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[Christoff Yurievich]

I swear I did this exactly like the book said to, but my graph for this derivative is not matching what the calculator says the graph should look like.

ln (x/(x^2+1))

ln x - ln (x^2+1)

(1)*(1/x) - 1 (x^2+1)*(2x)*(1/(x^2+1))

(1/x) - ((2x)(x^2+1))/(x^2+1)

(1/x) - (2x)(x/x)

(1-2^x)/x is what I get for the derivative.

 

[Aruarian Reflection]

You made an error going from this step to this step:

ln x - ln (x^2+1)

(1)*(1/x) - 1 (x^2+1)*(2x)*(1/(x^2+1))

 

[Christoff Yurievich]

how? I know the first half is right (not much to screw up with only an x) but the second half seems correct. I took the power of the sum and put it in front (1), I put the sum in parentheses(x^2+1), I took the derivative of the sum (2x), and then I put the sum under 1 (1/(x^2+1). Isn't that what you're supposed to do?

 

[nitewulf]

not a product rule.
just find the derivatives of both terms seperately.

 

[Christoff Yurievich]

oh, so I have to use quotient rule to get the first half, and then multiply by 1/(x/(x^2+1)) right?

 

[WHOAguitarninja]

No quotient rule. If I'm reading this correctly, you should just be using the chain rule, which is derivative of the outside multiplied by the derivative of the inside. which would be 2x/(x^2+1)

So the total derivative should look like (1/x)-(2x)/(x^2+1)

 

[Bishman]

Good thing I changed my schedule so I will not have to take calculus.

 

[nitewulf]

ln(x) - ln(x^2+1) isn't a product. it is just a difference. you can seperate the individual terms and find their derivatives.

ln(x) => 1/x
ln(x^2+1) => 2x/(x^2+1)

resulting in => 1/x - 2x/(x^2+1)
and then you can use tricks to combine the terms or whatever is required.

 

[WHOAguitarninja]

Good thing I changed my schedule so I will not have to take calculus.

It's really not bad once you get the hang of it.

 

[Bishman]

It's really not bad once you get the hang of it.

Don't feel like taking it my senior year.

 

[Christoff Yurievich]

I am left wondering why the example in the book was set up the way I did it the first time. Well, at least I kind of figured it out on my own. Thanks for the help.

 

[fallout]

I am left wondering why the example in the book was set up the way I did it the first time. Well, at least I kind of figured it out on my own. Thanks for the help.

A lot of textbooks use methods and steps that they figure would help you understand. Unfortunately, if it doesn't match up with how you learned, or where your strengths are, chances are, it'll probably just confuse you.

Worse yet, the example may contain something that might not be entirely accurate, but is thrown in for some half-assed pedagogical reasoning. Chances are, it'd make sense to you if someone explained why they did it, but without knowing, you could just be learning something that could turn into a bad habit.

 

[GaimeGuy]

A lot of textbooks use methods and steps that they figure would help you understand. Unfortunately, if it doesn't match up with how you learned, or where your strengths are, chances are, it'll probably just confuse you.

Worse yet, the example may contain something that might not be entirely accurate, but is thrown in for some half-assed pedagogical reasoning. Chances are, it'd make sense to you if someone explained why they did it, but without knowing, you could just be learning something that could turn into a bad habit.

I hate how some of the books give these long, wordy explanations for different theorems and processes.

And Rolle's Theorem is the stupidest thing I've heard in calculus

 

[truffleshuffle83]

calc 1 is cake. calc 2 sucks, but wait till diff eq

 

[WrathOfOtaibah]

calc 1 is cake. calc 2 sucks, but wait till diff eq

Damn, I have to do those classes in that order

 

[truffleshuffle83]

my schools on quarters so i had calc 1-4 then diff eq. that was a couple years ago though.
if youre goin for engineering just be sure to fully understand diff eq, especially laplace tranforms

 

[WrathOfOtaibah]

Yeah, I'm in Engineering. At least I don't have to mess with Calculus 3.

 

[truffleshuffle83]

calc 3 is actually the easiest i thought. mine was like vector calculus, partial derivatives and the like. fairl easy in comparison to calc 2. i wish i would have paid more attention in calculus, it would have made all my signal processing classes much easier

 

[fallout]

I hate how some of the books give these long, wordy explanations for different theorems and processes.

Eh, after time, you might learn to appreciate those. Theorems especially. In my discrete course, we ran through the last few sections incredibly fast and while trying to study for the final, I noticed that while the prof was accurate, he wasn't very precise. That is to say, nothing he did was wrong, but it wasn't very clear.

Really though, if all else fails, there's always Wikipedia for trying to understand theorems.

And Rolle's Theorem is the stupidest thing I've heard in calculus

I don't even remember that one.

if youre goin for engineering just be sure to fully understand diff eq, especially laplace tranforms

Heh, this is really good advice from what I've heard from physics profs. Do engineers have to take PDEs at your school?

