Elementary Linear Algebra for Engineering

Ozrat

Ozrat

Antediluvian as Feck
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How do you study best for this course? I find the following to be my best method of learning in this course. It takes a lot less time than the "read it and learn it" method, gives me the same amount of pain and discomfort, and also gives me roughly the same grade anyways.

Ozrat studying for Algebra

What do you do to study for math?

P.S. Do not mention Diagonalization and Eigenvalues to me unless you want similar treatment with my shoe.
 
Well, I don't have an Engineering course yet, but I usually take the 'pretend to read it, doodle in your notebook, and learn it somehow anyway' method for elementary linear algebra. It got me a good 3.96 in the class last year. I still don't know how. I only did half of my homework and never studied, but I did pass all my tests, except, like, one, but the whole class failed that one, so we all retook it, and then I passed, so it balanced out somehow. I think. Maybe I studied while I was seriously wasted and just don't remember any of it... and perhaps that's how I lost my pants as well...
 
Ok, I failed this course twice already (cries pathetically) so I can tell you which topics should you watch out for.

Matrixes and Lineal Equations are just delicious cake. The last topics where you input numbers. Easy, so take the chance to learn Gauss, Gauss-Jordan like the back of your hand. Practice a lot of inverting matrixes with the cofactors method as it is VERY annoying, long and prompt to lead you to mistakes.

Vectorial Spaces. I hate this topic and every teacher, person, book, neuron where this is mentioned. You have to do algebra without numbers and variables. This is the most BULLSHIT I have studied. Confusing as hell.

Lineal Transformations. *VOMITS*, sorry about that. Take vectorial spaces and add graphs, derivatives, integrals and whatnot. I hate this subject. Understanding what the fuck is the professor talking about is crucial to success. Don't give up and you should scrap a good grade.

I don't know if Lineal Algebra in your countries is taught like this and is that your girlfriend in that pic Ozrat? She looks like a fun person to have around.
 
Hrmm.

I haven't actually been to my Algebra lectures for almost two months now because of how shitty the professor is. He's Asian and barely speaks any English. He writes every single f-ing word that he says on the board. So... he... teaches... like... this... Anyways, just trying to understand it during the actual lectures without already know the subject material is just pointelss because it makes absolutely no sense. I just study the book on my own time now right before the tests. The tests are about two to three weeks behind the material, so I have absolutely now idea what bullshit Mr. Prof is spouting out right now.

Engineering math is harder than an old man on viagra at any decent school, so don't feel left out man.

Is she my girlfriend? Wouldn't you like to know? :P

P.S. Ratty, don't you have any comments about your linear algebra experiences?
 
Apparently my prefered method of studying for Algebra has paid off...

I just checked the last two tests I had taken. The first time I took Test #1, I recived a 11/20. Not being satisfied, I rewrote the test last week, earning me a 15/20 this time. Hrm, 75% is actually a score that I quite enjoy!

I also took Test #2 last week. I had studied most of the required reading, leaving out the section regarding eigenvalues, eigenmatrices and their respective diagonalizations. Well, 25% of the second test dealt specifically with this section of the book. I had puzzled over the other 75%, but had finally been satisfied with the results that I had worked out with nothing but my pencil, ereaser and brain. I then tackled this mysterious 25% of the test that was sure to be doomed. I had covered about two pages of the section in the book and looked over two of the example problems, so I had *some* idea of how eigenvalues worked in an equation form. In other words, I sorta know how they work, but I don't know what they ARE. Anyways, I attempted to solve the problem using some clunky method that I had seen in the book. After about going about what I would guess to be halfway through the problem, I gave up because I had no clue what was going on there. I looked at the problem again, put it into the simplest terms possible.

The question asked us to prove that if & is the eigenvalue of any square matrix A, then we need to prove that 1/& is the eigenvalue for the inverse of A.

