<p>Calc I and III were the easiest. Calc II was the hardest (all of those physics applications are pretty tough for a computer science major and math minor). I'm currently taking Calc IV, which seems very easy so far (I'm currently at partial differentiation and the applications of it, such as extrema points).</p>
<p>What did the links you provided have to do with what we are talking about? I read the wikipedia and skimmed the other one but I wasn't quite sure what your point was. No one ever said that you can't have 5D systems. We said the one you talked about wasn't 5D.</p>
<p>Let me put it this way. Without getting pedantic, something (well, technically, a manifold) is n-dimensional if at any point you can "wiggle" a little bit in n different directions, and still end up with a valid point. If you're given a 5-tuple (t, x, y, z, f(x, y, z)), then you can definitely "wiggle" a little bit in the x, y, z, and t directions. But can you "wiggle" in the f "dimension"? Not really, because that would necessitate that the values of x, y, z or t need to change as well. So you're not really "wiggling" in another direction because in order to go that "direction", you need to move a little in the other dimensions as well.</p>
<p>consider a semicircle. Any semicircle, say the unit semicircle, is one dimensional and given by (x, f(x)) where f(x) = sqrt(1-x^2). At any point we can wiggle a bit along the tangent line and still stay on the semicircle. however, it is not possible to wiggle radially (towards the center) because we would leave the set of points defining the semicircle.</p>
<p>you can still "wiggle" because fields are continuous and therefore there are isopotential families for any given field. because of this, the orthogonal projections represent lines that you can "wiggle" across, even if they are spatially and time dependent.</p>
<p>I get what you're saying about the dependence on other variables but I guess our definitions are slightly different.</p>
<p>Looking at it from an engineering perspective, it is more beneficial to see the problem in 5D for practical purposes. But since when did engineers care about mathematical rigor? :)</p>
<p>To linguae,
At Cal poly there are actually 5 calculus courses…
Calc 1 = differentials
Calc 2 = integration
Calc 3 = Taylor series and such
Calc 4 = partial differentials and applications using contour maps
Calc 5 = double and triple integrals,greens theorem, the curl n such</p>
<p>The whole calculus series gets easy after calc2 then it just starts to get easier</p>
<p>Calc III without a doubt was the hardest for me. Followed by Calc II. I think it was really the teacher’s fault as he basically just went through the problems in class. I would have rather have had a lecture about the concepts of what we were doing. </p>
<p><em>sigh</em> perhaps I should retake the class… soon, before I forget my calculus skills. And this time research on the prof. who teaches the class.</p>
<ol>
<li>Differential- Hard Hard Hard Hard. I got a 38% on an exam where the avg was a 40% </li>
<li>Integral- Cake minus the notion of work. </li>
<li>Sequences and Series- Easy if you love theortical math and proofs</li>
<li>Multivariable- Abstract theory easy class if you can handle 3-D. </li>
</ol>
<p>That’s strange. My high school calculus actually incorporated your Calc 1,2,3. I didn’t take calc 1,2 in college because I got credits for it so I don’t know what’s it’s like. Then Multivariable calc or Calc3 is your Calc 4,5. Why is divided into 5 separate classes for 5 semesters?</p>
<p>I’m on quarters too. If it takes one five classes to do it. It’s probably not worth it. Quarters are awesome 10 weeks of hell only to never see the material again.</p>
<p>Calc I: differentials and beginning integrals (rotational solids)
Calc II: techniques of integration, polar coordinates, sequences and series
Calc III: multivariate Calc</p>
<p>Calc I is a bear here. They don’t make it easy. They offer a “NC” because the passing rate is less than 50%. They purposely make it hard to “weed out” prospective engineering/math/cs majors. It’s a big state U, so they need to do that.</p>
<p>Calc II was difficult at first. Lots of trig integrals. I found polar coordinates and series to be quite easy.</p>
<p>I’m starting Calc III next week…I’ll see how it goes.</p>
<p>But in general, where you take your Calc sequence does matter. Some schools make it difficult. We aren’t allowed graphing calculators. We aren’t allow integration tables and formulas. Memorizing integration tables sucks.</p>
<p>You shouldn’t be allowed tables or formulas but I think you should be allowed calculators. Don’t memorize a table, learn the technique then apply it. But think you should be allowed graphing calculators. </p>
<p>Idk why people think calculus is heard. Honestly it’s a gift to people GPA and it can’t be that bad. </p>
<p>If you do have a calculator and wanna learn a cheat check this out. </p>
<p>If you wanna find the area under the curve from any point a to b it’s simple to do. This is helpful at times when you want to check your answer or want to find the moment under a shear diagram, impulse and etc. </p>
<p>If your working with a Ti-83 Hit math 9 you will see mathf(</p>
<p>first type your functions
then the variable it is respect to
the the bounds </p>
<p>i.e.
1.f(x)=3x^2
2.x
3.-4
4. 4</p>
<p>So put this in your calculator then hit enter. The answer should be obvious that it’s 0. </p>
<p>mathf((3x^2),x,-4,4)=0</p>
<p>This is a clear example why people like me shouldn’t be allowed graphing calculators. Muahahhahahaha</p>
<p>I think my main point is that Calc can be quite different from school to school depending on the setup, difficulty of the tests and tools allowed (graphing calculators/integral tables).</p>
<p>Kids in my Calc 1 class that had taken AP calculus were failing left and right because of the difficultly of the tests. 50% failed the class. I know of only 1 person that barely got an A. No curves, no extra credit. Just do it.</p>
<p>Not all Calculus classes are created equal.</p>
<p>FWIW, the difficultly of my school’s calculus sequence makes me a much better student.</p>