 

[WHOAguitarninja]

calc 3 is actually the easiest i thought. mine was like vector calculus, partial derivatives and the like. fairl easy in comparison to calc 2. i wish i would have paid more attention in calculus, it would have made all my signal processing classes much easier

Yup. I'm taking calc 3 now and it really isn't conceptually difficult at all. Theres some things that are easy to make stupid mistakes on because they involve alot of steps, but as far as the methods themselves being difficult, they're not. It's like calc 1 with a few extra terms.

 

[truffleshuffle83]

no PDE's thank god, we covered it a little bit towards the end. luckily the majority of my diff eq was spent in the s-domain, so it made it much easier. the prof was like, just know laplace i dont really care about the rest because this is all you need

 

[fallout]

no PDE's thank god, we covered it a little bit towards the end. luckily the majority of my diff eq was spent in the s-domain, so it made it much easier. the prof was like, just know laplace i dont really care about the rest because this is all you need

Heh, in my computational physics (2nd year) course last semester, the prof was using some PDEs in a problem. The following little conversation ensued:

Prof: Well, the 3rd year engineers taking this will know how to do PDEs, but for the rest of you, just trust me on it.
Eng: We uh ... don't have to take PDEs.
Prof: ... engineers don't have to take PDEs? That's insane[/i[! ... oh, I'm sorry, I shouldn't be saying such things.

 

[truffleshuffle83]

im EE theres no need for PDE's, but i do use Laplace on a daily basis.

 

[goodcow]

It's really not bad once you get the hang of it.

Who actually makes use of calculus besides engineers?

 

[fallout]

Who actually makes use of calculus besides engineers?

Well ... physicists and mathematicians. It has plenty of applications in chemistry and economics as well (though you really don't need to know it as well).

 

[truffleshuffle83]

id imagine architects use it to an extent as well

 

[nitewulf]

calc 1 - easy
calc 2 - too much to memorize, and the infinite sums/series part is difficult
calc 3 - easy
diff eq - easy
matrix algebra - too much to memorize, but actually pretty easy

in my school they didnt teach us laplace and fourier transforms in the math classes, we actually learned them during circuit analysis, control theory and DSP courses. and we did learn PDEs on the diff eq course.
true shuffle, dont you take electromagnetics? you have to perform PDEs for maxwell equations and switching back and forth from 3d magnetic and electric fields, of course EEs have to take PDEs.

 

[nitewulf]

Yeah, I'm in Engineering. At least I don't have to mess with Calculus 3.

what

 

[Aruarian Reflection]

Well ... physicists and mathematicians. It has plenty of applications in chemistry and economics as well (though you really don't need to know it as well).

^^

Yep. I worked in a bioinformatics lab last year and I used calculus ALL the time. Calculus is the most basic tool in a variety of fields... I would recommend understanding it fully.

 

[truffleshuffle83]

nitewulf yeah youre right about the PDE's and emag. right now im doin field theory so "i" dont do much of anything, but i sure put a strain on MATLAB, the best program ever made. aside from emag theres not much else in EE that you need it for. im takin alot of communications classes as well so im mainly just using FOURIER all day every day

i know at our school alot of engineers, and cs majors only have to go up to calc 3 and no calc 4 is necessary, so im sure on a semester schedule they omit calc 3 since it is essentially the same as a quarters schools calc 4

 

[nitewulf]

basically proves a suspision i had as to my schools engineering curriculum being the most rigorous there is. two electromagnetics (we had to do PDEs in the final by hand BTW, two kids were thrown out for cheating), one thermodynamics (which we really dont need. at all. ever. hottest professor ever though...i'll post her pic if i find it), two semiconductor devices (basically quantum mechanics), two electronics (this is more akin to the regular op-amp/transistors/diodes course), and the rest i think matches the regular EE curriculums of other schools.

yes, i found her picture!

THAT is my thermodynamics professor. can you believe that? how do you concentrate exactly?

 

[NotMSRP]

That's hot?

 

[nitewulf]

well, real life isnt exactly a james bond movie...real life wise, yeah.

 

[truffleshuffle83]

we dont have much for semiconductors, and not much PDE's by hand but everything else is the same. then we branch off our senior year in focusing on controls, signal processing, digital circuits, or emag. did you have any microprocessor based system design with the fun motorola hc-11 chip. terrible terrible class imo.

 

[Aruarian Reflection]

basically proves a suspision i had as to my schools engineering curriculum being the most rigorous there is. two electromagnetics (we had to do PDEs in the final by hand BTW, two kids were thrown out for cheating), one thermodynamics (which we really dont need. at all. ever. hottest professor ever though...i'll post her pic if i find it), two semiconductor devices (basically quantum mechanics), two electronics (this is more akin to the regular op-amp/transistors/diodes course), and the rest i think matches the regular EE curriculums of other schools.

What school is this? I think my engineering curriculum is the most rigorous, but that's because I'm a biomedical engineer at Johns Hopkins, which is ranked #1 in the country in this department.