What I got looked something like this:
(& is the symbol for an eigenvalue that I made up because I don't really want to looking to the keyboard map just to find something that looks more like the real thing)

&X=AX

The work:
(A^-1)&X=(A^-1)AX
&(A^-1)X=IX
(A^-1)X=(1/&)X

The answer was the last line. Of course, if you've done elementary linear algebra, you'll know that the rules of dealing with matrices is practically never this easy to deal with. But this was the only thing that my desperate mind could come up with having no real prior experience working with eigenvalues. I just had to be satisfied with this method because it would at least make it look like I had been fooled by the question rather than just being ignorant about how to solve such a complex thing like proving the associated eigenvalue of an inversed matrice.

Like I said before, I just got back from getting my test results and it was 20/20 for Test #2! What? 100%? How in holy engineering math heaven did I get a perfect on this test? I thought I was screwed on the questions I did have a clue how to solve!

It just goes to show you how crazy, yet perfectly rational and easy, math can be sometimes. Here I was trying in vain to solve it using complex engineering methods when I could just do some two-bit algebra that I learned in high school!
 
Get a decent HP calculator that can handle matrix algebra and you should be set. Of course you will have to learn RPN which is somewhat of a pain. In College I had the option of Linear Algebra or Statistics so I chose Statistics. And in an advanced Structural Analysis class we touched on Linear Algebra but had the calculator as a crutch. The basics are pretty simplistic but are time consuming. Better work for a computer IMO.
 
I think you're missing the point. We *can't* use calculators for this class. We're learning *how* to do this kind of math. In fact, the *only* calculator that's allowed to be used at my school is the Casio FX-991MS. That is, of course, assuming that we can use calculators in the course at all.

According to the stats for the Casio X-991MS, it's ideal for ages 11-16+. It's a high school level calculator that we use because we actually have an emphasis on learning the material in our math courses rather than just knowing how to throw a bunch of commands into a calculator. As you'll notice, there's absoulutely no memory for programing or anything in these babies.

I mean, c'mon, I had a better calculator than this for high-school! But then again, all I did was just put games on it to play during class to make it look I was doing homework rather than having my teacher make comments about me being a procrastinator all the time. Eh, she still did call me a procrastinator, and I did deserve it, but I still got the highest marks on all the tests despite the fact that some of the others used notecards to help them and I didn't. If I hadn't gotten so many late marks taken off my assignments, I probably would've gotten the highest marks in those classes.

You're right, this is work that would be better off being done by a computer. However, in order to tell a computer to use them, we need to know how they work. This is especially true for the engineering field as a lot of the time we'll be programming computers to do stuff for us. If we can't do it on paper, then how are we going to tell a computer to do it?

Ratty, I still haven't heard from you about your Algebra experiences. Aren't you required to take this for engineering over there?
 
Yep, I had Linear Algebra in first semester of the first year, I have B in it. It's generally considered to be one of the easier subjects, though many people have problems with it, simply because it's difficult to comprehend some areas of it, especially n-dimensional vector spaces and quadratic forms. Seeing how you aced your test, though, I figure you'll have no problems at all.

In my opinion, Ozrat, you should learn linear algebra well, because it's heavily applied in electric engineering (the only way to calculate complicated electric grids, especially those that involve alternating current, is with help of matrices), in advanced maths (you need to have a good understanding of vector calculus and linear operators), but also for programming. Of course, many linear algebra books tend to go into unnecessary detail. For example, you don't have to know anything about Jordan form, unless your professor insists (like mine did :( ).

That's all advice I can give you regarding lin.alg. Don't rely on my experiences, though, because you won't do so well. :P During the semester, I didn't attend a single class in lin.alg. and I started studying it seven days before the exam. After reading 200 pages of theory and doing another 200 pages of exercises, I discovered I would never be able to learn everything there is to know about quadratic forms. Nevertheless, I took the written exam and got an A (I even helped the guy sitting behind me get a C! :mrgreen: ), but I still had the oral examination. Normally that's the easy part, but my professor happened to be a bitch. She gave me six questions and I spent and two f***ing hours answering them. Though they were all relatively easy (1. planar equations in vector and scalar forms, including sketches, 2. solve a simple non-homogenic system of linear equations using Gauss method and prove the Gauss method 3. show that if k is dimension of KerA and r is dimension of ImA, k+r is dimension of vector space X (where A:X->Y), 4. Vandermonde's determinant, 5. prove that symmetric matrix can be diagonalized, 6. reduce a quadratic form to orthonormal basis), I didn't know how to do 6 because of my lacking knowledge of quadratic forms. So she lowered my grade to B! Thank God I'll never have to study that shit again. :eyebrow:

