http://en.wikipedia.org/wiki/Integration_by_parts

   L - Logarithmic functions: ln x, logb x, etc.
   I - Inverse trigonometric functions: arctan x, arcsec x, etc.
   A - Algebraic functions: x2, 3x50, etc.
   T - Trigonometric functions: sin x, tan x, etc.
   E - Exponential functions: ex, 19x, etc.

You probably learned something like it. I hope. Otherwise I now understand why integration by parts makes no sense...

You're already familiar with the concept of selecting a u and dv, correct? Since integration by parts is used when you have two functions multiplied together in an integral, you need to select one to be u, and one to be dv.

Now, which one should be u and which should be dv? If you select wrong, you can make life miserable. Select right, and it's not all that bad.

In order to select u, use the LIATE rule. It stands for (L)ogarithms, (I)nverse trig, (A)lgebra, (T)rig, and (E)xponentials

If you have an integral that needs to be integrated by parts, like (int) xe^x dx, first notice that you have two functions: X and e^x. Which to select as u and which as dv?

This is where the LIATE rule comes in. You have an algebra function (x), and an exponential (e^x). Since Algebra comes before Exponential, select x as your u.

If you had a log and a cos, for example, you'd select log as your u, since it shows up first in the LIATE list. From there, the other function is dv.

So, we have (int) xe^x dx. We have selected x as our u-value. e^x becomes our dv.

u = x
du = dx

dv = e^x dx
v = e^x

Now, plug in to [uv - (int) v du]

xe^x - (int)e^x dx

Calculate the (now easy) integral, and your final answer comes to be...

xe^x - e^x, or e^x(x - 1), whichever form you prefer.

Without the LIATE rule, or something like it, integration by parts will make little or no sense. (I.E. how does this simplify the integral at all?!)

If we DIDN'T use LIATE, and decided to make e^x our u-value, the following would happen:

u = e^x
du = e^x dx

dv = x dx
v = 1/2 x^2

uv - (int) vdu would become -->  1/2 x^2 e^x - (int)1/2x^2 e^x dx

Notice how our integral went from (int) xe^x to 1/2x^2 e^x dx... We're getting nowhere. In fact, our integral just got more difficult

Use LIATE, it's a life saver

That makes a ton more sense.  My professor never went over LIATE, at least not explicitly.  I don't even recall seeing it in the Khan Academy videos I watched trying to make sense of integration by parts.  What we were told was basically choose u such that the derivative is simpler than the original function.  I guess that kind of boils down to LIATE, but it's kind of ambiguous and having a n explicit rule makes it so much easier.

I'm glad it helped. The somewhat arbitrary rule of selecting a u such that the derivative is simpler does, in a way, boil down to LIATE, but an explicit rule does help. Try telling your professor about it. If they haven't heard of it, you may get some brownie points. If nothing else, it will help that professors future students understand it a bit better.


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Interesting way of teaching it.  I would always just pick what looked easiest, then redo it if the expression became more complicated after integrating by parts.  After a while you can pick out the patterns and almost always pick the correct u and dv.

Alright, as a proud Industrial Engineer (BSIE), I just want to make sure we get the order right......
Industrial is next to last-we look down on Civil Engs too.

Really?  I don't think you should, at the schools I have been at, the CE's take harder courses than the IEs.  Don't forget, CE's can easily go on to structural engineering, which is no joke, IE's not so much.

(I am an ME by schooling, so no dog in the fight there)

And not saying IE's don't have a place, either...certain things need certain skills.

Dude I didnt even know how to do trig 3 years ago and I will be graduating with my ME degree next year. If you want it bad enough you will put the time in and make it happen, just like anything else in life.

I would recommend (and did this as well)  taking math classes during summer school to help you get used to being in that mathematical mindset and so you dont forget what you learned 3 month ago in the spring. Just keep at it and it will finally click for you.

The universities that I'm familiar with that have industrial engineering programs all have at least 2 semesters of Operations Research.  Plus they require at least 3 semesters of Probability and Statistics and at least one semester of control feedback systems.  These are math intensive courses.

When I earned my Industrial Engineering degree, I had to take all of the flunk out classes of the other engineering disciplines (linear circuits, statics and dynamics, thermodynamics, mechanics of materials.  I also had to take the weed out classes from the school of management (engineering economics, accounting).  

I wouldn't say IE is any more or less difficult than other engineering disciplines.  It's just unique.

TL;DR

I've always said that if your brain functions somewhat at a normal level, there nothing (math) that can't be achieved with the proper amount of input from the pupil.  All your really doing in school is mimicking what others have already discovered and provided proof of.  If you don't want to, or can't dedicate what it takes, don't waste your time.  If you can, do it.

I remember in a intro level engineering class, the professor said 2 out of every 3 people in this room will not make it to graduation.  I looked to my left, right and though to myself, "that sucks for y'all".  Made my mind up in that instant that I will be part of the graduating class.  Work, partying, etc, it took me 10 years (two years of balls to the wall, six years of , last two years balls to the wall) but I did it.

Domestic engineer. Now go make me a sammich!

Isn't that kind of like asking which Medical degree isn't heavy in Biology?

