<p>So i'm possibly going to be a math major and I have been debating whether or not I should take Calculus II or Calculus III first semester. </p>
<p>I received a 5 on the AP Calculus BC exam, so supposedly I'm prepared to take Calc III I believe. But i've heard from some people that Calc III is extremely difficult and that you should take Calc II at the college because AP Calc BC doesn't prepare you well enough. </p>
<p>I've also heard the complete opposite that BC prepares you just fine. </p>
<p>I'm just curious to see what the misc thinks. I'm on a full ride so I'm not paying for classes.</p>
<p>I just don't want to waste my time nor do I want to get in over my head.</p>
<p>No, if you want to be a math major you are ready for Calc III. My brother is an engineering major and he skipped right to Calc III with a 4 on AP Calc BC and thought it was easy. My other brother is a CS major and he is going right to calc III. Don’t bother taking it, it would just be a waste of time.</p>
<p>1) limits – if you understand why the epsilon-delta definition is crafted like it is (actually doing the proofs isn’t a useful skill for the calculus series but will be useful in your later math classes), then you understand limits well enough</p>
<p>2) derivatives – if you know the derivative as f’(x) = lim h->0 [f(x+h)-f(x)]/h and can see why it gets you all the other things you know about the derivative, then you understand derivatives</p>
<p>3) integrals – integration is pretty technical actually and knowing the details is beyond the level of the calculus series, but it is good enough to know that integration is
the limit as the partition gets finer and finer of the riemann sum
different than finding antiderivatives of functions – however a theorem tells you that you can play that game of finding antiderivatives to integrate functions</p>
<p>anyone critique me on my understanding (or lack thereof) of these topics.</p>
<ol>
<li><p>The purpose of epsilon delta proofs is pretty much to show that if you’re given a limit and some boundary epsilon, the distance from the actual value and the limit can be reached for an x-value chosen within the boundary x-a or x+a?</p></li>
<li><p>I think of it like physics. on a Displacement (x) vs. Time (t) graph, when delta T goes to zero, a tangent line showing the local behavior of position at that given time is displayed. This is velocity, the derivative of displacement, and a derivative basically shows how a function is changing at a specific value for t.</p></li>
<li><p>Integration is basically the limit of a riemann sum as n (number of partitions) goes to infinite and/or lim of a riemann sum as delta X becomes zero. As N increases, the delta x becomes smaller and smaller giving for a more accurate “area beneath the graph” of the function.</p></li>
</ol>
<p>I personally always liked to think of integration as basically multiplication of changing quantities / quantities that are not constant.</p>
<p>Calling it the limit of a sum/area under a curve is cool too though. I always see people calling it that on this board, but the multiplication thing was a good aha moment for me in calculus and I’ve never seen it mentioned that way on this board.</p>