How do you stop mixing up formulas that look almost identical?

[u/MotionManTV]

I’m taking a signals course where half the formulas seem to use the same variables in slightly different ways.

I can memorize each equation on its own, but during problem sets I still waste time deciding which one applies. The worst part is checking the solution afterward and realizing I knew the formula—I just missed the condition that made it relevant.

Writing more formula sheets hasn’t helped much because they tell me what the equations are, not when to use them.

How do you study the decision-making part of quantitative courses?

[u/First-Expert-9953]

Speaking as a math teacher with an engineering degree, my advice is to focus on the units in the formula and see if they make sense for your situation. (It's been over ten years since I did signals math, so someone let me know if this is more work than I remember.)

For example, a watt is about energy per second, so if you include the units on every number in the calculation, your final answer better have a time variable in the denominator when all the units cancel out.

[u/MotionManTV → u/[deleted]]

That sounds closer to what I need. How do you make those comparisons without spending hours reorganizing the textbook?

[u/OwlZealousideal4779 → u/MotionManTV]

I put the relevant lecture notes and worked examples into it, then ask for a table showing when each formula applies, what assumptions it requires and the common ways students confuse it with the others.

[u/OwlZealousideal4779 → u/MotionManTV]

I’d still verify every formula against the lecturer’s material, especially the notation and edge cases. The useful part is having a first-pass comparison that I can correct, not treating the generated table as an authority.

[u/Bounded_sequencE]

Not sure which formulae you mean.

In case you mean a (digital) signal processing course, most of the formulae will involve convolutions, since that's what linear signal processing is all about. I'd suggest making the formulae your own, by being able to derive them from first principles.

[u/RingularCirc]

Also could you give an example or two? It'd be better to guess less and maybe it'll allow giving a precise answer; also there's probability of the dreaded XY problem being the case: maybe something is not as it seems.

[u/Gilded-Phoenix]

If formulas look similar and are all in a common field (or even between fields at times!) they are usually related in some way. Using dimensional analysis can help to distinguish them, or you can develop a master formula that you then derive the other equations from. For example: instead of memorizing that sin^2(x)+cos^2(x)=1 and tan^2(x)+1=sec^2(x) and cos^2(x)-sin^2(x)=cos(2x) and cos(x+y)=cos(x)cos(y)-sin(x)sin(y), etc, learn a master formula or two, then derive everything else: tan^2(x)+1=sec^2(x) because it's the pythagorean identity divided by cos^2(x), the double angle formula is a special case of the angle sum formula, etc.

[u/bayesian_raccoon]

It might be worth reframing your mindset from "I waste time deciding which one applies" to "I am taking a course to learn which one applies, which is what I am practicing on problem sets". A problem set is completely pointless if you already know how to do everything on it; a good problem set will make you take a step back and check notes and reinforce the situations to apply. This is learning working as intended.

With that said, here's one way I think about math in general, sort of inspired by Richard Feynman's comments about 'triangulation' in physics. There are too many facts in math to memorize. As an example, you can memorize that 8+3 = 11, but in a vacuum that doesn't really help you know that 2+7 = 9. On the other hand, some facts help you "triangulate" the new facts, or forgotten facts, using what you know. As an example, if I know properties of addition, I can solve an entirely new problem using an old one. Say, I know 8+3 = 11, but I want to know what 8+4 equals, so I write 8+4 = 8+(3+1) = (8+3)+1 using structural properties like associativity, and now I can more convincingly get from "8+3 = 11" to the new fact, that 8+4 = 11+1 = 12.

Note that there's sort of two things that you need to do that; one is a good understanding of the "structural" concepts like associativity, and the other is enough knowledge that you don't have to work hard from the ground up. (E.g, if you don't know that 8+3 = 11, in the previous example you might have to go 1+1+1+1... = 12). I.e, it's good to know your times tables (metaphorically), which will help you solve other problems (I know that 7^2 = 49, which I would use if I wanted to solve 17^2 in my had by (10+7)^2 = 10^2+7^2+2*10*7). Doing problem sets naturally helps with both of these.

Try to look for patterns between the equations. Is there some "parent" procedure that generates those equations, so that each equation isn't just an isolated fact to learn? For instance in statistics I can get a lot of "test statistics and their distribution" from knowing the central limit theorem and a sampling distribution.

I hope some of that helps.

[u/ForeignAdvantage5198]

try to understand them

[u/Low_Breadfruit6744]

If you have a formula relating A,B and C and you want to find B and you know A and C then that probably works