P.S. You get to use a calculator during tests?! You get to rewrite a test if you screw it up?! Damn, I wanna go to your college! :D
 
No no no, you misread it. You can use a calculator during a test IF they allow it. They don't allow it for Engineering Calculus I or Engineering Elementary Linear Algebra I. I do know that they allow it for Eng. Calc II however, but that's because they make the numbers too difficult to work out by hand in that course. Well, you could work them out, but that's not what you're being tested on now, is it? I'm not sure if you get to use a calculator in Linear Algebra II, but I'll find out next year when I take it. Actually, last year was the last time that they had Linear Algebra II as a required first year course. The faculty finally realized that its too advanced for first year students and that not every field uses that shit anyways. I lucked out by deciding drop it and to take Algebra this year instead. Damn, I'd hate to have already taken that stuff for no reason.

As for the rewrites... Yeah, the engineering faculty here allows students to rewrite their Calculus and Algebra tests. I mean, c'mon, they only have four, yet difficult, questions on them. And each test is worth 15% of your final grade. If you screw up on just one of them, you just lost about 4% of your final grade for the semeister. This started about five years ago or so here because too many students kept failing the tests because they were too far behind in their math studies while trying to keep up with chem, physics, c-programming, drafting and designing, an elective, the other math class... Well, you get the idea. The students did know the material and they kept failing. Personally, I think its a good system because sometimes when I've put my best effort into knowing and understanding the material, I've still done poorly on a test while other times when I completely skip a section of the book because I didn't have enough time I end up acing the test. It just balances out the score better.

As for not attending your algebra lectures... :naughty: I'm just kidding here. Actually, I haven't been to any of my algebra lectures since about the second week of this term. I just didn't learn anything from them and I figure I could be wasting that time doing more enjoyable things. Like posting here. I was just amazed last year how so many students just stop attending their math courses in engineering. You don't learn it from hearing about it. You only learn it by sitting down and hitting the books for hours at a time. What was originally over 200 students in my first calc lecture last year dwindled down to less than 20 by the end of the first term. Calc II had most of the students showing up again at the beginning, but then dropped down to about 10 by the end of that term. I only know this because I attended most of the first term and about half of the second term. I showed up to a couple of the final lectures and felt kind of imposing because the prof obviously knew I hadn't been there for a loooong time. :lol: Just imagine ten students randomly dispersed over the seating area for 200 people. Yeah, that was a really welcoming sight... :roll:
 
Hehe, that just goes to show you why we needed the rewrites.

During Calc I I rewrote all of the tests and probably got about a 65% average. I don't think that the final went too well, but I still passed the course with a D. I was happy that I passed and that was all I needed.

Second term comes around with Calc II and I study harder this time. Once again I ended up rewriting all of the tests and getting a 65% or so average. The final for this one, however, was quite brutal, to say the very least.

I ended up getting a big fat F on my report card for the course. However, about a week later I got an e-mail from the Engineering I department stating that all the finals for Calc II were being reviewed in light of so many students failing the course. I finally get my revised grade back in July and it was a D- this time. Believe it or not, I jumped with joy that day! Thank god I'll never have to take that course again.

That's why we have rewrites here at Mac. Nobody would still be in engineering if the profs didn't take pity on us once in a while. Standards weren't lowered, but the way we got graded changed, that's all.
 
Damn, our college really needs rewrites. If we had them, maybe there wouldn't be 80% people flunking Electronics and Programming. Maybe two thirds of 1st year students wouldn't leave the college if there was a possibility of passing Math II. Everything would be so much easier if there weren't so damn many things to know! For example, in Electronics I you have to know three books, 500 pages each, by heart, and that's one semester only! WHY?! And it's only one damn course!

Phew. Sorry about that, just blowing off some steam.

