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Please, help me me better understand physics/math proportions

  1. Mar 27, 2012 #1
    Please, help me me better "understand" physics/math proportions

    please read before answering, I would sincerely appreciate those of you who can guide me through my knowledge of physics and engineering.

    Ok, currently i'm a highschool grad, just got my associates degree in automotive applied science. I am a master of cars, a car guy, to say the least. But what interests me about cars is the complexities in physics in every broad field of such, mashed up into one piece of 4wheeled engineering.

    That being said, I am now pursuing my major in Mechanical engineering, I am in my basic classes, ie general chemistry and trigonometry. I wasnt good at math in highschool, just cause my mind is more visually inclined. But so far i'v maintained a 4.0 with alot of dedicated work in my basics so far, this is to ensure my successful transfer in to University of Texas in Austin.

    LETS GET TO THE POINT: I have seen alot of math, from algebra to calculus(basics of calc), as well as the math of physics and chemistry..

    ITS NOTHING BUT A WHOLE BUNCH OF FORMULAS (FRACTIONS SET EQUIVALENT TO ONE ANOTHER/EQUATIONS DESIGNED TO REFORM AND MANIPULATE). Its beautiful to say the least, having the ability to examine so many possibilities with simple formulas such as E=mc^2, PV=nRT, etc...

    But im having trouble visualizing these proportions, and i feel like the better acquainted I get with manipulating them and moving variables around, the better of an engineering student I will be, right? Im talking, things like "a" is directly proportional to "b", as "a" goes up in a graph, so does "b". This is me-visually seeing variables, etc...

    Can someone give me advice on where i can better understand these completely abstract versions of physics and math. Maybe I'm just going through a revelation. I only brought this up because my understanding of the overall goal in math is solid, but when I go into working out problems, I suffer abstract thinking, and find myself spending too much time on problems that other people see differently, and can work out through strict intuition.

    I understand this is essential, in the life of an engineer, to structure his brain around analysis and logically coherent thinking. As a car person, I think VISUALLY, but I want to be more inclined toward the geeky engineering way of life, cause despite the fact that those automotive engineers (for example) cant find the right place for a god damn oil filter in a subaru (right next to a hot catalytic converter), these engineers make the big bucks. (let me remind you that "bucks" are not my incentive here.. just an example)

    Thank you for reading, and I look forward to hearing from those of you who understand my difficulties.
     
    Last edited: Mar 27, 2012
  2. jcsd
  3. Mar 28, 2012 #2
    Re: Please, help me me better "understand" physics/math proportions

    I wasn't going to reply because I don't have much experience and I was hoping someone else with more experience would hop in, but because no one seems to I'll give my two bits.

    When there are just a view parameters and variables, equations are usually pretty easy to visualize (as you said). However, as you get farther and farther into math and physics, equations will get harder to visualize. If you are having trouble with an equation that is too big to visualize, try breaking it into segments.

    For instance, in the classical kinetic energy equation Ke=(1/2)mv2
    It might be hard to visualize how the whole thing changes when you change a variable, but if you rewrite the equation Ke=(1/2)pv (where p is momentum), you can probably visualize a change pretty easy.

    In a harder example, in the relativistic coordinate transformation: [itex]x'=\frac{(x-vt)}{\sqrt{1-\frac{v^2}{c^2}}}[/itex]

    There is no way anyone can easily visualize how the equation changes as v changes, but if you break it up into two sections (the top and the bottom), and you know that the bottom is just the lorentz factor and the top is the normal coordinate change (which you might not know now but you would going into a course using this), then it just becomes the simple top modified by a set value (the bottom), and in the simple equation x-vt it is pretty easy to visualize how the equation would change if you modify a variable.

    I hope this helped, and if not I hope someone else can help you.
    Cheers.
     
    Last edited: Mar 28, 2012
  4. Mar 28, 2012 #3

    chiro

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    Re: Please, help me me better "understand" physics/math proportions

    Hey hondaman520 and welcome to the forums.

