I'm a 1st year engineering student. How can I learn about chaos theory while using min. maths? How much proficiency in maths is actually required? What exactly is an attractor?
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http://en.wikipedia.org/wiki/Chaos_theory
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Hi, I am jam-packed with excellent maths websites, some of these websites you may have to become a member for but there top on stuff dude!\nI am a Yr 8 Student myself and I have to study a lot for examinations and I got tons of websites.\nEVERYTHING MATHS\nhttp://www.mathforum.org\nDIRECTED NUMBERS\nhttp://www.mathsrevision.net/gcse/pages.php?page=22\nGOOGLEPLEX\nhttp://www.fpx.de/fp/Fun/Googolplex/\nACTIVE REVISION - BECOME MEMBER FOR FREE\nhttp://www.activerevision.com\n\nI hope this helped you. \nKind Regards, Timothy H. (Age 12, W.A.)
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Took it last quarter, looked at it like a puzzle.  A puzzle is fun, math is not.  You start with the matrix given in the problem, and have to finish with ending matrix given.  Do what you need to do to get to the last matrix.  The best part, if you mess-up, just do another set.  There are no wrong answers, try doing it like a puzzle, more fun than Soduko.  Good Luck
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This is a good time to learn dimensional analysis.  It will come in handy for all of your physics courses.\n\nFirst, µ x M cancels one another leaving ohms x Farads\n\nOhm = volt/amp\n\ncharge = capacitance x voltage  so capacitance = coluomb/voltage\n\nOhm x Farad = volt/amp X coulomb/volt\n\nso the volt cancels leaving \n\nOhm x Farad = coulomb/amp\n\nAmp = coulomb/sec\n\nOhm x Farad = coulomb/(coulomb/sec)\n\n= (coulomb/1) x (sec/coulomb) = sec\n\nBy the way, Tau = RC is the timeconstant of an RC type circuit.. you remember for a cap charging it is I = V/R[exp (-t/RC)  RC is in units of time = sec\n\nI used to have to do this stuff all the time in my undergrad physics courses.
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Most introductory books on differential geometry discuss this. Looks at 'From Calculus to Cohomology' and 'Introduction to Smooth Manifolds' as references.
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A Student’s Approach to the Second Law and Entropy\nThis is written for you quickly to understand the second law and entropy. All but a few general chemistry texts have discarded “entropy is disorder” and adopted my approach. However, if your text and instructor describe things differently, don’t argue with or correct her/him! Just memorize what you read in the text and hear in class so that you can give the expected answers on exams. Grades are important at this time in your life :-( but the understanding that you will get here will last a lifetime.\n\nThe Second Law of Thermodynamics\nMany texts define the second law as “the entropy of the universe increases during any spontaneous process” and then throw qrev/T or free energy = ΔG and ΔS at you.\n\nThat’s too complex too fast.  We’ll see that the second law and entropy are simple, at the level of first-year university chem. \n\nThe second law is based on human experience.  It doesn’t come from complicated theory and equations.  So, think of these experiences that you have had:  A rock will fall if you lift it up and then let go.  Hot frying pans cool down when taken off the stove.  Iron rusts (oxidizes) in the air.  Air in a high-pressure tire shoots out from even a small hole in its side to the lower pressure atmosphere.  Ice cubes melt in a warm room.  \n\nWhat’s happening in each of those processes? Energy of some kind is changing from being localized ("concentrated" in the rock or the pan, etc.) to becoming more spread out. Look at those examples again to see how that statement fits them all.\n\nOK?  That’s it — a simple way of stating fundamental science behind the second law: \nEnergy spontaneously disperses from being localized to becoming spread out if it is not hindered from doing so.\n\n But what about “entropy” and “universe”  that is in so many textbooks and may be in yours? We’ll see what entropy is in a minute. But the “universe” just means “the system you’re looking at PLUS its surroundings, i.e., everything that’s close around it”.  System plus surroundings.  If that “system plus surroundings” bothers you, or if you want details of three of the processes mentioned above, read the next paragraphs. \n\nIf not, skip down to “What Is Entropy, REALLY?”\n\nThe rock has potential energy localized in it when you lift it up above the ground. Drop it and that PE changes to kinetic energy (energy of movement), pushing air aside as it falls (therefore spreading out the rock’s KE a bit) before it hits the ground, dispersing a tiny bit of sound energy (compressed air) and causing a little heating of the ground it hits and the rock itself.  The rock is unchanged (after a minute when it disperses to the air the small amount of heat it got from hitting the ground).  But the potential energy that your muscles localized in by lifting it up is now totally spread out and dispersed all over in a little air movement and a little heating of the air and ground. [System: rock above ground,  then on ground. Surroundings: air plus ground.] \nThe iron atoms in a hot frying pan are vibrating  very rapidly (like ‘dancing in place’ fast) and therefore the motional energy in the hot pan is localized. That motional energy will spread out — if it can.  Whenever the less rapidly moving molecules in the cooler air of the room hit the hot pan, the fast-vibrating iron atoms transfer some of their energy to the air molecules. The pan’s localized energy thus becomes dispersed, spread out more widely to molecules in the room air. [System: pan. Surroundings: room air.] \nIron in nails or other objects doesn’t have to be hot (i.e., with very fast moving atoms or molecules) to have ‘localized energy’ within it in a chemical sense: Iron atoms plus oxygen molecules of the air have more energy localized within their BONDS than does iron rust (iron oxide). (That’s why iron reacts with oxygen — to release energy from their
