<p>Every Calculus course I have taken at Iowa State has always been like.. WTH? </p>
<p>Calculus I- Crappy professor, crappy TA- barely passed</p>
<p>Calculus II- All the naysayers told me to drop out of Engineering because I barely passed Calculus I.I did much better than Calculus I putting in about half the effort.</p>
<p>Calculus III- Chinese professor, I can't hardly understand what she says half of the time. She is obviously not dumb but she is very confusing and her hand writing, I swear to God, it is not English</p>
<p>I thought I had dot product down after taking Mechanics but last week, she confused me to the point that I had to teach myself vectors all over again.</p>
<p>We use Calculus- Verberg, Purcell, Rigdon 9th Edition which has been an almost worthless book for me(I think I paid 150 bucks for it). I guess, teaching myself Calculus III is the plan here since lectures are basically worthless.</p>
<p>Any suggestions on how I can self teach Calculus III would be appreciated!</p>
<p>Practice, practice, practice along with online videos. Calculus is half algebra and half remembering the steps it takes to get to the desired answer. I believe the students that do the best in these math classes do not rely on the instructor for help but prefer to teach themselves out of the book.</p>
<p>This is some pretty bad advice. If all you are doing is practicing with the goal of memorizing the steps it takes to get to a specific answer, you aren’t going to learn calculus very well. Sure, that approach may get you an A (or at least a passing grade) in some classes, but you are going to struggle later on when you try to apply it because you only know how to follow the recipe, not why those steps were important.</p>
<p>I’m not saying you need to know all the proofs and the like behind the math. You definitely need to know, however, that taking a gradient produces a vector with both the magnitude and direction of steepest rate of change of a function rather than just the fact that the next step of a process is to take a gradient. That’s just an example and there are many others, but the point is that memorizing steps and how to just barf out a calculation is probably enough to pass most calculus classes, but those who take that approach struggle later on much more often than those who actually understand what they are doing and why.</p>
<p>Do not listen to the nay-sayers: Math is important for engineering, but having issues is not the end of your career. I practically drove the struggle bus during Calculus 3-4, despite my AP credit. FYI, since we do terms Calculus 3/4 is basically the “normal” Calculus 2.</p>
<p>The saying I’ve heard is “Every engineer can do calculus, but none can do algebra.” Having good algebra skills come with time and are really, really great in simplifying a problem. In ODEs, it is needed to decompose fractions and sort of finagling an expression into a usable form. Understanding the theoretical part of mathematics is important, but as a ME I mostly use the practical side of mathematics. Double integrations, solving ODEs, etc,…</p>
<p>Bonehead, reread what you have just posted
<this is="" some="" pretty="" bad="" advice.="" if="" all="" you="" are="" doing="" practicing="" with="" the="" goal="" of="" memorizing="" steps="" it="" takes="" to="" get="" a="" specific="" answer,="" aren’t="" going="" learn="" calculus="" very="" well…=""> then you go on to say <i’m not="" saying="" you="" need="" to="" know="" all="" the="" proofs="" and="" like="" behind="" math.=""> It is contradicting…
Practice is how you come to understand each component of a problem. It how you learn to look for reoccurring tricks and methods all while strengthening your algebra skills. Then after you have built that foundation, comes the insight to be able to manipulate problems. Yes, proofs are just as important but Calculus is not a proof based class and you can continue on to higher math without even re deriving the Fundamental Theorem of Calculus. Keep in mind that there is only so much time in a day and you cannot focus on trivial things that will not be in higher math. I must add that its silly how you think people who take this approach and get As will not be able to apply it later on.</i’m></this></p>
<p>It was not at all contradicting. Maybe you should go back and reread what I posted. I basically said there is no need to go and take real analysis or anything like that where you go through the rigorous proofs which underlie calculus (or at least there is no need for probably 99.9% of engineers to take that). However, memorizing a step-by-step, cookbook solution to a problem without understanding why each of those steps is performed is not the right approach either.</p>
