Homework Statement
The notation for a Riemann sum - Ʃ f(x*i)Δx - is very similar to the notation for the integral (the Ʃ becomes ∫, the f(x*i) becomes f(x) and the Δx becomes dx).
\int f(x)dx = \lim_{n \to \infty}\sum_{k=0}^{n} f(x_i) Δx
Is there a way to explicitly define the values on the...
Homework Statement
Generally the derivative has the limit x-- h applied to the whole thing like
$$\lim_{h\to 0} \frac{f(x+h)-f(x)}{h}$$
I'm guessing you can't express it as
$$\frac{\lim_{h\to 0} f(x+h)-f(x)}{\lim_{h\to 0} h}$$
because the quotient rule for limits doesn't hold when...
Absolutely a typo. :) sorry!
You'd be surprised at the quality of the instruction here - for example, one of my teachers didn't know what this
f(x+h)-f(x)
----------
h
lim h--> 0
was.
I understand that the upper limit is x, I just mean that that I would expect the definition of the...
Ok, here's what I meant:
I was looking at ## \int_a^b f(t)dt = \int_0^b f(t)dt - \int_0^a f(t)dt = F(a) - F(b)##
and I've been taught that F(x), or F(a) or so on, in this context, is an indefinite integral. Like this:
$$\int f(x) dx$$
But that didn't make sense to me because I don't...
Homework Statement
I hope this is in the right forum, because this is a question on theory and not related to a specific problem.
I was reading onlne about the Fundamental Theorem of Calculus. On one site the author wrote:
F(x) = \int_{0}^{x} f(t) dt
Later, he wrote:
\int_{a}^{b}...
Thank you both for your answers :)
I still haven't really managed to explain what I'm talking about...I'll have a look at related threads in the forum to see if I can clarify.
I think you misunderstood me, I probably haven't been using the correct terminology.
I dug up my calculus book, and I think what I'm thinking about is a step function.
In the book, it says the following:
"...if s(x) = c for all x in the closed interval [a,b], the ordinate set of s is a...
Homework Statement / The Attempt at a Solution
I know that given f(x)=c, the integral from a≤x≤b is c(b-a) (at least, I hope I know that! :D).
Is the integral the same value if you don't include an endpoint? That is, if you were evaluating f(x) from a≤x<b?
Intuitively I think it both...
I'm familiar with the A-Level system, although I haven't taken Economics.
I think that other than possible A-Levels universities will require in order to do physics/engineering (I imagine Math/Further Math, Physics and Chemistry will more than satisfy any prerequisites, although I haven't...
Jorriss - Thanks. I was worried that you have to do many classical mechanics courses in order to learn quantum mechanics - an intro course and an advanced course doesn't sound as bad as I thought.
Oh, I actually am looking forward to Thermodynamics/Stat. Mechanics :) When I said I was less...