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Difficult becomes Easy?

  1. Mar 27, 2007 #1
    Do you guys find that skills you may have been weaker in in early classes are more greatly developed in future classes? For example, if you have trouble grasping concepts in trig or calculus, do you master those as you go along in later classes to the point where they become second nature?
  2. jcsd
  3. Mar 27, 2007 #2


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    I found that it does happen. I had a hard time solving related rates and things like that, and now it's basically second nature. Same with solving some integrals although lots are still hard, but a lot of the ones in the past can be done in your head sometimes.
  4. Mar 28, 2007 #3
    Yes, that is how I have always learned. For example, takings circuits and having to analyze them without any prior E&M exposure (which was a prerequisite, I took it concurrently) was challenging at first, but then before I knew it I was studying AC power analysis and second order equations were cake even though I had never been formally trained to solve them. Heck, I had a lot of trouble in the beginning just dealing with Kirchoff's rules, but it all became intuitive.

    That is usually how I motivate myself to learn, though. I realize how difficult the material is at the time and how little I understand it. Then I realize that in a week or two it wont be so bad and by the end of the quarter I will not have to think twice in order to use the material. I also like to open my textbooks and see how difficult they appear to be in the later chapters, all the while happy that that material will soon be under my control.

  5. Mar 28, 2007 #4
    Yes. This constantly happens. In general, whenever one goes further into a subject, and returns to the basics, he/she discovers a better understanding of the basics.
  6. Mar 28, 2007 #5
    The really important stuff keeps popping up over and over again.
  7. Mar 28, 2007 #6
    Yes, I've definitely gotten better at basic physics as I've gotten into more advanced material for my physics major. Maybe that's because advanced physics really just builds on the fundamental principles. It seems to me that all of the physics you'll ever learn, you learn in your first two years. There's really no new physics in advanced classical mechanics or statistical mechanics, just more mathematically advanced techniques. So I guess you're bound to master projectile motion in the process of learning the new stuff.

    My experience was quite similar in math. I feel that I have a very in depth understanding of the concepts I learned in the first four semesters of calculus. But strangely enough, this is probably because I didn't take my math major too seriously. To quote my math advisor: "Arun, the reason you're getting good grades in math is because you take weak classes...at this rate you aren't going to get into graduate school." (little did he or I know that I'd end up going to grad school for physics instead of math). While all my peers were taking rigorous analysis and topology, I took advanced calculus, applied linear algebra, and complex analysis. So while all the other math majors were learning about important topics in mathematics, I was basically taking "calculus I for juniors."

    Oh, and I also tutored physics and math my last year and a half of college. I'd recommend this to everyone; being forced to explain this stuff to others really gives you a special insight.
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