Limiting the discussion

June 10, 2006

A message last night from a friend pointed out that this chapter may contain too much and might be unfocused. It was a great suggestion. I had just sent a note off to my editor saying that I had decided that chapter two would be about limits and that continuity would now become chapter three.

The down side is that this seems to extend the discussion of these two topics while the student is raring to go and wants to get to the good stuff. As they will later learn, however, this is the good stuff. So many of the theorems require an understanding of these two topics. The one I was tempted to give short shrift to is continuity – we’ll see.

As for limits, I’m leaving the formal definition until the end of the chapter. This means that I’m not providing formal proofs of any of the limit theorems. That may be ok. I want students to understand that if the limit as x -> a f(x) = 7 then lim x->a [f(x) + 3] is 10. I’ve seen tons of students who know the limit of the sum is the sum of the limits when they are studying that section of the book – can we get them to grasp these theorems at a gut level.

It also sets up nicely the expectation that the derivative of the product is the product of the derivatives.

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8 Responses to “Limiting the discussion”

  1. charlie angevine Says:

    You must have had a long week; in the final paragraph you typed product twice where you meant to say sum.

    In the calc books I’ve used all a student really needs to know about continuity is that they can draw a continuous function without lifting their pencil. Of course these books never try to prove theorems.

    I am so glad you are back to work on the book. I can’t tell you how excited I am about the prospect of a head first calculus book. If you would like an enthusiastic reviewer/typo-hunter/problem-checker I am willing.

  2. Pyracantha Says:

    Dear sir: I am a 53-year-old commercial artist and I am just learning calculus for the first time, on my own using books, along with some help from my math and science friends. Six years ago after a sort of “conversion experience” I decided to learn mathematics and physics, which I never learned in my high school or college days. You do not leave a private e-mail contact anywhere so I will give my Website address for you to look at. My Weblog, ELECTRON BLUE (scroll down to bottom of “index” page) is my journal of how an artist learns mathematics and physics. You may be interested in it. My site is at http://www. pyracantha.com. I am looking forward to your calculus text, I will still be learning it when it is published.

    Yours, Pyracantha

  3. Franje Says:

    You haven’t blogged in some time. Are you alright? I hope you are fine.

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  6. Idetrorce Says:

    very interesting, but I don’t agree with you
    Idetrorce

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  8. Doiy Says:

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