Engineers, I need some help w/ math... Options

[Guardsman]

Hey guys, I want to go to school for engineering, Electrical or Electronics (both, if they have a program like that).

Anyhow, I have a big problem that currently prevents me from finishing even my Associates (Community College of the Air Force).....I can't do text-book algebra.

I can do applied algebra, I've been doing it since I was a kid. But, put a text book in front of me, with x=axb+c2/d, and I might as well be reading Latin.

One test study guide that I looked at had a question asking what the square root of i is. I can't even begin to understand how I get an answer to that. My line of thinking is that an imaginary number doesn't exist, therefore, it can't have a square root. Nothing = nothing.

I worked at Stanford Linear Accelerator Center until recently, and I looked over some of the papers and machine technical stuff, in how the accelerator works, beam physics, etc.

When I look at that kind of stuff, it makes sense to me....I may not know the exact answer, but if I had all of the necessary information, I could figure out the answer.

I also picked up a book, "Engineering Formulas", by two German guys, and looking through there, the formulas make sense to me.

Has anybody had this kind of problem before, or know somebody that did, or just have any suggestions that might help me out?

I love doing math, but it frustrates the crap out of me that I can't get past this. I tried taking algebra twice in high school, flunked both times, tried it again in 1998, and got a D on that.

I don't want to just pass the classes, I actually want to learn the stuff. Any help would be appreciated. Thanks.

John

[pknowles]

My only seggestion is private 1 on 1 tutoring. If you have done the work, read the book and still don't get then you need someone to teach it too you. Where do you live?

[slowTA]

From what I remember I is the square root of -1. That's right... a negative number with a square root, thus I^2 is 1. But I'm not sure what the square root of I is, 1 possibly? Hope it helps, and good luck.

[Guardsman]

I live in California, not too far from Modesto.

[pknowles]

Square root of i
i=(-1)^(1/2)
so to find the sqaure root of i you need to solve the following eqation:
(a+b*i)=i^(1/2) where a and b are what you need to find. a and bi are just the real and imaginary parts of some number whose sqaure is i. Note: a and b are real numbers (no i's hidden in them)
Sqaure both sides to get
(a+b*i)^2=i
expand the term (a+b*i)^2 to get a^2+2*a*b*i+(b^2)*(i^2)
now i^2=-1 and plug the expansion back into the formula to get
a^2+2*a*b*i-b^2=i
now sepperate real and imaginary parts
(a^2-b^2)+2*a*b*i=0+i
now you can split into 2 eqations to solve for a and b because the 2*a*b*i term is the only one with an i in it so 2*a*b=1 and a^2-b^2=0.
That's the hard part!
Now take the eqation a^2-b^2=0 and add b^2 to both sides to get:
a^2=b^2, so a=+b and a=-b
However if you take the next eqation 2*a*b=1 and plug in each answer (a=+b and a=-b)
if you plug in a=-b you get -2*b^2=1 which can't be satisfied if b is a real number, so a=b.
Now 2*b^2=1
divide both sides by 2:
b^2=(1/2) so b=1/((2)^(.5)) or the way math people like to see it (no sqaure roots in the denominator (sp?)) b=(2^(.5))/2 so plug those answers back into the very first eqation [(a+b*i)=i^(1/2)] at the top and [(2^(.5))/2+i*(2^(.5))/2=i^(1/2)]

DONE!

EDIT: -b) is a smily

[sgarnett]

My first wife had the same problem.

For example, should could not grasp inequalities and absolute values.

We went through what was for her a seemingly exasperating and pointless conversation:

Is Louisville east or west of Lexington? West.
How far is it from Louisville to Lexington? ~90 miles.
How far is it from Lexington to Louisville? ~90 miles of course.
Is Ashland east or west of Lexington? East.
Is Ashland east or west of Louisville? East, of course.

etc.

OK, now substitute "east of" for "greater than" etc. The concepts make sense, but put a different name on them and the brain locks up.

In a first year circuits course I took, the op-amp circuits were all drawn neatly with inputs on the left, outputs on the right, and a neat arrangement of components. On the first exam, the circuits were easy but they were drawn strangely - flipped, inverted, twisted and bent. It's amazing how many people failed because they simply didn't recognize a simple circuit that they knew how to solve.