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The background is , as you rightly say , very technical in the mathematical sense. It starts with developments in Differential geometry ( Marsden Morse) , leading to the catastrophy theory of Renee Thom. Essentially if you have a 'smooth' function ( i.e. differentiable several times ) such as ax^i+by^j+cz^k=0 , then this is actually a prototype for a whole range of functions if you vary a,b and c.if you , perversly , analyse the functions with respect to the a,b and c , there are often areas where a sudden discontinuity occurs.so , for instance your equation may have a solution  for x where a=5 say. if you change a to 5.000001 , then the solution for x is suddenly very different. A way to picture this is to look at the situation where the equation is that of a Corkscrew. for a given x and z , there are many values of y which fit the equation(one for each turn of the screw). I could go on here but hopefully this is enough to get you started.Thanks for the question.
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What school do you want to get into? Do you want to, or just think you should? Is math going to matter that much in the rest of your life? You need basic skills, but most of the stuff you learn in school you never use again, unless you are an engineer or an architect. Seriously. And if you are desperate to learn it, you can take remedial courses. And take a deep breath, it's not worth panicking over.
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why? can't do math? talk to your tutor, and help is there to overcome if there is any issue that puts you of it. if there is none (and you ought to know it pays well later!) switch to something else like biology or physics or law. tutors have all your marks and know where you go wrong and why you are disappointed. if they ask you to switch and you sure dont like engineering please switch.
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As weird as this sounds, I have always found that for me math needs time to absorb.  And while I will never be an engineering major, I would suggest going over the next section or chapter that will be discussed in class, listening to the lecture with lots of Red Bull if it helps, and then going home and studying for an hour right after class.  Do math problems right then and then do a couple  everyday.  If you are able to, review all the formulas everyday as well.  I know it sounds like a pain to do math at least an hour everyday, but I have always found it is the best way.\n\nP.S. - Please give me best answer.
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honestly....good luck\n\ntry www.mathworld.com\n\ndo a search for differential equations, i think that would be your best bet...but that can get confusing...good luck
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I would suggest that you cannot be good at physics without being good at maths. Applied maths is fundimental to physics (dynamics, electomagnetism, optics,hydrodynamics etc).  Chemistry requires both physics and maths especially algebraic knowledge eg to work out chemical formulas from observed data.  There is nothing hard in algebra just keep practicing.
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Both require some learning.  But both can do pretty much everything you want.  I happen to prefer Mathematica, but it's soley becuase I used it extensively for 3 years, and only played around with MathCAD.\n\nTalk to some of your Profs, find out what they use.  That should influence your decision more than anything else.  :)
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I've heard very well of Mathematics for Economists -- by Carl P. Simon, Lawrence Blume as a basic calculus book. Forget the "for Economists", calculus is calculus. It is expensive though.
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Check out Stewart's Calculus(refer to the first link). If you are looking for something  more rigorous refer to Apostol's Calculus(refer to second link).
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Sometmes when you see the actual application of mathematics things start to make more sense. Mathematics is the heart of engineering. If you like engineering and have love for it then you will then work hard to adore mathematics. ANd if you start to adore mathematics you are going to be a great engineer. \n\nAbout english ... read the news daily.....look up in dictionary if you don't understand. speak often.
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Honestly how good is your chemistry to start with ? mine was awfull but getting your head in the books helps . Maths is always good to have but is more essential in inorganic chemistry . Organic is great and is a lot more logical and easier to learn providing you have a good base in chemistry . they are not impossible but you do need to realise which are you better at ....inorganic or organic if your maths is dodgy then go organic . or find a tutor and learn.