Turndown375 wrote:
Prometheus18 wrote:
Turndown375 wrote:
Prometheus18 wrote:
What is it, specifically, that you struggle with about calculus? The central idea in calculus is the infinitesimal limit; once you've spent a large amount of time meditating on this idea, maybe things will fall into place.
Pretty much everything gives me trouble if I’m being honest. I was able to occasionally do some basic limits and derivatives last semester but that’s about it. I don’t seem to be able to retain anything number related whether it’s complex stuff or basic dates. Any time a fraction is introduced, or letters (especially Greek letters) I get completely lost.
Do you understand the concept of slope when it comes to linear equations (y = mx + c)? If so, it may be helpful to just view differentiation as a generalisation of this principle. The derivative of a function is basically just its slope at any given point, assuming that it's perfectly linear at that point. Once you've mastered differential calculus, integral calculus comes at once.
I don't understand why you'd be using Greek letters for elementary calculus, with the possible exception of theta (θ), but maybe it would help to learn the Greek alphabet by heart? You don't seem to have impaired linguistic ability, so this shouldn't be a problem. It helps to emphasize the fact that letters simply serve as placeholders in mathematics. Maybe revisiting the elements of algebra would help with this (things like solving 3x + 2 = 17 for x). Fractions, of course, are just division and should be viewed as such.
It might help if you presented one of your calculus problems to us, from a textbook, along with your attempts at an answer; we might then get a better idea as to where you're going wrong.
I understand that slope measures the rise/run on a graph but im not sure what else that means exactly. I know we have used greek letters for summation, theta is obviously used, and in Physics we use quite a bit of greek letters in various equations. For the most part I understand what the summation is asking for, but when there are other letters and numbers placed ontop or below thats when things go haywire because there are so many letters and numbers to keep track of.
Basic linear stuff like solving for x I'm usually okay with, but again when there are frctions or radicals my knowledge of what to donext dissipates. I have a packet I'm currently attempting to work on in preparation for an exam in the morning tomorrow so I'll try to get a photo uploaded here after breakfast.
The concept of slope is useful because it tells you
how quantities change; it's difficult to see this on a graph of y against x, because there's no physically useful interpretation, but it becomes apparent when talking about distance (usually x) against time (usually t). For instance, everybody knows that speed is distance divided by time (miles per hour, metres per second, etc.) And this is easy to read off a linear graph of distance against time (x = mt + c), where speed is just the slope of the graph or m (change in distance over change in time), but when you have a nonlinear function of time (for instance, x = mt²), it's impossible to just divide change in distance by change in time because there is no one answer, but rather, we must "zoom in" to the graph until we get to a point where it is approximately a straight line - at this point, the same way of talking about speed as for a linear graph applies. This is one of the immediate uses of the derivative, which is a technical way of talking about "zooming in" to a graph. The derivative of mt² with respect to t is 2mt, so that we now have a function which will tell us the speed of the particle with the trajectory x = mt² at any point in time.
As for summation, just worry about one thing at a time: the most important part of the summation notation is the expression right of the sigma sign (Σ); given an expression like (a trivial example) Σn² with 3 above the sign and 1 below it, just focus on one term at a time. We start with 1, so work that out (1² = 1), writing it down if necessary, then check the indices around sigma again (2² = 4) and it's not too difficult, if you don't worry about other information unnecessarily, to get the answer (14).
10 Feb 2019, 9:40 am