Often the first step is just to look for something familiar in what seems like gibberish at first glance. You may not know the answer, but start with what you DO know and work from there.

[Guardsman]

Phil, that still makes absolutely no sense to me..... (IMG:http://www.frrax.com/rrforum/style_emoticons/default/banghead.gif)

"a and bi are just the real and imaginary parts of some number whose sqaure is i"

If I can visualize things (6 stones, 5 amps, etc.), I can figure them out......how can I calculate something that is imaginary (see where I'm going here?).

Maybe I'm missing something else that would make sense to me......how can an imaginary number affect a real number? If it's imaginary, it doesn't exist, and something that doesn't exist can't influence something that does exist.

In the same sense, when I'm trying to do any regular algebra problem, as they show up in a text book, the values could be anything......so my answer could be anything.....and I would believe that I'm trying to find a specific answer.....or is that where I'm going wrong?

Sean, I see what you're saying, but when I'm dealing with circuits, I can visualize what I'm working with. Even if the circuit is in a different configuration, I can eventually identify the components of it by going through what the circuit is supposed to be doing, and figure it out from there.

The problem with the book algebra, is that I'm not even dealing with a circuit that I can eventually recognize. I simply have a bunch of "anythings" that I'm supposed to do something with. But I can't do anything with them until I can assign some type of value to them.

Then, it goes on to, I can assign a value to one, but then, how do I know that the value that I assign to the others are going to be the prpoer values to complete the equation?

I gotta run right now, but this is how I'm stuck, if it makes any sense to you guys.....Thanks again. John

[Jeff97FST/A]

(IMG:http://www.frrax.com/rrforum/style_emoticons/default/blink.gif)

Now I remember why I work in restaurants!

(Any my father-in-law has a PhD in statistics - makes for some interesting holiday conversations)

[Crazy Canuck]

I would gladly help... but seems that quite a distance separate us (IMG:http://www.frrax.com/rrforum/style_emoticons/default/sad.gif)
Feel free to send me PMs if you are faced with some issues and need help... I'll gladly help.

[pknowles]

Think about imaginary numbers and real numbers as different directions on a x-y graph. For instance think about real numbers as going from west to east on the x-axis and imaginary numbers going south to north on the y-axis. Sure they are both directions (x and y) but you can't travel in y no matter how far in x you go if you go purely in x. Imaginary numbers and real numbers are the same way, they are related but are a completely different directions. Apples and Oranges are both fruit, but they are completly different. The only connection between imaginary and real numbers that you need to be concerned with at this stage is:
i^2=-1
i^3=-i
i^4=1

If you need help you can e-mail me as well.

[bigshoe]

Ok, Phil obviously knows this better than me, but i'm gonna give try to give you another point of view (to me multiple points of view help me grasp ideas and concepts better, which may be what you would need?) I also second the tutor idea, and if there is a study group that you can go to, do that (not all of us have that luxury though).

I sucked at complex numbers when we did that in precalculus, but i've been out of the loop for a while mathematically, that and the instructor had something to do with it.

I hope this wont confuse you, mathworld (great mathematics resource) has this link: http://mathworld.wolfram.com/ComplexNumberParadox.html which shows a false statement, hopefully that will help?

Now, I busted out my precalc book, and i think they have a decent explanation of the need for the "complex number system" and simply put, the "real number system" cannot compute x^2= -1 since you cannot take the square root of -1 (in order to get x by itself int he first equation, you need to take the square root of both sides). So this is why imaginary numbers were created, merely to be able to evaluate such problems

well, i'm probably better off taking a picture of the book, so here it is, and if anyone has a problem with it, the credit goes to the writers of the book, Tomas W. Hungerford of Cleveland State University, book called Contemporary College Algebra and Trigonometry, published by harcourt college publishers. (sorry, for no proper citing).

(IMG:http://www.members.cox.net/mikic/image1.JPG)

(IMG:http://www.members.cox.net/mikic/image2.JPG)

so I hope that helps, as far as being able to "visualize it" I don't knwo, you need to be able to see that the system was developed to be able to solve what cannot be solved with the real number system, so its what we have in place in the modern world as the solution for those particular problems when you need to take the square root of a negative number.

btw, i really hope i have my info straight, i havent used imaginary numbers since last year,
Miki

[Matt]

Its difficult to complete Engineering if you can't understand Algebra. Everything above Algebra relies on it.

