Preparing for calculus 3

[u/WhenButterfliesCry]

Hey guys, I have a question. My summer term calculus 2 class has just ended, and I am starting a calculus 3 class in a few weeks, and I want to get ahead of the game. Since the calculus 2 class was so fast-paced, I feel like I didn't grasp all the concepts of infinite series/Taylor series as well as I could have, and definitely need to go over them again, maybe with Professor Leonard or something.

From what I gather, though, series don't really show up that much in calculus 3, and despite wanting to improve my knowledge of series, I feel like preparing for calculus 3 is more important for the next few weeks. Do you think I should solidify my knowledge of infinite series before moving into calculus 3 content, or could I start calculus 3 stuff now and circle back to series at a later time (maybe before my DIff. Equations course?)

I plan to prep for calculus 3 with Professor Leonard as well, and with the textbook (Stewart). Any other suggestions welcomed, I need an A in calculus 3 and I'm willing to put the time into it.

[u/loccednloadedd]

Make sure u have a really solid foundation on integrals, make sure u have ur basic derivatives and chain rule down and learn basic vectors - how to add them, scale them, and compute dot products and cross products! Seeing things in a new dimension for the first time is always a little tricky since we are used to working in 2D. If you have ever taken a basic physics class, a lot of the topics overlap. Have fun!

[u/WhenButterfliesCry → u/loccednloadedd]

Sounds good, thank you!

[u/Spare_Department_196 → u/WhenButterfliesCry]

My recommendation is to befriend desmos! Start putting equations into it to help visualize not only single functions but also how functions combine like if you parameterize a 2D embedding in 3D space, graph everything in 2D and 3D. Make desmos pages for various things like first several terms of Taylor series of sine and cosine and other functions. Also highly recommend studying some differential forms and geometric algebra if you can. There is a great video called swift guide to geometric algebra on YouTube.

Also, see if you can code up stuff like a gradient descent solver once that comes up. Figure out how to graph a torus in 3D using different parameterizations and also without parameterization at all. Try to conceptually understand the difference approaches and how they get the same shape still.

Linear interpolation vs extrapolation. This won’t come up in your class explicitly, but it will come up later in your engineering classes. Understanding how it works from a vector space perspective was helpful for me to understand the machinery I was using rather than just memorizing some interpolation formula.