(no subject)
Today was rather intense. 10 -5 math. Nonetheless i must say it has been extremely fruitful.
We arrived at the institue at 9, after a short briefing and video, we plunged straight into calculus. The extremely varied levels of familiarity was obvious from teh get go. Some guys had already taken advanced placemetn courses for universeity in calculus, while others hadnt learnt any calculus before. Basically teh stuff was pretty simple imo, the usual stuff we do in schools anyway. I spent the time proving the power rule, chain rule, and trying to prove d/dx of f(x)^g(x) instead.
After lunch, they decided to split the group into 2. Those who knew calculus and those who didnt. From what i heard the gap was pretty large. We were brought to another conference room, where we proceeded to have an informal discussion/lecture on whatever calculus we felt was fun. During this time, i learnt a great deal. We went through partial differential equtions, which now appears to be extremely simple i.e. easier that normal calculus, hehe half the work. Then we went through sinh, cosh, which i've always been wondering about. Furtheron, we went into proof of d/d/x f(x)^g(x) which to my surprise was extremely simple, given that one first knows of a weird exponential relation. i.e. f(x)^g(x) = e^(g(x) * ln f(x)) Finally, we did abit of integration, an explanation of the first principle of integration, and some techniques.
We then merged with the rest, and did complex no.s. This topic was rather new to me. However, it wasnt difficult either. The most difficult part was probably the phasor notation. And this required knowledge of a nice nifty equation. i.e. the Euler formula. The lame guy spent about 30 mins proving it, cos he used some inefficient method. This then led to us being taught polar coordinates, i.e. another way of describing a vector: via rotation about origin, and magnitude from origin. It is at this tiem that i realised why during hte project with Dr Yeo, e^i theta kept on appearing. I must say this long awaited udnerstanding brings alot of satisfaction.
We then had a brief intro to matrices. Hence concluding the day.
The institute was a pretty swanky place. Alot of glass, concrete and steel, new age architecture. The interior was quite cool too. Even the chairs were like space-age ones, with hinged arm supports and back rests etc etc. Also, they had pletny of small lounges with sofas for ppl to convene and talk. Also, there were numerous blackboards littered about, for their scientists to write on and discuss in front of.
Overall, I am pleased with how much i've learnt today. Alot of teh stuff was however much easier than i expected. Its probably highly consolign that there are alot of noobs around. Of course ath teh end of the spectrum, some of them here are seriously pro. I must admit tho that i think the day has been extremely draining. I doubt i can continue this level of energy for 6 or 7 more days.
We arrived at the institue at 9, after a short briefing and video, we plunged straight into calculus. The extremely varied levels of familiarity was obvious from teh get go. Some guys had already taken advanced placemetn courses for universeity in calculus, while others hadnt learnt any calculus before. Basically teh stuff was pretty simple imo, the usual stuff we do in schools anyway. I spent the time proving the power rule, chain rule, and trying to prove d/dx of f(x)^g(x) instead.
After lunch, they decided to split the group into 2. Those who knew calculus and those who didnt. From what i heard the gap was pretty large. We were brought to another conference room, where we proceeded to have an informal discussion/lecture on whatever calculus we felt was fun. During this time, i learnt a great deal. We went through partial differential equtions, which now appears to be extremely simple i.e. easier that normal calculus, hehe half the work. Then we went through sinh, cosh, which i've always been wondering about. Furtheron, we went into proof of d/d/x f(x)^g(x) which to my surprise was extremely simple, given that one first knows of a weird exponential relation. i.e. f(x)^g(x) = e^(g(x) * ln f(x)) Finally, we did abit of integration, an explanation of the first principle of integration, and some techniques.
We then merged with the rest, and did complex no.s. This topic was rather new to me. However, it wasnt difficult either. The most difficult part was probably the phasor notation. And this required knowledge of a nice nifty equation. i.e. the Euler formula. The lame guy spent about 30 mins proving it, cos he used some inefficient method. This then led to us being taught polar coordinates, i.e. another way of describing a vector: via rotation about origin, and magnitude from origin. It is at this tiem that i realised why during hte project with Dr Yeo, e^i theta kept on appearing. I must say this long awaited udnerstanding brings alot of satisfaction.
We then had a brief intro to matrices. Hence concluding the day.
The institute was a pretty swanky place. Alot of glass, concrete and steel, new age architecture. The interior was quite cool too. Even the chairs were like space-age ones, with hinged arm supports and back rests etc etc. Also, they had pletny of small lounges with sofas for ppl to convene and talk. Also, there were numerous blackboards littered about, for their scientists to write on and discuss in front of.
Overall, I am pleased with how much i've learnt today. Alot of teh stuff was however much easier than i expected. Its probably highly consolign that there are alot of noobs around. Of course ath teh end of the spectrum, some of them here are seriously pro. I must admit tho that i think the day has been extremely draining. I doubt i can continue this level of energy for 6 or 7 more days.