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Not enjoying Calculus 2 at all, advice?

  1. Feb 15, 2016 #1
    Hey everyone,

    First of all, let me start out by saying that I am not enjoying this class, not because I'm not doing well, but frankly because I find it boring. It's not that I'm not challenged, I am. The material can be meticulous. But, it just seems like a lot of algebraic manipulations and tricks rather than theorems like in Calculus 1.

    We had our first test which covered integrals through improper integrals (which was my favorite section). I made a 94 on it. The mistake I made was a stupid one, and I caught my error at the end of the test but didn't have enough time to correct it.

    Will this course pick up like Calc. 1? I don't mean in difficulty, but rather the depth content itself. I feel like in Calculus 1 I was learning all this cool material, and analyzing things that I've never thought of before. Now I just feel like I'm doing intermediate algebra on crack to solve an integral. Which, is relatively frustrating because we have CAS systems that solve them, and integral tables. Of which, my book covered and we were required to learn, but aren't allowed to be used on a test (amplifying my frustration even more). Conceptually this class seems like a breeze so far. It's more of learning methods for different integrals you encounter, and without constantly reviewing I'll forget them. I get that it's an exercise of the mind, and that it's the thought process behind them, but honestly this all just reminds me of trigonometry proofs (manipulating expressions to resemble something you want -- which ironically was my favorite part of trig). Except instead of 1-2 sections devoted to the idea, an entire chapter.

    How did you all study for this class? I have really short term memory, but hate repetition, so I've yet to find a good balance. Previously, I'd work every odd problem in the book, but I've found for this class that it's really tedious and repetitious. So, instead of practicing over and over, I've been watching KhanAcademy, MIT, and PatrickJMT and working about half of our homework assignment before the lecture on it, then the other half after lecture. All said and done this takes me roughly 4-6 hours additional every week to learn the material before class and work the homework problems. I feel like it may be better to spend this time WORKING additional problems, rather than doing this. But, I don't know if my time could be better spent.

    It just sucks that the joy I used to have in learning math is slowly depleting. I feel really burned out and we're only 5 weeks in.

    Also, sorry for the novella of a post. I just feel discouraged right now because I used to be excited about this stuff. And being in engineering I have a feeling that feeling burnout at this stage is not good.
     
  2. jcsd
  3. Feb 15, 2016 #2

    Orodruin

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    This question is utterly impossible to answer on an internet forum as "Calculus 1" and "Calculus 2" offers absolutely no information on the courses themselves. What is covered in such courses will generally differ from university to university and even between professors. Some may be more proof based and some more computation based. Nobody will be able to answer your question in a meaningful way unless you specify which exact class you are taking and even then you would need to get lucky to find someone to answer it here. You would be more likely to get a reasonable answer from older students.
     
  4. Feb 15, 2016 #3
    Calculus 1 covered Limits, Derivatives, Applications of Derivatives (related rates, optimization), anti-derivatives, approximate integration, and Integration through U-Substitution. Calculus 2 covers anti-derivatives, integration techniques (u-sub, by parts, trig, partial fractions, improper integrals), applications of integration, differential equations, and infinite series.

    More directly, we are going through Stewarts Calculus. Calculus 1 covered chapters 1-5.6, Calculus 2 covers 4.8-8.

    Or from the course description themselves:

    Calculus 1: Topics include inequalities; functions; limits; continuity; the derivative; differentiation of elementary functions; Newton's method; applications of the derivative; the integral; integration of algebraic functions and the sine and cosine functions; numerical integration; and basic applications of the integral.

    Calculus 2: Topics include integration of elementary functions; techniques of integration; integrals with infinite limits of integration; integrals of discontinuous integrands; applications of the definite integral; an introduction to differential equations; infinite series; and other applications.

    Calculus 3: Topics include polar coordinates and polar curves; vectors and analytical geometry in three dimensions; vector-valued functions and curvature; components of acceleration; functions of several variables; limits and continuity in three-space; partial and directional derivatives; gradients, tangent planes, and extrema of functions of two variables; multiple integrals in rectangular, polar, spherical, and cylindrical coordinates; applications of multiple integrals to area, volume, moments, centroids, and surface area.
     
  5. Feb 15, 2016 #4

    micromass

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    Yeah, I feel your pain. Calculus is a lot of computations which do seem useless a lot of the time (certainly given that I would never compute an integral myself anymore). This is amplified by the fact that you're an engineer, which means they won't bother to teach you much extra theory. Everything in calculus II is absolutely necessary though. You need to be very good at integration by parts and other stuff. Will you do series and sequences this semester? Something tells me you'll enjoy those a lot more, so wait until then.
     
  6. Feb 15, 2016 #5
    We do, unfortunately it's our last section. Ha. Are differential equations similar to the rest of integration? In terms of the computational methods?
     
  7. Feb 15, 2016 #6

    micromass

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    Well, differential equations have some amazing theory behind them. But sadly, you won't see any of this. I'm afraid it'll be just more of the same: computational methods.
     
  8. Feb 15, 2016 #7
    If you think of the course as teaching you a lot of stuff that (for whatever reason) you shouldn't have to learn, then that chip on your shoulder will make it a lot harder and more painful to learn.

