tag:blogger.com,1999:blog-7691251033406320222.post2399186738208964613..comments2024-03-26T04:19:38.862-07:00Comments on kitchen table math, the sequel: lsquared on what you must know to take calculusCatherine Johnsonhttp://www.blogger.com/profile/03347093496361370174noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-7691251033406320222.post-31641228268792738242011-05-25T18:20:14.460-07:002011-05-25T18:20:14.460-07:00Allison added "to get that, you need to under...Allison added "to get that, you need to understand limits and you need to understand trig."<br /><br />As a calculus teacher, I expect the students to come in knowing trig, but I don't expect them coming in knowing anything about limits. I agree that they make infinite series make more sense, but, again, I expect them to come in knowing how to work with finite series, but not infinite series. Teaching limits (and infinite series) is part of my job in teaching calculus. Thus, if you wish to learn limits in pre-calculus, that's fine (and if it is done in the pre-calculus C took, then you probably should--it may be part of the expectations for calculus at your school), but if a student turns up in my calculus class never having heard of a limit before, it's not a problem: I have 2-3 weeks built into my syllabus to teach them what they need to know about limits. If, on the other hand, they come in not knowing trig, they are up a creek without a paddle, because I don't have enough time to also bring them up to speed on the trig they don't know.LSquared32https://www.blogger.com/profile/00858524638866166691noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-76469812646465978112011-05-24T20:12:15.332-07:002011-05-24T20:12:15.332-07:00In addition to Lsquared's suggestions, I'd...In addition to Lsquared's suggestions, I'd add a bit of motivation: there are two ways to understand derivative calculus. Derivative calculus is understood by seeing how a certain function works in a given limit, or derivative calculus is understood in terms of how a certain trigonometric function works.<br /><br />So, to get that, you need to understand limits and you need to understand trig.<br /><br />Demoivre's Theorem is usually part of a precalculus class. Understanding why it's true is usually not something students learn, but they do learn the formula. Ideally, you'd like a teacher who knew the formula and knew why it was true. In fact, if I were interviewing a potential precalc teacher, I'd ask them to tell me what Demoivre's theorem was and what it meant.<br /><br />Before you get to sequences and series, you must be taught limits. Limits are really the bread and butter of understanding derivative and integral calculus. Sequences and series make sense only after limits make sense. Understanding convergence and divergence is critical to being prepared for calc.<br /><br />Properly knowing how to find the limit of a polynomial or trig function requires mastery of the underlying algebra and trig. If you really don't understand polynomials, you will have a hard time with limits, sequences, and series.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-49313971107581439382011-05-24T18:58:25.868-07:002011-05-24T18:58:25.868-07:00EPGY has placement tests for math from algebra thr...EPGY has placement tests for math from algebra through calculus at http://epgy.stanford.edu/applyandregister/upexam.html .Bostoniannoreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-51379697445051773242011-05-24T18:54:34.525-07:002011-05-24T18:54:34.525-07:00I wonder if some basic complex analysis should be ...I wonder if some basic complex analysis should be taught concurrently with trigonometry, so that formulas such as that for cos(2x) can be derived from Euler's formula,<br /><br />exp(ix) = cos(x) + i*sin(x)Bostoniannoreply@blogger.com