Whoa, Ozrat, is that really you on that picture? But, um, why are you disguised as human? :P
 
Yes, it's me. As you can see, the very contact of the book on my body is enough to bring cries of pain out of my poor body. You should hear me when it's completely embedded up my bum. :cry:

I have a scan of a diagram in the book that I want to post here, but I'll need to bug Kharn hard enough so he'll host that for me as well. And possibly an example problem or two.

/me starts pulling on Kharn's sleeves to get his attention.

Can you believe that they introduced eigenvalues in the third chapter of this book? Damn, that's heartless!
 
Gah-dammit, there is a lot of Gingerbeers here.

Matrices are alright, but if you really want to take the cake you need to start looking at your partial diffs, series and transforms. The only thing hard about matrices is you often stuff em up when writing them down. You end up with pages full of one matrix... yeugh!

Nothing quite like taking the integral in the period domain of the natural logarithmic to the power of the function.
 
I did partial differentials last year. Yay for multivariable calculus! :wall:

I actully enjoyed series even though I never did too well on the tests for series. I'd get the concepts, but then always screw up on the calculations somewhere.

I probably blocked transfroms out of my head as I recognize the name but I have no recollection of what they actually are.

Beer. An engineer's best friend. IF they have the time for it.
_______________________________________________________
You Might Be An Engineer If...
  • You have no life - and you can PROVE it mathematically.
    You enjoy pain.
    You know vector calculus but you can't remember how to do long division.
    You chuckle whenever anyone says "centrifugal force".
    You've actually used every single function on your graphing calculator.
    It is sunny and 70 degrees outside, and you are working on a computer.
    You frequently whistle the theme song to "MacGyver".
    You know how to integrate a chicken and can take the derivative of water.
    You think in "math".
    You've calculated that the World Series actually diverges.
    You hesitate to look at something because you don't want to break down its wave function.
    You have a pet named after a scientist.
    You laugh at jokes about mathematicians.
    The Humane society has you arrested because you actually performed the Schrodinger's Cat experiment.
    You can translate English into Binary.
    You can't remember what's behind the door in the engineering building which says "Exit".
    You have to bring a jacket with you, in the middle of summer, because there's a wind-chill factor in the lab.
    You are completely addicted to caffeine.
    You avoid doing anything because you don't want to contribute to the eventual heat-death of the universe.
    You consider ANY non-engineering course "easy".
    When your professor asks you where your homework is, you claim to have accidentally determined its momentum so precisely, that according to Heisenberg it could be anywhere in the universe.
    The "fun" center of your brain has deteriorated from lack of use.
    You'll assume that a "horse" is a "sphere" in order to make the math easier.
    The blinking 12:00 on someone's VCR draws you in like a tractor beam to fix it.
    You bring a computer manual / technical journal as vacation reading.
    The salesperson at Circuit City can't answer any of your questions.
    You can't help eavesdropping in computer stores... and correcting the salesperson.
    You're in line for the guillotine... it stops working properly... and you offer to fix it.
    You go on the rides at Disneyland and sit backwards to see how they do the special effects.
    You have any "Dilbert" comics displayed in your work area.
    You have a habit of destroying things in order to see how they work.
    You have never backed up your hard drive.
    You haven't bought any new underwear or socks for yourself since you got married.
    You spent more on your calculator than on your wedding ring.
    You think that when people around you yawn, it's because they didn't get enough sleep.
    You would rather get more dots per inch than miles per gallon
    You've ever calculated how much you make per second.
    Your favorite James Bond character is "Q," the guy who makes the gadgets.
    You understood more than five of these jokes. :rofl:
    You make a copy of this list, and post it on your door (or your home page !)
 
Have you got into vibration analysis yet? This is pretty cool because this is where you start applying some of this high end algebra that you learn. The other one is FEA and CFD where you apply a lot of your high end matrix algebra.

Have you used the program called Matlab yet? This is a marvelous engineering program that allows you to numerically solve differential equations, work directly with matrices, solve response equations directly, generate bode plots, etc. I always wanted to get a pda with it on but there isn't a version for Windows CE. Woulda been so cool in exams, much better than HPs.
 
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