 

[truffleshuffle83]

i was BME, god that was hard, in one quarter i was scheduled to take
organic chemistry
diff eq
physics 2
and anatomy
all with lab
i switched to EE that quarter

 

[nitewulf]

yeah our senior year was also based on whatever you wanted to focus on (i did power systems and control theory). i did take one microprocessor design elective (aside from the two required digital courses)...we used the 8 bit motorolla CPU. i forget whats the actual designation, im not into digital too much, took it cause it just fit my schedule. im an analog guy.

edit:
snowwolf, my school is The City College of New York. its not very highly ranked but very rigorous and old school. i graduated from a specialized high school so most my friends ended up in ivy leagues, so i sorta knew that even in MIT they had an easier curriculum. our school is just difficult since its a public school, they want students to drop out. as opposed to say, MIT, where students pay a lot of money (either way the college gets paid a lot from some source or other) so they want you to stick around. that was my ongoing theory anyway.

 

[truffleshuffle83]

are you still in school? im contemplating getting my masters after i graduate, but i think i want to work for a year or so before i get back to it, im tired of school

 

[nitewulf]

are you still in school? im contemplating getting my masters after i graduate, but i think i want to work for a year or so before i get back to it, im tired of school

i graduated and am working as a design engineer for a power company.
yeah, you should definitely get a job if you could find one. believe me.
i actually recently got accepted into the biomed program at polytechnic university (nyc)...but ill deffer that a year and switch to EE. work experience is very important, unless you wanna just get a PhD and teach.

 

[truffleshuffle83]

yeah thats what i figured, im looking forward to getting a job. i live in dayton and the Air Force Base hires a ton of engineers here so it shouldnt be to hard to get a job, plus the job security will be awesome

 

[Suranga3]

I'm in EE aswell, I'm half way done getting my degree as of yesterday. I only have two more years left, and I'm only 19. For you guys that finished, how's the job market been like for you? How seriously do employers take your marks? Also, how strongly would you guys recommend getting a MSc or a M.Engg?

 

[WrathOfOtaibah]

what

I don't have to take Calculus 3 but I do have to take 1, 2, and Differential Equations.

physics 2

How is that class? A lot of people hate it and last semester, supposedly the cutoff for As was a 70%

 

[teiresias]

For an EE I feel I'm pretty weak at math above plain calculus. In fact, the only C I ever got in college was in my diff eq class. I think that was really the bad thing for me as math had been pretty simple for me up until that point. However, the professor in that class had a VERY thick accents, one of those accents that is so thick it wears you out trying to just understand him, so I was always exhausted by the end of the class and was concentrating more on understanding him and getting the right notes down than on learning the material.

So of course, my signals courses sucked as a consequence, :lol. However, my school at the time was teaching the signals material in one semester that most schools teach in two, so it was doubly a pain in the ass. I, as a consequence, loathe signals (though I know enough about aliasing, etc. to properly sample and low-pass filter my data samples), and made sure to do the computer engineering tract (so I've never had microwaves and photonics or that kind of thing), and now focus on small, digital embedded system design and am writing my thesis on an area of infrastructure network security. No diff eq for me!!

 

[GaimeGuy]

Rolle's theorem is basically this:

If the points (x1,y1) and (x2,y2) are defined so that y1 = y2, then the slope of the secant line between the two points is 0.

Yes, that's Rolle's theorem. A horizontal line = slope of 0.

 

[truffleshuffle83]

physics 2 for me was the hardest becuase it was all fields, magnetic electrical, and its hard to understand conceptually.
edit* coincidently i chose emag to focus on, go figure

 

[Dilbert]

Rolle's theorem is basically this:

If the points (x1,y1) and (x2,y2) are defined so that y1 = y2, then the slope of the secant line between the two points is 0.

Yes, that's Rolle's theorem. A horizontal line = slope of 0.

That is INCREDIBLY wrong.

It's been a while, but let's see if I can do this from memory: For a continuous, differentiable function f(x) on the closed interval [a, b] such that f(a) = f(b), there is at least one point c in [a, b] for which f'(c) = 0.

In more plainspoken terms: If you have two points on a function with the same y-value, there is at least one (local) extremum between those points, or the function is trivially constant.

 

[GaimeGuy]

That is INCREDIBLY wrong.

It's been a while, but let's see if I can do this from memory: For a continuous, differentiable function f(x) on the closed interval [a, b] such that f(a) = f(b), there is at least one point c in [a, b] for which f'(c) = 0.

In more plainspoken terms: If you have two points on a function with the same y-value, there is at least one (local) extremum between those points, or the function is trivially constant.

Well, yeah, but still, it's fucking LOGICAL that that's true. You don't need to be some super mathematician to be able to think that. That's why I say it's so fucking stupid.

 

[Dilbert]

Rolle's theorem is used in the proof of the Mean Value Theorem, which is one of the most important theorems in all of calculus. Yes, it may seem intuitively obvious to you, but intuition is not PROOF.

 

[fallout]

(...) but intuition is not PROOF.

Sadly, neither are purdy pictures ... as I once learned on a calc test.