<p>So I’m teaching myself multivariable calculus over the break. The thing is, I can’t visualize a function such as z = 4x+10y and then integrate it over the function x^2-x frex from 1 to 2. Is this a problem that almost everyone else has? And do I really have to visualize triple integrals to do them? They need even more visualization to plot the points and I’m getting rather concerned.</p>
<p>in other words, is multivariable calculus most difficult due to the visualization required or not?</p>
<p><a href=“http://epgy.stanford.edu/courses/math/M115/M115lecture.html[/url]”>http://epgy.stanford.edu/courses/math/M115/M115lecture.html</a></p>
<p>Damn, this is good… Makes me want to drop out of college and take Stanford EPGy courses.</p>
<p>You don’t generally have to visualize them to do them as you should generally be able to algebraically solve for whatver boundary points you might need that you’re not already given, but if you need to, there’s always Mathematica. But a little common sense will generally do it. In this case, your first function is defining a plane, and the other two are defining bounds in the xy plane (under or over the first plane) which define the three dimensional region which you are finding the volume of, so to speak, by integrating.</p>
<p>And the first plane is oftentimes (in the introductory level) defined by z=0, when z = f(x,y), correct?</p>
<p>Ah yes, I have to learn to use Mathematica</p>
<p>Yes, that is your basic xy plane.</p>