When I started taking classes to get my EE degree, I started with a college Algebra class since it had been more than 10 years since I was in High School, now I'm about a week away from being done with calc3.

The best thing I can recommend is do problems, lots of them until the method makes sense. You don't have to do the difficult problems, just the simple ones at first to get used to it.

My other favorite place to get Math help is SOS Math Help There are some pretty intelligent people on there who can help you understand the most basic math.

[Guardsman]

Miki,
That actually did help....it didn't answer all of the questions (number 5 in the book there doesn't make any sense to me), but I see how the imaginary numbers work now.....That also reminded of something that I've been thinking of trying, to see if it might help....

I remember in school, I if I had a hard time with problems, I would get the answer, including all of the work, and then reverse-engineer, so to speak, and that would help me figure out how to do the problem.

I've been wondering if I might be able to do the same thing with math in general, i.e., start at a very high-level of math, like calc, and then work back from there.

Looking at that one page on that book, it actually makes some sense to me, more than what I seen in algebra books.

I'm going to be trying to test for my math class again (CLEP test for the military), and/or take a class (taking a class if I fail the test), so I'll probably contact you guys on that.

If you don't mind, I'll try and keep this thread going, and start digging up some work, and figure it out on here.

Matt, thanks for that link, I'm also going to check into that.

John

[bigshoe]

I'm glad it helped, I may even post some of my problems now! We are doing Reimann sums and the Fundamental Theorem of Calculus right now in my Calc I class.

about jumping into a class like calculus and trying to get things figured out, i would strongly suggest against it, here is why, I went through precalc and trigonometry getting c's, and my understanding of the concepts was there, but I sucked at doing the math, its something you need to learn by repitition and working problems. Anyways, so far calculus is an extension of algebra, using trigonometry all over it to be able to evaluate equations that change, calc 1 being mostly differentiation and intro to integration, and calc 2 being integration. I find it really interesting, the relationship of position vs velocity vs acceleration (position being like an equation that you're using now, velocity being its derivitave, and acceleration being the derivative of velocity)

now, what i was getting to about jumping into calculus, calc 1, looking back now, is easy stuff, the problem is learning the theorems and identities and memorizing them. the biggest problem I see with it is that there is so much going on in calculus that you need to have your algebra down pat. I hope that doesnt discourage you, it just takes practice, and for what its worth, i havent seen imaginary numbers used yet. If you will be taking a regular calculus class (unlike business calculus), there is gonna be alot of trigonometry, and you need to have an understanding of the unit circle and the classic triangles (45-45-45, 30-60-90, 60-60-60), and you'll see another measurement system pop up (it's kinda necessary in calculus) called RADIAN MEASURE, as opposed to what your using now called cartesian coordinates or the x-y plane or whatever its called, the reason is because you will be working with circles, and things that oscillate (if you've dealt with sine waves or anything like that you might know something about this?). So with the pace of the class in universities, I don't think its a good idea to go into calculus right away, I feel will be really easy to give up? take it slow man, thats all you need, practice and take it slow.

Now, for the working backwards thing, I do agree with you there, when it comes to learning math and such, for me it really helps to know how the math will be used in the future, and therefore you can kind of tailor how you approach learning it from an understanding perspective. Its kind of like seeing the end result and then making a direction to approach it, instead of blindly being fed information, not knowing how you will be using it in the future.

But there is one thing for sure, to succeed in the later courses you need a good understanding of how math works, if you can accept that math requires a "type of thinking" and put yourself in that mode, things will get logical mathematically, and you will be able to "read and comprehend" it by looking at a theorem, just like you say you have by looking at formulas. My current instructor preaches on "math speak" if you talk and think mathematically, mathematical ideas will be understood easily and quickly.

i'm no master of anything, but to succeed in this you need to do the following:
1. study and study consistanly
2. ask questions as often as you can
3. don't get pissed when you cant figure something out, I remember reading you have to be "humble" in order to learn, otherwise your attitude rejects learning
4. don't get behind, its harder to catch up

I did #4 alot, and thats why i'm struggling with C's at the moment, i suffer from procrastination.

