Dave

Sorry if i chucked everyone in at the deep end a bit; if you'd like, I'll do the first question as another example.

Using this method' date=' yes. Yeah; you need to get it in a form which makes sense for h = 0.

He's always around

Yeah, you need to apply first principles before you can put the value in.

In short, don't build one unless you know what you're doing with it.

rofl, bit harsh tbh, FreeBSD isn't the ideal brand of *nix to be starting with. Something like redhat or suse is probably better.

Well, quite

You're slightly out on the second one; first one is quite a way off.

Might've installed some plugins that restrict cookie length (without realising) or maybe he just flicked the option without noticing.

A package is very similar to the installation shield on windows, yeah. I'm not sure you're right about the port though.

Sorry, forgot to attach my graph:

Probably. It'd be nice to have a load of publically accessible stats - I think atm only the admins have access to that.

Well, mine counts 10%, so not lots really. Brought my average down, but still got 79% overall

Hmm. There's been a couple of mentions of problems with the read system, perhaps it's to do with browsers. I find it quite annoying that even after I've read all the topics in a forum, I have to then go back to the forum that they were written in before it indicates the forum is read on the main page.

rofl

Btw, Calculus help is now UP, yippee (and this is my 2,000th post, woot)

Nope, I haven't done any number theory. Maybe next year after I've taken the module