    If instead you accept that learning to do integrals in the absence of a computer algebra system will inform you in valuable ways that you may not yet be aware of, the course will become a lot less unpleasant, maybe even pleasant.

    And there are really only a few techniques for integrating:

    * Just taking the antiderivative of a function that you've seen as the derivative of something;

    * doing ∫ f(u) du for some function u(x) when you already know how to do ∫ f(x) dx;

    * using a substitution (which is very similar to the previous method);

    * integration by parts; and

    * various combinations of the above.

    If you treat the material as mainly stuff to understand rather than stuff to memorize (and of course there is at least a little memorization at first), you will find it a lot easier to absorb.

    And if you notice that older integration methods were taught so long ago that you are forgetting them, then probably the homework is not being chosen optimally . . . but if the teacher doesn't help you consolidate your learning that way, you would be wise to refresh your memory yourself.

    Hope these tips help.
     
  9. Feb 15, 2016 #8

    fresh_42

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    That is correct. But aren't the computational methods by far the most needed for engineers? I have always this picture of giant books with endless calculation tables in mind when it comes to engineers of all kind.
     
  10. Feb 16, 2016 #9

    Student100

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    That's kind of a loaded question, since it depends on what you end up doing in your engineering career. You might not need any more math than basic algebra computation skills, or you might end up needing to understand the constraints placed on a certain physical model that is very theoretical/computationally heavy.

    I personally avoid videos, to me they're worthless. I prefer to read the book, and figure out the problems. Works for me, may not work for you. With that said, like any skill, repetition is the key to long term retention, So while you may not enjoy the repetition, you need to keep doing it.

    Sounds like a good review, and a way to broaden the number of integrals you can solve.

    The class isn't a tutorial on how to use CAS though. Everyone who uses CAS needs to understand the algorithmic steps, and a method to check accuracy. We also can't always count an a software package to do what we want to do, so sometimes we have to design our own. Maybe not so much these days, but it's still an important skill to know how to do computations by hand.

    My advice to you would be to take linear algebra next semester, instead of progressing straight to calculus three. Not only will you get a change of scenery from calculus, but LA theory also underpins a lot of the stuff you'll see in calculus three. It's also one of the "funner" math courses, in my opinion.

    Your calculus two class will pick up, series and sequences are interesting like Micromass says. By the end of the course you should be able to approximate integrals like:

    $$\int_0^{10} x^{-x}\,\,dx$$

    Which uses a little bit of everything you learned in the last two courses.
     
  11. Feb 16, 2016 #10
    Just an input from another student
    I literally endured calculus 1, 2 and 3, i was sleepy during class, barely paid attention and passed because i kept telling myself it was useful (because for me it as the same, math was ruining my joy for physics, and until i saw applications, i felt kinda empty)
    And it actually was, the physics phenomena these tools let you explain are just outright fascinating.
    I never liked proofs, or by-the-book definitions of integration, it didn't help me understand what they were at all (i still have a hard time understanding Riemann's integration, is that mediocre of me...?), and since calculus are taught by mathematicians, and not physicists, in my uni, the courses didn't have many applications on them.
    But after i took differential equations i understood the magnitude of what i just had learned, and the potential uses it has, ∑F=ma is a massive one.
    Then i took oscillations and waves, thermodynamics, statistics....for all of those integral calculus is of paramount importance.
    PS= I'm just a 3rd year student of geophysics :D
     
  12. Feb 16, 2016 #11
    Your calc class does seem a little boring based on the description. You might enjoy sequences and series - a lot of people hated them but I found them extremely useful and really cool. They are the second most important thing to knowing integration by parts.

    And to study, rather than doing a lot of small repetitive problems, pick the hardest problems in the book and go at. Start with one you know how to do and increase the difficulty until you are really stuck.
     
  13. Feb 16, 2016 #12

    bcrowell

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    I teach calculus, and I completely agree with you. First-semester calculus is a "great ideas" course, while second-semester calculus is mostly about learning a bunch of stupid integral tricks. This is the reason that I have only been requesting to teach the first-semester course. As you've pointed out, the stupid integral tricks are pretty useless these days because we have CAS.

    Are you a math major?

    If it makes you feel any better, IMO most of the rest of the undergrad math curriculum is a lot more fun and interesting. Linear algebra and vector calculus are both really cool, and I enjoyed almost all of my upper-division classes. In my experience, the only other undergrad class that tended to degenerate into a bag of useless tricks was differential equations. I've used differential equations constantly throughout my career, but I have almost never used any of the tricks they taught me in that course.
     
  14. Feb 17, 2016 #13
    That is correct; the engineer is going to use differential equations to compute numerical approximations to solutions that are needed for examining the physical phenomena they're trying to model (eg finite element analysis to find the mechanical deflection of a beam or to calculate the magnitude of an electromagnetic field in the cross section of a part, etc).
     
  15. Feb 17, 2016 #14

    Student100

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    Or not.
     
  16. Feb 17, 2016 #15
    Not really, differential equations are used by engineers soley to model physical processes and in the real world they are done by numerical approximation (finite difference, finite elements, etc) since real systems don't behave so nicely that you can get pretty analytic solutions.
     
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