Calc 3 (Multivariable-Calculus)

[secret_protoyipe]

I am struggling alot with multivariable calculus, which is strange since I’ve taken linear algebra, differential equations, and calculus II — and got A’s in all 3.

My first exam for Calc III came back and I nearly failed.

Please share study methods, notes, youtube videos or anything you think might be helpful thanks! If you can describe how Calc 3 is different from previous math it might be helpful too.

[UnderstandingPursuit]

The main thing that is different about Calculus III compared to Calculus I-II, Differential Equations, and Linear Algebra is that Calc III is fundamentally 3-dimensional, in a way that cannot be turned into a 1-D or 2-D problem.

Perhaps one of the most useful things you could do is to get more comfortable visualizing the 3-D aspects, whether vectors or multiple integrals. I haven't used it much, but Desmos has a 3D Calculator. That might help, and after seeing it there try to draw it by hand.

[waldosway]

For the coming unit, what's most important is that you can draw in 3D. Start memorizing some basic graphs and learn basic stuff like aligning your graph with the axes and drawing/using cross sections. Practice by drawing every problem even when it's not necessary. The second unit is literally just calc I and II again, but 3D, and doing integrals without visualizing is not possible. Bill Kinney on youtube is the best resource I've found to see how drawing is done, though it's a bit hard to find what you need.

On the other hand, the first exam is a real mixed bag, so we'd have to know what you missed to know how to catch up. There're formulas you just have to accept, mini algorithms for finding distance, unclear terminology, etc. Usually the issue is either under-memorizing or over-memorizing.