<p>The bottom line is that rote memorization is not the solution for understanding math. For the most part, yes, practice is essential to most people, and it is certainly important to actual go and do problems, but blindly practicing in order to memorize the steps and pattern match is silly and going to take a lot longer than if you you try to achieve a measure of understanding of why you perform each step.</p>
<p>The reason I say that people taking that approach often struggle to apply it later on is because they do struggle to apply it. They may be great at solving a problems in calculus class based on their memorized steps, but when they get to later engineering classes or the real world and have to translate an open-ended problem into mathematical statements and then solve the problem that rarely mirrors the book problems from calculus class, they struggle. I’ve watched them struggle as a peer, as a tutor, and as an instructor. But by all means, tell me I’m wrong.</p>
<p>And to those emphasizing algebra skills: I couldn’t agree more.</p>
<p>Here’s an example of what I am trying to describe:</p>
<p>I was teaching a course on compressible flow and gave a problem about air escaping a pressure vessel and determining how long until the pressure inside was half its original value. From the class, they knew that the mass flow rate depended on the pressure inside, so they should easily be able to figure out that it changed with time. The problem boiled down to a very simple equation:</p>
<p>dm/dt = C*m</p>
<p>where C was a constant, albeit a slightly messy one. If I just gave them that equation with initial conditions, I bet every one of them could just tell me the solution no problem. Unfortunately, many, if not most, had a hard time writing down that equation in the first place because they don’t recognize a derivative as a rate of change of some quantity and therefore have a hard time relating what they learned in calculus and differential equations to real-world problems. That comes from spending too much time memorizing steps instead of trying to understand what you are actually doing.</p>
<p>Thanks for your replies! I think I am going to buy the solutions manual and try to work out as many problems as possible. In the past, I have made my own “study guide” by rewriting the important concepts in the book, in a format that I can actually understand.</p>
<p>My professor is obsessed with proofs and last time, she spent 10 minutes showing us some geometric proof with vectors.</p>
<p>I swear, at the end, most people were like WTH? Especially, since her handwriting is bizarre, I think she probably gets Chinese characters and English letters mixed up, so sometimes vector “u” looks like a squiggle that I can’t really understand.</p>
<p>I had a professor who was Greek who would spontaneously start writing in Greek characters on the board from time to time before catching himself. He was a really good professor though so mostly people just laughed.</p>
<p>In all seriousness, though, you have the drive to will yourself to succeed, that much is pretty clear. Just stick with it and try to work smart so you don’t have to work too hard.</p>
<p>Ditto what Boneh3ad said. That’s true of any discipline. Having a professor with poor communication skills (if that’s the real problem) doesn’t help, but you’ve got to grab the bull by the horns.</p>
<p>I’ve been a fan of Stewart’s Concepts and Contexts Calculus 4th ed. book whenever I’ve had to review a concept from the calc 1-3 series. I believe a digital copy is even available and the solutions manual isn’t too much money. I never appreciated his examples until I saw Zill’s ODE book or even worse Lay’s Linear Algebra book.</p>
<p>One of the greatest skills in life…education, business, whathaveyou…is to assess what information, assistance, and cooperation you are going to get from those you’re working with (instructor, boss, team members), and move ahead to determine how you are going to obtain the rest of the information or materials needed to succeed. The only variable here is you. The instructor isn’t going to change. So, find another text as a resource, online resources or tutorials, a study group, see your TA, a tutor if it comes down to it. Whatever works for you.</p>
<p>To teach yourself Calculus III:
Find good practice problems and give yourself an overview on how to approach them.
Then you hold yourself accountable to doing them over and over until you get the correct answer. Try variations to the problem and see how your work turns out.</p>
<p>Calculus III is in good part understanding the concepts behind what you’re doing and the work to solve the problem flows naturally with it–so flip back to the book’s explanation and it’ll give you good insights.</p>
<p>P.S. Someone said engineers can’t do algebra… I laugh, because it actually is somewhat true for me. That’s why DE’s was a pain to get an A in / it was much more of a steps to take based class over a concepts based class in which you make so many dumb mistakes and have to use memory quite a bit ;)</p>