Ok, sorry for the long post, but I hope it helps and doesnt discourage you, it takes work.

btw, to explain the 5th property of the complex number system that you asked about, it just means that

a+bi = c+di whenever the quantity a=c AND the quantity b=d.
what I think they are trying to show here is that i really isnt a variable, and that the two equations are the same, you may run into something like that if you are given two equations, and you can prove that a=c and c=d, so then if you cannot find the value of any one variable (a,b,c,d) that you can use that property to say its equal since this property says it is.

Miki

[sgarnett]

One thing that I find very useful when working through a complicated "application" problem is to be very rigorous with the units. It can help keep you on track and validate the answer. For example, if you are expecting an answer in pounds (or whatever) and you end up with inches, you made a mistake along the way. Looking back through your steps, everything after the last instance of "pounds" canceled out is wrong. The actual mistake may be even earlier, but that will help narrow it down. I also helps keep things making sense along the way.

Let's say you want to know how far (in feet) the of the car will rise while braking if 400 pounds is transferred to the front wheels. Let's assume the effective spring rate at the wheels is 100 pounds/inch. There are two springs acting in parallel, one per side.

RISE(feet) = (400(pounds) / (2 * 100(pounds/inch))) * (1(feet))/12(inches))
RISE(feet) = (400/200) * (pounds / (pounds/inch)) * (1/12) * (foot/inches)
RISE(feet) = 2 * (1/12) * (inch) * (foot/inches)
RISE(feet) = (2/12) (feet)
RISE(feet) = 0.167 (feet)

First of all, notice that the units match on both sides of the final equation. That's a good sign that the answer might be right. Second, it's early and I haven'r had much coffee. I did NOT just recite that first equation from memory - I used the units. I knew if I was starting with a force in pounds and a rate (also known as a derivative) in force per distance and wanted to end up with distance, then I had to divide so that the units of force would cancel. Similiarly, looking at the units tells me whether I need to multiply the result in inches by feet/inches or inches/feet. If I want inches to cancel and leave feet, it better be (inches) / (inches/feet). Without the units, it's easy to multiply when you should divide, etc.

OK, that's a pretty simple example. You probably coulds arrive at the same answer with just a calculator and common sense. However, note two things:

1) The units are treated as actual terms in the equations. They follow the same rules.
2) The units look an awful lot like the symbols in textbook algebra, don't they?

In fact, the following is perfectly valid:

feet = (pounds / (pounds/inch)) * (feet/inches)
feet = (pound/pound) * inch * (feet/inches)
feet = (inch/inch) * feet
feet = feet

So, the practical application isn't really all that different from the "textbook" stuff.

[CMC#5]

John, I would suggest you hook up with a buddy from class or a tutor. I had one hell of a time my first year in Mech E undergrad until I found some friends I could study with. You just can't teach yourself engineering IMHO (well, the vast majority of us can't anyway). Just like its happened in this thread, when you discuss the problem with someone, the both of you understand it better.

[Guardsman]

Al,
I agree with you, but, 1) I'm not in school yet, and I'm not sure when I'd be able to start for sure, and 2) I want to make sure that I have a good understanding of this stuff before I start school.

I think that I may be a bit cynical about how much I expect to actually learn in school, after my previous experiences. I expect to learn more before, outside of, and after school, than I expect to learn in the classroom, unless I happen to get lucky and get an exceptional teacher.

So, for me, by my thinking right now, engineering school is a very expensive, very time consuming problem that has to be endured if I want my degree.

I would rather get a job, and learn on the fly, as I learn very well that way. Unfortunately, nobody hires a wanna-be engineer to be trained and schooled on the job (IMG:http://www.frrax.com/rrforum/style_emoticons/default/blink.gif)

I'm going to dig up some books here, and start working on problems, which I'll post up here. You guys can be my study group (IMG:http://www.frrax.com/rrforum/style_emoticons/default/thumbup.gif) . (That's be doubly good, because then my wife couldn't complain about me spending all of my time on here (IMG:http://www.frrax.com/rrforum/style_emoticons/default/biggrin.gif) )

John