Any engineering degree will be filled with math. My advice is to go for it anyway. A good knowledge of calculus simply opens up a world of understanding, to the point I wish they made math through calc II required to graduate high school. Words cannot describe it's usefulness both in these career fields, and understanding how the world works.



Universities have TONS of resources to help students in math. The vast majority of students never use them. Among them are the following.



1. Tutoring centers.

2. Professor's office hours.

3. Teaching assistant office hours.

4. Online materials.



et cetera.



It is a lot of work, but if you keep yourself focused, have a good work ethic and SEEK OUT ALL THE HELP YOU NEED you'll most likely do fine. I was awful at math in high school. After I got a C on my first college calc test, I spent two days a week talking about algebra and pre calculus concepts with the professor. I ended up with an A in that class, a math minor and am now in a math based PhD program. If I can do it, anyone can. Trust me on that.

No calculus physics is horrible.  Without calculus you don't understand where any of the equations came from.  You don't understand simple concepts like when you graph velocity that acceleration is the derivative (slope) or that distance traveled is the integral (area under the curve).  I tutored physics for years, and I found it much easier for the students to learn both calculus and physics at the same time than it was for them to try to learn physics by itself.z

This is a fantastic point. Without any knowledge of derivatives or integration, students have NO idea where the formulas came from. Even if their mathematical skills aren't quite up to part with deriving simpler forms of the equations themselves, a professor should do it at least once, at least, for example, showing how you get momentum when you integrate newton's second.

You can teach them free body diagrams, and some newton's second kinematics, but outside of that, you're just poking around in the dark without a background in calculus.

There is always going to be some disagreement within the differing engineering specialties as which is the easiest and which is the hardest. Most programs will require you to take Calc I,II,III, Differential Equations, Chem I,II, Physics I,II, Statics, Dynamics, Fluid Dynamics, Mechanics of Materials, Thermodynamics, and a basic circuits class and after that you'll specialize. I've seen a few deviations based on the school. For instance, Civils may take a Heat Transfer class or they can take the same Thermodynamics class that MEs and others take at the University of Florida.  Depending on where you might find yourself in the Civil program, you might be in a less math intensive specialty like Construction, or a very heavy math intensive program like Coastal or Structural. Civil is one discipline that has probably the most variability in difficulty so if that's something that interests you, you could easily find something to meet your skill level/limitations. Mechanical engineering has a bit of a variation as well. Some of the easier ME classes at UF involve HVAC design, at other schools, it might be different.

I tend to look at the different engineering fields like this: Civil is more concerned with infrastructure - from parking lots, to high rise skyscrapers and bridges (hence the differing difficulty levels in civil). Mechanical engineering can go from robotics to previously mentioned HVAC. Aerospace (IMHO) tends to be overall harder, and more so concerned with a narrower focus - making things fly or fly better. EEs are a funny bunch. If there is a discipline that is the most nerdy, it is most likely the EEs and anything with circuits is in their wheel house. Industrial can be a major benefit or the most useless, depending on the application. They are great at optimizing things, but usually lack the knowledge of how things actually work due to physics. I know of an IE that works at AT&T that was responsible for an upgrade in an area. He tried to use Google Earth to get the distance from one point to another point to use as a cable length. Two problems with that - google earth is not accurate enough for that type of application and he didn't take into consideration the sag that a cable will under go, no matter the tension applied to the cable that will necessitate a longer length. IE's take a lot of statistic based classes and some linear algebra, but in overall difficulty, their hardest math is no where as difficult as the hardest math other specialties will encounter. I haven't personally known any nuclear engineers so I can't  directly comment on their program. Shared a few classes with them, like Thermodynamics and they did well, but no better than anyone else in other programs so I don't tend to view them as geniuses.

Bottom line, if you are math phobic, find something else to do. At least some point in any engineering program, you are going to be doing a fair amount of math based work. If I could go back and do it over, I doubt if I would have gone into engineering. I am at my happiest when I am working on firearms, so maybe in another life I would have enjoyed gunsmithing school.

Most of those classes listed are to get an engineering degree from an ABET (Accreditation Board for Engineering and Technology) accredited school.
The only extra I see (IIRC) is Fluid Dynamics.

ABET accreditation is required in many states to even sit for any portion of the PE exams.

Having a PE is more important in some engineering specialties than others, but is almost always a plus.

First off, ABET doesn't accredt schools--it accredits individual programs within a school.

Second, ABET accredits two different kinds of engineering programs--classical engineering (BSME) for example, and engineering technology programs (BSMET for example.  A given school might offer both types of programs.

The classical engineering programs have considerably more emphasis on calculus and require calculus based physics.  The two types of programs target different types of students who might have different career interests. Analytical versus hardware emphasis for example. Lots of insecure classical engineering folks like to trash the ET side because of the allegedly easier curriculum and that's their privilege.  The practical facts (job opportunties and salaries) don't support the trash talk, however.

I should have said Fluid Mechanics instead of Fluid Dynamics, but I think most people probably understood.

