Why am I struggling with Differential Equations?

  1. Why am I struggling with Differential Equations??

    Please help: I did well in Calc I-III, and now am struggling in Diff.Eq. Anyone else find themselves in the same situation, and how did you save yourself? TIA:)
  2. jcsd
  3. mathwonk

    mathwonk 9,673
    Science Advisor
    Homework Helper

    Re: Why am I struggling with Differential Equations??

    is it bad to struggle? apparently it is new.
  4. Re: Why am I struggling with Differential Equations??

    Yes, it is bad. And yes, it is new. If I am hindered in my progress and can't get a fix on how to adapt, I've wasted my time in this course. I was hoping to hear constructive advice from others who experienced the same. No guarantee, I know, that it will apply to my particular case, but one can always try.
  5. Re: Why am I struggling with Differential Equations??

    How can you expect constructive advice when the explanation for your situation is literally one sentence? Maybe you should expound a bit on what you're facing, why you feel like you're struggling, what exactly you're struggling with, etc.
  6. Re: Why am I struggling with Differential Equations??

    Ah, but there is a commonality of struggle:) Most students find the same things challenging in the same courses. I was hoping to hear the perspective of others who mastered diff.eq with effort. How about you- how did you find it comparable to your calc series? Were you well-prepared? Looking back, would you have preferred a different text? No intent to be cryptic, but others' hindsight about their own experiences can inspire a wealth of advice- perhaps better than if I solicited info specific to myself.
  7. Re: Why am I struggling with Differential Equations??

    I think the best differential equations book is Ross, Differential Equations.

    There are common themes of what give people trouble but it's still helpful to know what is hindering you.
  8. Re: Why am I struggling with Differential Equations??

    The only struggle for me in diffyQ was staying awake. The course is purely algorithmic, decide on the correct recipe to apply and watch your sign errors.
  9. Re: Why am I struggling with Differential Equations??

    ^^What Poopsilon said...^^
  10. Re: Why am I struggling with Differential Equations??

    What helped me a lot was Schaum's Outline of Diff Eq (I used the 3rd Edition). With the book we were using, it would often just present the theory, but not an example of the theory in action. What also helped me was to understand how to identify basic forms of differential equations such seperable, homogenous, etc.

    I'll also add that cramster helped loads to. Many times you might get the right answer, but be unsure of it was coincidence or the correct method. Using cramster, I could follow the steps and see if they matched up with mine.
  11. Re: Why am I struggling with Differential Equations??

    There isn't always one way to get the correct answer. Also, I have seen quite a bit of mistakes on that site.
  12. Re: Why am I struggling with Differential Equations??

    I've never known anybody having troubles in an ODE course if they were adequately prepared for it, it's pretty cut and dry algorithmic solutions and whatnot ... and if you did fine in calc 1-3 not sure what the problem would be ... linear algebra maybe? If that's the problem, then just start reviewing the most important computational sections of LA for ODEs (determinants, wronskian, eigenvalues/vectors).

    I guess some profs may put some 1st order problems on their exams that involve solving tricky integrals ... if that has been a problem, spend time reviewing integration by parts, trig substitutions, and partial fractions decomposition.

    Other than that, my best advice would be to make an outline for yourself ... maybe a page long on the categories of DEs (with examples) you're dealing with and then their solution methods. Examples:

    x^2y'=Ay >>>>>>>> separate to get x's on one side and y's on the other then integrate and solve for y.

    Ay'' + By' + Cy = 0 >>>>>>>>>> solve Ad^2 + Bd + C = 0 for d by factoring or quadratic formula, then putting the solutions into y=(c1)e^(d1)x + (c2)e^(d2)x ... or making whatever adjustments you need (like repeated roots, converting e^(a+bi) stuff into sin/cos, etc...)

    Ax^2y'' + Bxy' + Cy = 0 (cauchy-euler) >>>>>>> solved by y=x^p ... substituting, and solving for your p values.

    so yeah just do that for everything you've learned so you have a cheat sheet to use until it's all second nature.

    to make it second nature, just practice loads of problems, and try to do it randomly (possibly by having a friend pick problems for you from various sections of your book and writing them down for you to solve in a jumbled order), so you won't already know the solution method ahead of time due to the section of the book you're in (since all the problems in section 3.2 or whatever are the same solution method = just repeating the same thing over and over rather than having to analyze which solution method to use like you'll have to do on exams).
    Last edited: Mar 2, 2012
  13. Re: Why am I struggling with Differential Equations??

    It's true there is more than one way and there may be errors there, but I still maintain the sites helpfulness.
  14. Re: Why am I struggling with Differential Equations??

