you won't forget that in a semester ;)
    Last edited: Aug 9, 2009
  11. Aug 9, 2009 #10


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    from rubrix:
    Nearly every bit of Calculus II was used and needed in Calculus III, where I attended. Don't try to depend on Calculus III avoiding dependance on Calculus II.
  12. Aug 9, 2009 #11
    I think that a lot of schools are now combining linear algebra and differential equations, I'd look at a syllabus before you jump into linear algebra. I mean after all it is a relatively easy math class which can (fairly) easily be self taught/picked up.
  13. Aug 10, 2009 #12
    But calc III builds a lot on linear algebra too, while the reverse is not true. I would say that it is better to take linear algebra first.
  14. Aug 10, 2009 #13
    tell me specific topics from calc II that you were tested in calc III.

    like said before a good portion of calc III course is spend on basic vector geometry i.e vectors in 2D, 3D, dot product, cross product, cylindrical and spherical coordinates. For this portion You don't need any prior knowledge of calculus whatsoever.

    Next a massive portion of calc III is spend on differentiation in multivariate (which includes partial derivatives, gradient, Lagrange, optimizing with a constraint etc) and multiple integration (which includes double and triple integrals in polar, cylindrical, and spherical coordinates). Of course you are required to know how to differentiate but they won't test you on most of the differential techniques taught in calc II. The most they will make you do is u-substution.

    similar is the case in DFQ, you are required to know basic deriv/integrals but as per techniques of differentiation go, u-substutition and partial fractions is just about enough.
  15. Aug 10, 2009 #14


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    That's it. Here at my university Linear Algebra is a prerequisite for calculus III (multivariable and vector calculus).
    In calculus 3 you'll have to calculate the determinant of linear transformations (Jacobian). I guess they'll teach you how to do so, but maybe you won't have a good understanding of why things are the way they are.
    I'd take Linear Algebra and then Calculus III. Linear Algebra will also help you for other courses so it's worth studying it.
  16. Aug 11, 2009 #15
    In calc 3 those are usually not linear transformations :tongue: , but since every smooth transformation is locally linear you have to calculate a position dependent determinant.

    Anyway when you do the normal u-substitution in calcII you are actually doing such a transformation and then taking the determinant of it. If you know linear algebra well then calcIII got almost nothing new, since all extensions are natural after what you got from linear algebra if you understood what you did in calcII well.
  17. Aug 11, 2009 #16
    I am terribly confused as to why you are call referring to "Calc II" and "Calc III" as if you all went to the same university :-/
  18. Aug 11, 2009 #17


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    Me too, but that's probably due to all the US students here, who for some reason seem to have a lot of identical courses all over the country.
  19. Aug 11, 2009 #18
    Take linear algebra. Its a lot more useful. Honestly, I learned Multivariable (Calc III) by doing E&M, much more than I learned it through the actual math class. Its just extending concepts you already know (except for some things at the end, like stokes and greenes, but my math course taught them sooooo poorly in the last two days of class).

    I think because AP exams have kinda standardized what's meant by calc II and calc III. Calc I is AB, Calc II is BC, which is essentially some applications of the basic calculus learned in AB (like sequences and series, physical applications, and some other things). Calc III is multivariable. I think...
  20. Aug 11, 2009 #19
    I am not an US student but I know how their course system works and it is mostly similar most over their country.
  21. Aug 11, 2009 #20


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    From Rubrix:
    The key idea is "Pre-requisite"; Calculus III depends on good knowledge of integration and differentiation. The Calc III material also includes continued use of techniques of integration.

    Ignoring the prerequisite of Calculus II for Calculus III is a bad academic risk.
  22. Aug 11, 2009 #21


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    These are like the most important part of multivariable calculus though! It's basically the culmination of all the work you have done on integrals over regions and surfaces combined with the differential forms!
  23. Aug 11, 2009 #22
    I know, and that's what's sad. We spent almost all semester "parameterizing" curves again and again and again and then spent the last week on the important culminating theorems. I don't know them at all, neither does anyone else in that class, which is why I can't even read Maxwell's Equations in their differential forms with grads and curls and stuff.

    But I figure my intermediate E&M course is going to straighten me out on that.

    And by the way, I was taught by the co-chair of my math department. Great guy and brilliant, but I just feel like my superb high school teacher could have TAUGHT it to me better.

    And I don't just mean "Compute the curl of this" or "state the divergence theorem" I mean actually learn them. Its funny....on the exam we had a question which we were supposed to solve with the divergence theorem, but it looked to me a lot like two electrons so I just used Gauss's theorem and "added up" the "electric flux" going through the Gaussian surfaces. And it turned out I was right, even though the method I used was actually not rigorous (ok, so I used an analogy to solve the problem, but my physics teacher would have been proud!)
  24. Aug 12, 2009 #23
    If you do a more advanced vector calculus course you will learn those properly, they are not as integral to the first multivariable course usually.
  25. Aug 12, 2009 #24
    You sure? Pretty much everyone there has already had a basic multivariable course, this course is the only vector calculus course offered in the undergraduate curriculum. And it is called vector calculus, here's the synopsis:

    Math 105 is a course in vector calculus that uses linear algebra. Topics to be covered include: iterated integrals and partial derivatives, optimization (constrained and unconstrained) in multiple dimensions, the Implicit Function Theorem, cylindrical and spherical coordinate systems, vector fields, divergence and curl, parameterized curves and surfaces, arc length and surface area, and Green's, Stokes's, and Gauss's Theorems.

    Considering how everything else on the list before those last three are practically obvious, I wish they'd spent more time on them. The only thing that needed any thinking was that Lagrange multipliers stuff (had an interesting proof). I really wish we'd gone over a more rigorous treatment of all the various multivariable versions of taking the product and how to interpret their differences and convert between them (in a more physical way I guess) instead of just learning how to compute them.
  26. Aug 12, 2009 #25
    You got any course on tensors then? Because it sounds a lot like that is what you want.

    Anyway, where I go we do gauss, stokes, greens and such in the first multivariable but just a little the last weeks. Then in vector we used them all the time.
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