    I am a mathematics major and I have come to have my own opinion about mathematics really is all about in both pure and applied scenarios.

    To cut to the chase, math is about three things: representation, constraints, and transformations.

    The representation deals with how we define something. We use numbers because they can take on many values which means that we can look at things with 'many possibilities' and if we understand what those possibilities are and mean in the context of our problem, then indirectly we understand our problem in some way. So the representation deals with how we describe what we are working with. We need to do this straight away.

    The next thing is constraints. All a constraint is, is a way to look at something that is simpler (less general) and as a result, easier to manage and understand.

    We all use constraints in some way, some more than others. For example a pure mathematician might have lower constraints (i.e. looking at something more general) while an engineer will be looking at something more highly constrained (i.e. something less general) because they are focusing on different things. Also in one context the engineer is actually looking at something more general because they may have to deal with problems that are highly dimensional whereas the mathematician might be looking at things involving one a few dimensions.

    The final thing is transformation. Think of a transformation of taking one representation and changing it into another. If you have an equality and you add 2 to both sides, that is a transformation. If you take a function and convert it to a taylor series (provided it has one) that is a transformation. The transformation might end up not preserving the equality if you are just interested in approximations, but again its a transformation. Think of it as a black box and you feed in the current mathematical relationships and it spits out new ones.

    Now in mathematics we start off with a problem that says that if we are given a starting condition with a well defined representation (i.e. problem has been converted to language of mathematics) and we also have a target representation (what we are trying to show in language of mathematics), then we basically have to find a way to go from A to B, from start to finish.

    In the process we will have to use constraints and transformations to get there and this is what mathematicians (both applied and pure) actually do.

    The symbols you see are usually not understood by what you see but why what they mean in English (or another spoken/written conversational language). It takes a bit of practice to see this, but I assure you that behind any problem there is an intuitive explanation in English of what that problem refers to and why it is of interest.
     
  5. Mar 28, 2012 #4
    Re: Please, help me me better "understand" physics/math proportions

    From a note about General Problem-Solving Strategy download from internet it says
    1. Conceptualize
    2. Categorize
    3. Analyze
    4. Finalize

    In the Conceptualize.
    "Imagine a movie, running in your mind, of what happens in the problems."

    I think its a good idea to visualize the events happening, from initial stage to final, must be a complete film. Normally the question asked is what's status at ending.
     
  6. Mar 28, 2012 #5
    Re: Please, help me me better "understand" physics/math proportions

    thank you guys very much for giving me some insight. I will take these things into account, and i look forward to hearing more from those of you.

    Although I have yet to begin my calculus series, It seems most people only struggle due to their lack of perfection in the study of algebra. Its all built off of algebra, so i hear.

    Gladly, I did pretty well in algebra, only a couple things like intervals of quadratic equations got me stumped at times. Right now Im doing trigonometry, its really just a bunch of memorization of identities. Given information to find values of trig functions, proving equivalent expressions etc...

    This summer im taking precalc which should perfect my algebra skills. Then im off to the real test of Calculus series. I make a big deal out of this, because I, unlike many studious people, take my social life seriously. I try to manage my free-time/work-time with the studying, where maintaining a competitive gpa for my UT transfer is my number 1 priority.
     
  7. Mar 29, 2012 #6

    chiro

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    Re: Please, help me me better "understand" physics/math proportions

    Just one last piece of advice for you: if you don't know what is going on or what the whole point of the lecture/subject is, just ask point blank. I think you'll find that if you know this up front you won't have to spend as much time struggling to figure this out which will give you more time for other things.

    You need to realize that most of the people teaching have been doing this for many years possibly even decades: they have been focusing a lot of their time and effort on this and they have made it their career of not only paying attention to what is happening but also usually by solving problems of some sort on a frequent basis.

    This might save you many hours per week of obtaining this information when it matters most (as early as possible).
     
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