"Lots of insecure classical engineering folks like to trash the ET side because of the allegedly easier curriculum and that's their privilege. The practical facts (job opportunties and salaries) don't support the trash talk, however. "

The only thing that really gets me is when someone claims to be an engineer that really isn't any type of engineer. I equate it to me claiming to be a doctor of nurse because I know a little anatomy and have attended a CPR class. Also annoying when a company throws the term engineer around to different job titles to bolster someone's self esteem or company image when it is completely inappropriate and does not apply to their level of training/education/job duties.

The best engineer I ever worked for was a senior manager at McDonnell Aircraft--and he had no degree. His kind are probably long gone.  I've never thought it necessary to whip out my diplomas to convince anyone of my competence.  My accomplishments (or f'-ups) spoke for themselves and there were plenty of examples of both. I believe I can see through a fake after ten minutes of technical conversatipn, i've met plenty of folks with advanced technical degrees from prestigous institutions that couldn't tie their own shoes. Of course I've also met similarly credentialed individuals who were brilliant and very humbling to be around.
My point is, after nearly fifty years in the business of engineering, I place the most priority an an individual's demonstrated competence and it doesn't take long to shake out the fakers or slackers--degreed or not.

A distinction without a difference in terms of the present discussion.

I do not recall fluid mechanics, but my BS EE is 30+ years old.

Not required for an MS or PhD either.

The technology degrees remain watered down.

I've got a two good friends who started as MechEs, grades weren't great so one went ET.  Both graduated and both are successful today.  I think there is a place for ET, just as there is a place for operators, techs, PAs, nurse practitioners, etc.   However, classical engineering does provided the background as to where and how we got to where we are today and why things work.  Just as you can teach physics without calculus, you can teach engineering without all the fundamentals.  However, I think without the background it makes it more difficult for society to innovative and continue to develop.   Same argument goes when I hear people bitch about having to learn Algebra.  Sure a large portion of society doesn't use it in their adult careers.  However, if we just quit requiring and people no longer took it we'd go back to the stone age.  It would be like one of the best movies of all time, Idiocracy.  Then there are those who just know stuff and can figure anything out without school.  I wish I was one.  I do agree, you don't need a piece of paper to be good "engineer" and make things work, but for the rest of us at least we have the background to be on the same playing field.

That extra letter (the 'T") will cost you a lot in salary until you prove yourself at an employer.
And then moving to another job can still be a problem.

The large company i used to work for called 'T' degree holders 'Engineering Designers' and routinely paid them a reduced rate compared to folks with actual engineering degrees.
Many got relegated to the 'production test' staff

I have taught EET degree classes (filling on for a friend) and even the textbooks are noticeably different.


A typical EE electronics book provides two of the three amplifier hookups for a 3-terminal device, and leaves the student to develop the equations for the third.

The EET books just give all three equations and leave you to plug and chug changing variable values.

The amount of analysis taught is not nearly as high.

i know a circuit will work before I ever bother using SPICE, EESOFT, or even a digital simulator.

The T degree guys seem to work by throwing parts down, hooking them up, then trying to simulate to get things working (some of the lousy EEs do the same thing, we avoided promoting them).

When faced with something they have never seen before (like a very high source impedance) the EEs have a much better chance of using it effectively.

To the OP, when I was in school, every degree took the same amount of math-4 qtr/3 semesters of calc, differential eq, and a math elective (often specified by the department as linear algebra, the IEs and Textile engineers could take an easy math class or statistics (while not easy per se, there was substantial overlap with engineering probability classes, that one of the classes was easy)

EEs went on to take lots of EE classes that seemed a whole lot more about math than electricity (boolian algebra, communications (the first com class was nothing but fourier transforms/series and laplace transforms), even the first power class seemed like a math class.  And you have to relearn algebra using complex numbers.

Mechanical engineering to me, was much more about using simplier math to describe the physical world (hydraulics, statics, dynamics, strengths of materials, thermo.)  And this is comming from a guy who was a ham operator, and had an electrical liscense.

IIRC, almost every program required some form of probability and/or statistics, and engineering econ (which was one of the more valuable classes I took.

I've known a lot of sharp, practical minded people who couldn't make it past the math.  But you really need it to get a handle (in EE) on the foundation of electromagnetics, control systems, communicatons, or power grids.

I've never understood the public perception that civil engineering is easy.  My mom as a HS teacher, was astounded when one of her better students majored in CE.  Kind of like when I had a copy of the ASHRAE (American Society of Heating, Refrigeration,and Air Conditioning Engineers) fundimentals handbook on my desk and a fellow student thought it was a joke, like custodial engineering, or something.

My employeir will not hire engineering technology grads off the street.  if they can show several years of experience, they can be hired.  Hell my boss has a community college computer degree, but it meant she was selected solely based on her experience and abilities, and she started out making less then secratary.

      +1




Just to add that Chem E's are by far the smartest.  


and include the hottest engineering graduates.  

I am in the exact same boat as your but I'm starting an industrial engineer technician course come January. My degree definitely wont be the same as an actual engineer but the math classes are a lot less and hopefully it gets me off working on the shop floor sooner into a job where I can actually use my brain. Here's what I'll be taking.