    I thought ODEs wasn't too bad but there were some tricky problems in the class. One of the problems was taking this higher order differential equation and turning into a 4 x 4 system of differential equations. That was tricky.
  15. psparky

    psparky 854
    Gold Member

    Re: Why am I struggling with Differential Equations??

    Diff EQ is one of your tougher courses in engineering.

    You are suppose to be struggling, therefore you are right on track. Congratulations.

    The only thing that is going to help you.....is hours and hours and hours of studying. There is no shortcut. Eventually, the bell will ring and you will pass a test. Keep in mind too....your fellow students are also struggling...you are not alone!
  16. Re: Why am I struggling with Differential Equations??

    I disagree--ODE is NOT one of the harder courses in engineering--did you have to do dynamics? Mass and heat transfer? Mechanical vibrations? ODE is a joke compared to those--IMO, of course.

    Hell--calculus 3 (for engineers, with all the application problems) was harder than ODE.
  17. psparky

    psparky 854
    Gold Member

    Re: Why am I struggling with Differential Equations??

    Difference of opinion. I thought dynamics was simple.....and I thought calc 3 was a cake walk because it was identical to calc II with just the extra z dimension that followed the same rules. Didn't take the other two because I'm an EE.

    Diff EQ is just tough because it's a different way of thinking.

    Just my opinion though.
  18. Re: Why am I struggling with Differential Equations??

    I agree Dynamics is not the hardest but it is harder than ODE simply because it involves thinking--ODE does not IMO. As someone pointed out--it's a cookbook type class. Oh--Bernoulli--apply method. Oh, Cauchy-Euler--apply method.

    Like you said--difference of opinion--I respect that.
  19. Re: Why am I struggling with Differential Equations??

    I blame the lecturer :D

    Well if you are taking a course and you usually do or did well in other courses even less advanced, then I definitely blame the instructor. I had a bad experience with some of the most beautiful topics in math to find out later it was not my fault or any student at the same class. It was the teacher who deliberately succeeded in making us hate the subject at that time. And he was enjoying it. It's not about bad teaching skills, it comes to the fact that some uni's try to make many student re-take the course so they can upgrade their marks., so simply it's $$$ matters. However I've encountered teachers with very bad teaching skills so we had to do much work on our end, but we did well because the teacher's intention was not to screw up students for whatever psycho-economic reasons. When the instructor lacks the teaching skills, then I'm with the argument that get a good mark and do it later yourself.
  20. Re: Why am I struggling with Differential Equations??

    lol, yeah. I struggled in almost every class I ever took in college because I specifically took the hardest courses my adviser would let me. If you're not struggling then you're not learning anything.

    Not really, I self studied some things the summer before I took it.

    I didn't mind the text although I would have preferred more insights into physics because DE's and physics go together so well but it is a math class. If I ever had a problem with the textbook I would be in the library searching for another book that would better explain whatever I was struggling with.
  21. mathwonk

    mathwonk 9,673
    Science Advisor
    Homework Helper

    Re: Why am I struggling with Differential Equations??

    I also struggled in an algorithmic ode class as my first math course after being out of school a year. I began supplementing the course with a schaum's outline series, and also going to the library for an hour after every class to review the notes. Finally at the end the class got less routine when the prof gave a proof of existence of solutions by the beautiful contraction mapping method. That even made it interesting. I went from a D to an A.

    Then when I taught it I tried to use more interesting books, like Martin Braun's well written book, supplemented by V. Arnol'd's book. The standard books like Boyce and diPrima really left me cold. Almost everyone agrees that he best, clearest book is probably the following one by Tenenbaum and Pollard. Try that one.


    Here is my review:

    10 of 10 people found the following review helpful
    5.0 out of 5 stars unique, March 28, 2006
    By mathwonk - See all my reviews
    This review is from: Ordinary Differential Equations (Dover Books on Mathematics) (Paperback)
    i discovered a "new" method of solving constant coeff linear ode's this semester while teaching the course, No one I asked knew it and no books had it, but it was so natural as to have no chance of being really new. Still I searched and searched, Courant, Loomis and Sternberg, Edwards Penney, Coddington, Braun, Dieudonne, without success. then I found it here on pages 268-292.

    i was impressed. this book was written back when clarity and completeness were the goal. then i began looking at the problems. it is very hard to give reasonable example problems using variation of parameters that cannot be solved better by guessing, but tenenbauim and pollard do it.

    this is a classic introductory text. they even define differentials correctly, almost unheard of in an elementary book. all this for only 16 bucks!
    Last edited: Mar 15, 2012
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