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Which Math Class to Take

  1. Mar 30, 2006 #1

    mrjeffy321

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    I am trying to get a jump on picking classes for next semester, I do not want a repeat of what happened to me last time (I waited about a week too long and I couldn’t get any of the classes/time I wanted).

    My problem comes when trying to choose a math class. Now that I have Calculus II credit (or soon will), my options really open up. I have three lower-division classes to choose from,
    -Linear Algebra
    -Differential Equations with Applications
    -Multivariable Calculus and Applications

    All three have the one prerequisite of Calc. II.

    Looking at other classes down the line, I see that it would be to my advantage to get Diff. Equations and Multivariable Calc. out of the way as quickly as possible since they are required to get into the Physics classes I want (and, of lesser importance, more advanced math). But is there any advantage in taking Linear Algebra first…or at all? I do not see that being very important (at least as a pre-req. for other classes). Is there a preferred order in which to take Diff. Equations and Multivariable Calc.?

    And then there is the other option of taking one of them over the summer as well.
     
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  3. Mar 31, 2006 #2

    JasonRox

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    In all honesty, I think Linear Algebra strikes almost or even the same amount of important as Differential Equations.
     
  4. Mar 31, 2006 #3
    I would say that as well, I've never taken the class or studied much of it, but since I'm trying to learn differential equations on my own I'm really starting to see the uses that it has in application to solutions of higeher order differential equations and other areas of mathematics.
     
  5. Mar 31, 2006 #4
    There is an advantage in taking LA before DE in that some of the theory and proofs you encounter in DE make use of results from LA, however its not crucial. As far as multivar calc and DE, one doesn't depend on the other, so they can be taken in any order. As it goes for physics, all three math classes are crucial, but for the first few physics classes DE and multivar calc are more useful.
     
  6. Mar 31, 2006 #5

    0rthodontist

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    Adding to that, multivariable calculus also depends on linear algebra.
     
  7. Mar 31, 2006 #6

    jtbell

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    Mr. Jeffy, which physics classes have you had already, and which ones are you planning to take next? That will have some influence on which math classes you should go for.

    I'll assume for the moment that you're just finishing freshman-level General Physics now. Among the couses you're likely to take soon, Electricity & Magnetism will definitely use multivariable calculus, and a lot of it. So will Thermodynamics. Classical Mechanics will use differential equations, and some multivariable calculus (but not nearly as much as E&M does). None of these use much linear algebra, at least in my experience.

    You should also check syllabi for those courses at your school so see if they actually teach the required math as part of the course. For example, it's common for E&M courses (especially two-semester sequences) to start with an introduction to vector calculus. The Mechanics course may introduce enough material about differential equations to handle the d.e.'s encountered there.
     
  8. Mar 31, 2006 #7
    At my school linear algebra is a pre-req for multi-variable calc. But I am currently in Calcullus 2 and I am also taking both Diff E and Linear Algbebra and I am having no trouble with taking these at the same time. I think that you should just take both Diff E and Linear Algebra. Does your school not have a Calculus 3 class, or is that the Multi-Variable class you are reffering to?
     
  9. Mar 31, 2006 #8
    At the University I'll be attending they combine Linear Algebra and Differential Equations into one class and recommend that you take that before Multivariable. Could you fit Linear Algebra and Diff Eq in the same semester?
     
  10. Mar 31, 2006 #9

    mrjeffy321

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    So it is the general opinion that Linear Algebra should not be skipped.
    I have heard from other people that taking Linear algebra first really makes learning Differencial Equations easier. I couldnt remember if they said Diff. Equa. or Multivariable Calc., but from what you all said, it must have been Diff. Equa.

    So far, I have had only 1 real Physics class while at college, "Contemporary Physics", which covered Optics, Diffraction, and Special Relativity. I tested out of "Physics I" (Mechanics and Heat) and I plan on taking "Physics II" (Electricity and Magnetism) next semester (I couldnt get in this semester because it required a Calc. II credit).
    But beyond E&M physics, they next course in the line is called "Theoretical Physics" which requires E&M, Diff. Equ. and Multi Variable Calc. All Physics classes beyond this require Theoretical as a pre. req.
    If my previous experience in my one physics class counts for anything, then the professor does not spend much/any time teaching the required math involved. If it is assumed you know it, they assume you know it, if they dont require it for the class, they try not to use it.

    My school does not have a formal class called Calculus III, just the classes listed above with no indication of which one might be considered a calc. III, if any.
    Taking 2 math classes at the same time is a possibility, in theory I could squeeze both in...barely. I am not too sure how much I will enjoy that. So far, my Calc. classes have been my most time intensive, most difficult, lowest scoring classes of all. Taking two at once (unless for some reason they turn out to be much easier than other math classes) might not be the best idea for success in either.
     
  11. Mar 31, 2006 #10

    jtbell

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    Then you definitely need to give preference to D.E. and M.V.C. I would talk to some math and physics profs and ask if they think you should also take linear algebra along with these, before moving on to Theoretical Physics. Curricula do differ from one school to another, and it's dangerous to ask people who are not familiar with local curricula for recommendations. Don't you have an academic advisor among the faculty that you can ask about this?

    By the way, which college is this? Not that I'm trying to track you down personally, you understand... :smile: I'm just curious about their curriculum and would like to check it out for myself, as a matter of professional interest.
     
