New answers tagged notation
0
Don't. The language is highly imprecise, confusing, contrary to the precise usage you hopefully will be teaching them, and in my experience not useful for doing calculus.
1
I agree with most of what's already been said so far, but wanted to add one point---that the answer is surely going to depend on your audience. Of course, this is going to be people who have never learnt calculus before so their mathematical maturity and exposure to such things is definitely going to be limited, but depending on where you're teaching the ...
8
I think that there may be advantages to introducing the idea of asymptotics early, and I think that it might be interesting to experiment a bit with curriculum by bringing in asymptotics in calculus. However, there are caveats:
I think that students need to have a solid understanding of limits and continuity, first. I don't necessarily mean that the ...
7
I've never known or needed that notation in my life. And I've used lots of calculus for science and engineering. So one of your assumptions is wrong. I think it would be more efficient to teach a normal calculus class. Leave the esoteric abstractions for later, and for the kids who will really need them (a small subset of the typical calculus population, ...
10
When I was an undergraduate, the big and little oh notations were taught to me in a first-year math course ostensibly aimed at physics students. The class was strong - several of us are now mathematics and physics professors in universities - and the attempt was, to my mind, moderately unsuccessful (although one could make the counterpoint that I still ...
0
You could start with two tables of values for x (the input variable) and y (the output value) in both. To start, each should represent a permutation on say, the set {1, 2, 3, 4, 5}, but don't use the word "permutation."
Label one "Table A", the other "Table B".
For each line in Table A, introduce the notation A(1)=, A(2)=, etc.
Similarly, for Table B.
...
0
Many answers already, so I'll keep this one short: it has been realized by researchers in didactic that one difficulty in the concept of function is that it changes status: at first each function is considered as a process (a verb in @ΦDev's answer); they meet several of them, each being akin to a (unitary) operation, not very different from addition or ...
2
In the Yoruba Language, we use the word òǹkà to refer to tokens for representing numbers. Thus, it would correspond to the word numeral. The word òǹkà literally translates as 'that which is used for reckoning.' The prefix on (the n is a nasal) means thing, and the other part, ka, means to reckon, count, calculate, etc.
On the other hand the word number ...
-1
It's the whole subject of the Bourbaki's book IV Integration.
First generalize your notion of derivative: a derivative is any function $d:A \rightarrow A$ of the space $A=\mathcal{C} ^ \infty(\mathbb{R})$ such that
$d(f+g) = d(f)+d(g) $
$d(\lambda f) = \lambda f $ ($\lambda \in C^{te}) \cong R \subset A$
$d(fg) = f d(g) + d(f) g $
The first two mean the ...
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