<p>Self studying BC, pretty much got everything down except differential equations.</p>
<p>Pretty much all I know:
-general solution: dx/dt = t^4 - t^3 + C
-particular solution: if x(0) = 3, x(t) = t^4 - t^3 + 3
-slope fields: graph of possible general solutions.</p>
<p>Questions:
-What do I need to know for calculations like in Euler's method?
Example 6, Chapter 9, Barron's: Let dy/dx = 3/x. Use Euler's method to approximate the y-values with four steps, starting at point P*(1,0) and letting ▲x = 0.5. *= naught, subscript 0.
What are they talking about with naughts and ▲x? I know what they mean but how do they relate?</p>
<p>-Can you outline Diff EQ's in simple terms? Like how I wrote "pretty much all I know" above. Topics covered in Barrons under Diff EQ's include: Euler's method, solving first-order diff eq's analytically, and exponential growth and decay.</p>
<p>For eulers method, its basically taking the tangent line at different steps. Say you want to approximate f(2) but you only have the point f(0) and f`(0). Instead of using the f(0) tangent line and plugging in 2, (which will give you large error), you use the f(0) tangent line to approximate f(.5) and then use the tangent line of f(.5) to approximate f(1) and then use the tangent line of f(1) to approximate f(1.5) and use the tangent line of f(1.5) to approximate f(2). This will give you an approximation with less error. As this shows, the step size was .5 (the different between each step, 0,.5,1,1.5,2 and there were 4 “steps”).</p>
<p>dunno about the others, im pretty tired right now -_-</p>
<p>Step size is dx AND how much the x (NOT dx) changes from step 1 to step 2 to step 3 to how many you need. I think this answers your question where you have delta x.</p>
<p>The x and y values from each row can be plugged into to determine how much y changes into the next step.</p>
<p>Ask back if you need more help I’m tired too I’m watching Mavs vs Spurs playoffs. It was a confusing topic to me at first.</p>
<p>There is sometimes an FRQ or a MC question on logistic differential equations. The questions that they ask are pretty predictable; I think that everything posted on that page on logistic diff. eqns covers pretty much everything that would be asked on the AP exam.</p>
<p>The Euler’s Method on the exams are tougher than it is on the prepbooks, you have to figure out your own step-size. But you just take the average</p>
<p>Alright, thanks a bunch for all the replies.</p>
<p>I understand the question now, I was just a bit intimidated by the symbols.</p>
<p>Oh and Barron’s does give a table:
Psub# | x | y| (SLOPE) x (0.5) = ▲y | TRUE y
P0: 1 | 0 | (3/1) x (0.5) = 1.5 | 0
P1: 1.5 | 1.5 | (3/1.5) x (0.5) = 1.0 | 1.216
etc. to P4 –> 3.296</p>
<p>Ah this makes so much more sense! But question - since they give us P0 (1,0), this is the graph of a particular solution, right? Had there been no known points, it would just be a slope field? Also, how do they get the TRUE y value?</p>
<p>Edit: And why can we assume dy = ▲y and same for x?</p>