Help Creating ODE Winter Break Study Schedule

[median ether]

My teacher had anyone who didn't do "great" (like less than 75%?) make a study doc. This works best with a lot of students, but what they'd do is have students make a google doc with all of the chapter/unit's content, plus some problems, and he'd proof it. If you have some friends/want to make some, this seemed to work!

[fleet mango]

what were your weaknesses in the calculus fundamentals?

[timber reef]

My basic calculus skills are lacking. I freeze up taking basic derivatives and integrals, and I often forget important identities, like Euler's identity and the Half Angle Formulas for Sine and Cosine. I do not want to memorize these formulas, but understand where they come from, how they work, and have a basic understanding as to deriving them with my math fundamentals. I also struggled writing the series solutions to differential equations, and with problems that required iterative problem solving in general (repeating the same step many times in one problem). I believe this to stem from my lack of understanding on the following:

Trig Functions, (their integrals, derivatives, graphs, origin*(not in the math sense), inverses, everything)

Series, (power, maclaurin, taylor, especially fourier series and the heat equation)

Recognizing the situations in which certain first order differential equation methods need in order to be solved

The concepts (we have the solutions to a differential equation when we can solve every initial value problem, why? what role does the wronskian play, etc.)

I prompted Gemini with this to help me make a schedule

I just wanted to think on it/discuss it a lil more before I commit to it

[fleet mango]

theres actually a huge underappreciated build up to odes that i can recommend if u have time but it will take a lot of time

when does ur spring sem start

also what did gemini suggest? maybe we can go off of that

[timber reef]

I'd love that

[timber reef]

My spring semester starts January 25th

[fleet mango]

deriving an identity for 3 days is crazy work

i recommend skimming through stewart calculus 9th edition (or whatever edition u want)

chapters 1-11

u can skip 2, 6, 8, and 10

11 will be very important

then id suggest reading boyce for odes

chapters 1-7

for this, there is no skipping, all of it is quite fundamental

but perhaps the most important part is chapters 1-5

make sure to focus more on solving practice problems than spending too much time on reading

i think 1 chapter every 2 days should be doable

[timber reef]

Lol those are both of the textbooks we use in our courses

[fleet mango]

yeah theyre quite common for a good reason

[timber reef]

Was this the long build up you mentioned?

[fleet mango]

https://youtu.be/5zi5eG5Ui-Y
you can also go through this video if u feel really uncomfortable with trig

but the main gist is just the book chapters, yeah

[timber reef]

beautiful thats exactly what I was looking to do

[timber reef]

I realized just how little of trig I understood when Fourier series hit, that and the reoccurrence of integrals like 1/1+x dx

My biggest conceptual holes are trig and the idea of a differential equation. Derivatives make sense, but equations involving them makes a lil less sense, conceptually/in plain English.

[fleet mango]

3b1b has great videos on differential equations, those might help with the "big picture" of DEs

but they are in no way a replacement for practice problems

[timber reef]

yeah I’ve tried looking at them and I haven’t done/thought critically about enough to really grasp them

[timber reef]

Thank you both! Are either of you active in the #odes-and-pdes channel and if so can I keep you guys posted on how it goes?

[fleet mango]

i do breeze through #odes-and-pdes every now and then

u can definitely keep me posted there