  12. Mar 31, 2006 #11

    JasonRox

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    The purpose of taking Linear Algebra is to benefit yourself... in your own career.

    First and foremost, choose classes that lead to the degree, but then after that, take courses that benefit yourself before taking anything else.
     
  13. Mar 31, 2006 #12
    A lot depends on what textbooks are being used. I've seen some lower division DE books that make use of Linear Algebra and some that haven't. The Calc class introduces you to DE, and is probably going to be the single most useful class for lower division physics work. After that comes DE, then linear algebra. However, for upper division physics, DE and linear algebra are pretty much essential, and it's pretty impossible to function in mechanics or E&M without multivariable. My recommendation is definitely the Calc class, then the linear algebra and DE equally.
     
  14. Mar 31, 2006 #13

    mrjeffy321

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    The next step is definatly to talk with one of the teachers, I would agree. Would you thin a math teacher or Physics teacher would have more insight on this? The math teacher would know in more detail what is actually covered and how, but the Physics teacher would know how it is used later on. I am reluctant to depend too much on the help of my "advisor" since in my limited experience with her so far, she doesnt really do so much advising as she does just approving whatever you decide on your own and asking you questions like "what do you think you should do?".
    The college are talkig about is the University of Texas at Dallas.

    Well in that case, then the answer is clear, taking Differencial equations and Multivariable Calculus needs to be the priority, Linear Algebra (although important) is secondary.
     
  15. Apr 1, 2006 #14

    mathwonk

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    linear algebra should definitely be taken before either of those other two, because the ideas of linear algebra are rperequisite to understanding the other two subjects.

    and multivariable calc should probably be taken before diff eq, because partial derivatives and path integrals and vector fields, (not to mention power series, and fourier series and convergence of functions), play a role in understanding diff eqs, especially the "exact ones".

    linear algebra is the study of linear operators L acting on linear spaces. A linear space is one closed undera ddition and scalar multilication, such as the space of all differentiable functions, i.e. if fmg are differentiable then so are f+g and cf.

    A linear operator is an operator L acting say on functions such that L(f+g) = L(f) + L(g) and L(cf) = cL(f). A primary example of this is a linear differential operator such as L = D^2+D+1, which sends f to L(f) = f''+f'+f.

    The correspondng linear differential equation f''+f'+f = g, can thus be written as L(f) = g. Solving such lineat equations is the domain of linear algebra. thus it is prudent to study the general ideas and theories of arbitrary linear operators before trying to understand the theory of the particular case of linear differential operators.


    As to several variable calculus, differential calculus is merely the art of transforming non linear rpoblems into linear problems. thus one should know how to solve linear rpoblems before attacking non linear ones.

    while it is true one can take those other courses without taking linear algebra first, one cannot understand the material in those other courses without it.

    the fact that those other courses are often taught without linear algebra is an unfortunate historical and political phenomenon. i.e. the ideas of abstract linear algebra did emerge later than the study of differential equations, and hence have historically been taught later.

    even after linear algebra was realized to be basic to those other courses people with a narrow view of how one should rpepare, i.e. withoput understanding what one is doing,l have urged a hurried approach to course taking, which is wrongheaded from the standpoint of mastery of material.
     
  16. Apr 1, 2006 #15

    mathwonk

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    uh you just got me, i have only now read the details of the sale of physics forums to a group of scientologists backed by tom cruise.
     
  17. Apr 2, 2006 #16
    Ah hah! Let me guess you goto UTD? Im a jun/sen physics major at UTD.
    My suggestion, do what I did. Take DE and LA over the summer, so you can get into MVC next fall. And yes you absolutley need to take linear algebra before you take anything else.
     
  18. Apr 2, 2006 #17

    mrjeffy321

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    Indeed, I do attend UTD. Now there are 3 of us here on this forum that I know of.

    How would you compare these 2 (3) classes' difficulties to say Calc. I and II? Easier, Harder, [unGodly harder], aboue the same? I am trying to decide if I am up to taking more than one math class at once, be it during the summer or normal year.
     
  19. Apr 3, 2006 #18
    Linear Algebra is easy, I dont know what choices you have now, but take it with Dr stanford. DE is hard(harder than cal 1 and 2 id say) and requires alot of work practicing problems. I took it with Turi, hes a monster but I learned alot. I think LA and DE over the summer is very doabale as long as you arent working 40hrs a week. I got A's in both and worked like 20 hrs on the week ends. I also got A's in both calcs, just to give you a point of reference.
    Linear algebra may not be REQUIRED, but you will not have to spend time wondering what certain things mean when mentioned in DE,MVC, or theoretical. At the very least knock it out this summer, but I dont think its all that time intensive of a class (compared to DE)
     
  20. Apr 4, 2006 #19

    mrjeffy321

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    Then it is decided, I will take those two over the summer.
    Good bye fun, relaxing summer, hello differential equations. Now no one can say that mrjeffy321 isn’t willing to make sacrifices in the name of science.
     
  21. Apr 5, 2006 #20
    Does some students really just do nothing over the summer besides goof off? Everyone I know either goes to school (most do this), work, or does both over the summer. I don't think I know any students that just do nothing for 2-3 months. Maybee that is what those students that has mommy and daddy pay for everything does. You know the type, their parents pay 3 thousand dollars so they can go on spring break to cancun, and stuff like that. What the hell is up with parents that do that? I find that to be absolutely crazy.
     
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