![]() ![]() Helped me, although not really sure why or how exactly this helped me learn to visualize in 3D). Btw, a good starting place is drawing stuff out for every problem until eventually you don’t need to draw it anymore. For me, my biggest issue was visualization in 3D but after a couple of weeks of intense studying (and training myself to visualize in 3D. Calc 3 is really just calc 1 and calc 2 but in three dimensions. I feel like the issues with calc 2 come from people having to learn the material for conceptual understanding alongside drilling problems to “sear” integration techniques and certain patterns into their brain (so when they look at an integral they immediately know how to solve it, in an algorithmic sense). Then, when you get to integration in calc 2, this is not just new territory conceptually speaking for most people, but also requires a much more rigorous treatment/approach since integration is usually more about finding a way to express the function you wish to integrate in a particular way that allows it to be integrated (lol that sounds stupid but hope you know what I am trying to say there). The mathematical rigor of calc 1 is fairly easy though and it’s difficulties are usually mostly conceptual imo. Once this conceptual hurdle is overcome, it becomes very straightforward and even fun to tackle problems with calculus as it is very versatile in many applications and can allow one to solve a problem uses many different approaches. I feel like calc 1’s difficulties are due to having to think about things in a different, more abstract way then in prerequisite math classes. I thought calc 2 was harder personally and calc 1 was on par with calc 2 in my opinion (they are all easy in hindsight but of course it wasn’t this way when I was first learning them). So why do people actually think calc 2 is harder? I just don’t get it. I went to my professor’s office hours, I studied weeks in advance, and still bombed my exams. ![]() I literally studied way more for calc 3 than calc 2 and still ended up failing. But for calc 3, you have to be able to know how to visualize a function in 3d space, how to graph it, and how those graphs relate to whatever you’re learning. The way I see it, calc 2 is more integration based, if you keep practicing integrals over and over you will succeed. Now I most likely am going to end up with a D and having to retake it. There’s so much stuff to remember that it was difficult for me to master a concept, and trying to visualize functions in 3 dimensional space is something I am absolutely terrible at. But for calc 3 I feel like it’s different. I got an A in calc 2, and I had to work my ass off for it practicing problems over and over again. Seriously, I went into calc 3 thinking it was going to be a breeze after calc 2 but boy was I wrong.
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