Okay, since a few people seem quite keen on this idea, I'm going to start it all off and begin with an introductory online calculus tutorial - for free Lessons Syllabus I'll attempt to cover the following topics over a 10-lesson period (notice I'm not constricted by the number of lessons, they're pretty flexible): Background to differentiation, first principles and an introduction to limits (2 lessons) Basic rules of differentiation, essential notation and examples (1 lesson) Maxima and Minima (1 lesson) Applied differentiation (2 lesson) An introduction to integration (2 lessons) The chain rule (1 lesson - maybe 2) Rounding it all off (however many lessons ) Some Information Here's some basic information for you all to read: Each lesson will be posted mid-afternoon every 3-4 days, depending on how much time I have. I'll post an introductory post at the beginning of the thread with the core knowledge required, and then some questions for you to attempt. If you have problems with anything to do with a particular day's topic, then please post it in the same thread rather than creating a new one. Please read other people's replies to save duplication of questions Please try and use the LaTeX facilities to typeset your mathematics properly if you have any questions. Please rate each thread so I can see what the response is. If you're really confident of the answer and get it within 2 seconds or you're quite advanced already, please give people a hand and don't just post the full solution to a problem. Finally, the most important thing: spread the word! These things are only so successful if we have a limited number of people. Please not that this course is not intended to be a replacement for real teaching - it is only intended as a supplement. Prerequisites There's only so much I can do: I'm assuming that you've got a solid basis in algebra, and I will start from about the level of maths GCSE. I assume that you will understand the concept of a function (e.g. f(x) = x2) and understand various concepts such as graphing techniques. For the later stages, I assume some knowledge in the area of trigonometry, mainly the sine and cosine functions. For the more advanced calculus, I will be working in radians instead of degrees for the measurement of angles. There is one other thing: GRADIENTS - know that the definition of a gradient of a straight line between two points (x1, y1) and (x2, y2) is [math]\frac{y_2 - y_1}{x_2 - x_1}[/math]. Having said all of this, let's get stuck in Lesson 1 - A background to differentiation Now, a lot of people have asked me the question: "Just what the hell is calculus anyway?" And my response is: "Probably the most important area of mathematics you're likely to come across, and the basis of most modern physics." And this is not an understatement. I won't go into much more detail historywise, but needless to say the original inventor of calculus was Sir Isaac Newton, who used it to solve the classic two body problem back in the 1600's. Since then, a new notation has been commonly accepted (created by Leibniz) and many, many advances have been made. And now onto the mathematics. Calculus encompasses three major topics: the study of limits, differentation of functions and integration. We will be starting to look at limits and differentation over the next couple of weeks, and integration will come towards the end of the course. So what actually is a limit? It's a very hard concept to define in layman's terms (although relatively easy from a strictly analyitical point of view). I think the best way to think of it is in terms of sequences. Imagine you have a sequence of numbers that goes like this: 1, 1/2, 1/3, 1/4, 1/5, ... and so on. If we call the nth number an, then it's fairly clear to see that a1 is 1, a2 is 1/2, and so on. The mathematical definition for the nth number is obviously an = 1/n. Now we look at what happens as we get bigger and bigger values of n. We can notice that each term in the sequence gets progessively smaller as we increase the value of n, and it doesn't take a genius to work out that as we get really big values of n, we get excruciatingly small values for an. So we can say that the "limit" of an is 0 as n gets really big (i.e. as n tends to infinity). Don't start crying just yet over how complex this all is; it's an abstract concept to understand, and it'll take some time just to understand the idea, let alone how it all works. A quick remark on this: we won't be using limits that tend to infinity much in calculus at all, I just used it as an example. A very important idea to understand is the fact that we're not actually saying that the sequence will ever hold a value of 0 - what we are saying is that if you were to go on and extend the sequence forever, then you'd be continually getting closer and closer to zero. Quickly, some notation. You won't be using this every day, but it's handy to know. Instead of writing "the limit of f(x) as x tends to infinity is 971283.2", we can write: [math]\lim_{x\to\infty} f(x) = 971283.2[/math] - so remember this, it's a very useful shorthand! So now onto first principles of differentiation: this is where I tell you how to actually go about differentiating something and what we actually mean by the term 'differentiation'. A classic problem in a GCSE maths paper is to sketch a curve out (like the classic y = x2) and then they say to you: "draw a tangent to the curve at the point x = 2, and hence find the gradient at that point". And you grudgingly scrawl out a quick graph between this and that, shove a quick tangent on and get an approximate value for the gradient. We all know it's dead easy to find the gradient between two points on a straight line, but on a curve? Bah, impossible. But this is not so. Let's draw ourselves a graph of y= x2, and have a look at a better way of doing things. Have a look at the graph at the bottom of the page, and observe the points I've drawn on it. We have a point P, and a position (1,1) and then a point Q at position (1+h, (1+h)2). I initially got confused here: basically, we're looking at a point where x = 1, and then a point a little bit further down the x-axis at x = 1+h, where h is some value (we don't really care all that much). Now we're going to consider what happens to the gradient of the line PQ when we decrease the value of h - i.e. we move the point Q closer to the point P. If you look closely, you'll notice that as you draw the two points closer and closer to one another, you're going to get a better and better approximation for the value of the gradient at the point x = 2 on the curve. And now you scream "so what?!?!?" - and then I say "Well look - we have a method for finding the precise value of a gradient at a point on a curve!" And then you probably say "so?!?!" again, and I don't really care by this point What we really want to know is how we find this value. Let's look at the gradient of the line PQ. This is equal to: [math]\frac{(1+h)^2 - 1}{(1+h) - 1} = \frac{(1+h)^2 - 1}{h}[/math] Now just a second. We want to find the limit of this as we decrease h (i.e. as h tends to zero). But we've got a silly h lying around all by itself on the bottom, meaning that if we just stick h=0 into here, we get something divided by zero - we can't do that. So now we have to play around a bit with the fraction, and this is the key operation of this lesson. Make sure you watch very, very carefully and understand each step in the minutest of detail. First of all, notice that (1+h)2 = 1 + 2h + h2. So now we have the gradient equal to: [math]\frac{1 + 2h + h^2 - 1}{h} = \frac{2h + h^2}{h} = 2 + h[/math] Hurrah! Now we have something that we can work with. Notice now that as h gets very, very small we have that the gradient of PQ will tend to 2+0 = 2. So we have a method for finding the exact value of the gradient at a certain point. All those hours of drawing tangents to curve wasted whilst your teacher can work out the answer in their heads Next time, I'll extend the method to work for all values (i.e. find the gradient at any point) and introduce some very important notation that you're likely to carry around for a very long time. Questions 1. Find the gradient of the function y= x3 at the point x = 5. 2. Find the gradient of the function [math]y = \frac{1}{x^2}[/math] at the point x = 5. I may post further questions; I just can't think of any yet. Hope you enjoyed this and found it useful, Dave

ack, linear algebra 101 Stick to calculus for now

My problem was I did no revision for the module

Doesn't matter, the more the merrier

I've just joined the channel, nick davem.

Cheers, I'll have a go with that.

It's not really tourism either; not exactly your average holiday

So he is. At least he's still alive then