Numerical Methods
This was one of those annoying papers where, for the most part, you learn a bunch of formulae without a proof and when you’re given the proof it’s all funny. Boring, but easy since you don’t have to do much work. However, sometimes you just need all the formulae, you need a cheat sheet, because the exam is tomorrow. Unfortunately, I couldn’t manage that, so a lot searching, a little deriving, and some searching for old books allowed me to type them all up and print them up. Might as well save some other soul some trouble. Go to Mathworld for the proofs. You could also wander around the Springer Encyclopaedia of Mathematics or PlanetMath.
Most of the stuff is particular to the course we’re doing, so some things are assumed. For example, the Runge-Kutta method refers to the Fourth Order Runge-Kutta method and stuff like that. Also, parts may be technically inaccurate or may be plain unhelpful :) , but that’s because that part will just jog the right part of my mind. Sorry.
And here you go:
Numerical Methods, List of Formulae, B.Sc. Math, Semester V, Madras University [PDF]
Numerical Methods, List of Formulae, B.Sc. Math, Semester V, Madras University [ODT]
Posted by roshan.george under College, Math |
We had this shit last semester. Random forumulas used to solve meaningless problems with no relevance to the real world. Engineering.
Comment by Marc — November 1, 2007 @ 3:22 pm
Fortunately it only takes a few minutes to study :)
Comment by roshan.george — November 1, 2007 @ 4:46 pm
Haha. I remember how we had more fun trying to figure why the name of that method rather than applying it. Some of them were real hilarious.
(Don’t even think about explaining the real reason for those names!)
Comment by Chetan — November 2, 2007 @ 6:32 pm
Ha ha, I won’t dare try. The best part is when a famous textbook misspells something and it is forever remembered by the misspelled name. One of those things there that starts with a B is like that.
Comment by roshan.george — November 2, 2007 @ 6:45 pm
Ah. We had that subject last sem. Funny subject, that one. Had a lot of fun in class whenever our lecturer said Runge Kutta or some such funny name. Ultimately panicked during the exams, and scraped through with the barest minimum. Lotsa failures in that one.
Comment by Sundar — November 5, 2007 @ 11:06 pm
Ha ha, yeah, I completely missed most of the classes in this course so I didn’t get to have that fun. However, our papers are real easy.
Comment by roshan.george — November 5, 2007 @ 11:49 pm
One of my classmates is nicknamed Kutta, so you can imagine the fun when that particular method was mentioned.
George, they’re easy only for super geeks like you.
Comment by Marc — November 6, 2007 @ 12:02 am
Ha ha, that’s funny. I remember in school there was that big fuss about Kundt’s method or something.
No really, it’s trivially easy stuff for us. Plug numbers into formula. That’s it.
Comment by roshan.george — November 6, 2007 @ 12:16 am
Maths is always horrible…
Comment by Isha — November 6, 2007 @ 12:44 am
Agreed!
Comment by Marc — November 6, 2007 @ 3:09 pm
What, no, it’s lovely! I’ll admit, I know nothing about numerical methods yet, but it isn’t horrible!
Comment by Arundhathi — November 6, 2007 @ 8:34 pm
Exactly, someone with some sense comments. Nothing wrong with Maths, it’s some of the most beautiful stuff in the world.
Comment by roshan.george — November 6, 2007 @ 8:50 pm
Thou art mistaken… One day you shall see the truth: Maths is horrible. Period.
Comment by Isha — November 6, 2007 @ 9:27 pm
If Math were lovely/beautiful then Isha and I would agree. Since we don’t, it isn’t.
Comment by Marc — November 6, 2007 @ 10:14 pm
It’s not my fault you two have no appreciation of beauty.
Comment by roshan.george — November 6, 2007 @ 10:39 pm
It’s not our fault that your idea of beauty is warped.
Comment by Marc — November 8, 2007 @ 8:06 pm
It’s a matter of taste, particularly your lack of it.
Comment by roshan.george — November 8, 2007 @ 8:09 pm
Whoa, I thought Numerical Methods was only for Engineers. Seems like I was mistaken. I am actually currently working on a numerical methods library. (in programming parlance.)
Numerical methods seems trivially easy. I am actually in love with this paper. Only people who understand modelling/framing the probelm to be solved and it’s solution understand the ingenuity of numerical methods.(Often framing the model is more difficult than solving it.)
As a paper for exams I am highly critical of this paper. I mean there is no point in doing 15 iterations manually knowing perfectly well that I will screw some substitution. It’s an easy mechanical process of substituting numbers in formulae and that’s why we have computers- to crunch numbers.
Numerical methods finds applications in a whole range of fields. As an electrical engineer I used it extensively in Power Systems.
To appreciate the concept of Numerical methods, you should try solving the problems with the conventional methods. Then you will know the beauty of it.
If you thought NM has no practical applications in engineering or otherwise, then it is used right from plotting curves on your monitor (even in Games) to
Optimising designs in Power systems and other design oriented streams.
Try the book by Gerald and Wheatley if someone is really interested. Gives you an insight into why use numerical methods at all.
As for the ‘random formulas to solve meaningless problems with no relevance to real world.’ you couldn’t be more wrong about it. Myopic vision prevents you from appreciating the beauty of NM.
Instead of critising the random formulae, we should appreciate them and see if we can devise better methods to get the same thing done. Mostly it’s(the formulas) just common sense. If you understood the physical interpretation of the problems,you might be able to see more clearly.
Comment by Karthik — December 30, 2007 @ 1:07 pm
Thanks for the comment Karthik. I was not criticizing NM itself for existing. However, I did not join a Mathematics course to learn how to operate a calculator.
As for ‘random formulae…’, my criticism was directed at the fact that it did appear to be random formulae. There is no reason that the formulae should seemarbitrary . Here I have to give my teacher a little credit: Though she didn’t go about very well, she did make an effort to mention the proofs .
It would be interesting to know what exactly one learns by simply plugging numbers into formulae. Also, the whole substituting thing is a bore. Fortunately, I didn’t have to keep doing it, with a decent calculator substituting is trivial and there’s little scope for error.
Honestly, theproofs at Wolfram’s MathWorld were far more interesting than the formulae themselves. One doesn’t need a B.Sc. Mathematics course to learn how to memorize formulae.
PS: Don’t blame me. I really am myopic. -4.5 :)
Comment by roshan.george — December 30, 2007 @ 3:58 pm
George, that was infact Marc’s comment :P Where did you say ‘random formulas to solve meaningless problems with no relenace to the real world.’ ? But it’s understandable. This post must have been really old. I just saw ‘Math’ in the categories and simply had to see it.
You are right about plugging in numbers into formulae and I thought I agreed with that in my earlier comment. It’s pointless.It should be taught as a lab or something.
Engineering is even worse. We were never told to reder to proofs. We are simply expected to accept whatever is taught to us. No wonder then that Marc feels the way he does. Our staff are simply pathetic and have no idea of the geometrical meaning of the stuff we do.
Comment by Karthik — December 30, 2007 @ 7:34 pm
Ha ha Karthik. Yes, I guess we’re on the same side here.
My mistake over the comment, I should read context the next time :)
Comment by roshan.george — December 31, 2007 @ 10:58 am
Stop bumping up old posts!
My opinion of NM has in fact changed and it’s the one Mathematics subject that makes sense only because I took the trouble to understand it.
Comment by Marc — December 31, 2007 @ 12:21 pm