Mechanical Engineering



EML3041: Computational Methods: Fall 2015

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In Summer 2010, I assigned the class to write a two-stanza poem for the EML3041 Computational Methods course.  Here is their attempt.


Engrossed in code with a large data chart 

Numbers, graphs, and lots of information 

Gleefully discovering ways to start  

In applying different computation. 

Naive-Gauss, Interpolation or Spline 

Eliminate plenty of matrix fear 

Expressing a more optimal design  

Reserving time to play and have a beer! :)



The decade is ending with a depression,
Life is too short with many situations,
Memories and experience of regression,
Can be solved using differential equations.
To succeed in life, one needs to initiate,
They who wait will run out of time,
With many variables to differentiate,
Which can be fit via splines. 


On our goal to solving Simultaneous Linear Equations 

We have learned the method of Gaussian Elimination  

Partial Pivoting has proved to be more precise 

But all the math ends up being not so nice.    


Have to love that matrix multiplication 

Or how about that backward substitution?  

So make sure to not make an error 

The larger the matrix, the more the terror!



Keep pluggin' and keep chuggin', 

Whether you Newton_Raphson it up or you Gaussian. 

You see the hate, that Computational Method serves on a platter. 

So what we goin' have, Absolute Value or Error.   


I never thought I'd be hating like this,  

When I look at my book, my mind goes on a trip. 

Then LU came in, and knocked my pride on my face. 

Feel like I'm in a pit,  But I already dug myself a grave.   



Numerical methods is the thing for you

If calculus makes your brain feel like goo 

Lots of simple math and repetition 

Just manipulate the matrix like a magician


Filling in the blanks with interpolation

Is about as easy as building the space station

Integration without my TI-89 

It’s tons of fun, so get in line



To integrate numerical methods with a rhyme, 

Takes so much time, 

For between Math and English I interpolate,

But between them, I no longer differentiate.   


Both are subjects taught in schools, 

To be used through life as tools, 

Once it was assumed that they diverge,  

Oh what an error, for they really converge!   



When doing interpolation of linear spline,  

which is forming consecutive of straight lines,  

one should do when assigned,  

if not in this course one will fall behind,  you will be given a chart with velocity vs time . 


So study instead of listening to music with rhymes that are not kind. 

Which corrupts your mind when doing spline.  

On the exam you will be asked to find the distance

which 4 or five constants having to integrate with respect to x’s.



Computational Methods   

Just one more day until the test  

Why do I feel the need to regress 

Interpolate, extrapolate  

Here comes the need to acclimate   


Dr.Kaw’s calibration  

May just be my abomination 

Will my retention  

Affect my compensation?     



I separate and differentiate

 the variables of my life 

evaluate and approximate  

the outcome finite.   


Look no further than the knowledge at hand 

and you soon will see 

we've only to have a continuous drive 

for convergence of success.   


This is the wonderful class of Numerical Methods 

Where Dr. Kaw adds fast, he must have broken records 

So, everyone races, without tying their laces, 

In crunching up numbers in different bases.   


If you can’t differentiate and integrate 

Well, you better you can interpolate 

If someone calls you Naïve, they’re talking about the Gauss Elimination 

And the easiest thing you’ll learn is the LU Decomposition.   



There's so many ways to find the wrong answer 

When the exact solution is so simple to find. 

To my summer this class is kind of like cancer 

It's taking up all of my vacation time.   


Yet I know that this course is needed 

If I want to graduate soon. 

To the lessons and lectures I should've heeded 

For I don't want my grade to be doomed.   



There is no sunshine with Comp Method 

But it’s not warm without the math 

I have heard that this class is so hard 

Unfortunately I had to see it first hand   


I wonder this time if I will pass 

I need to work very hard to pass with A 

But I know I know I know I know I know 

There is no sunshine unless I pass   



Interpolation, integration 

It’s a sensation that's sweeping the nation 

Forward elimination, back substitution  

That’s a way to find a matrix solution   


Even with the country in a recession 

That won’t stop me from learning regression 

Computing velocity versus time 

Using “fancy” calculators should be a crime.



Math is good 

Math is great 

Oh this class, I can not hate 

Though I think I could   


All the things we approximate 

Head spinning as I integrate 

Don't forget to differentiate 

Gotta run, can't be late  



An ancient math has come to be, 

seems so foreign to you and me. 

Full of wonder and full of grace, 

she's more than a just pretty face.   


The passion that was, through space and time, 

proved to fit on just one thin dime. 

Though my love had come and pass 

still I'm stuck here in the class.   



Numerical Methods is a subject so peculiar 

But converting from base 2 to base 10 is oh so familiar  

From differentiation, Gaussian Elimination and quadratic spline 

To curve fitting, interpolation and regression for a line   


Yes there’s more to learn than could fit on a wall 

But there’s only one method that will find them all 

Formulate, implement, solve and interpret 

After this class, you’ll do everything perfect   



If you have numbers and unknowns all in a mix, 

Then solve for the variables using a matrix. 

Numbers may be large, a real base 10 load, 

Well shorten the notation with binary code.   


I can easily distinguish Chris Brown, Soulja Boy, and Yung Joc when I hear 'em, 

Yet, I have trouble understanding the Gaussian elimination theorem. 

Our ability to solve problems is our greatest possession, 

We've learned to use integration, interpolation, and linear regression.    



When I enter the room, 

I can feel the crowds doom, 

As Dr Kaw teaches, 

the differentiation he preaches.   


While the central divide makes your answer precise, 

the fdd takes only two measurements, how nice, 

so when the test comes, I won't be stressin, 

I'll be able to derive every single expression.



With the final questions laid before me 

A sudden rush of anxiety floods my being 

Can i get my will to match my ultimate desire 

As that looming expectation vibrates my facial attire   


Though I yearn for success 

Will my persistence in Comp Methods end up being a valid tool 

That of which my professors have told 

We will redesign a better future and watch it unfold   



Numerical Methods, the art of approximation 

Includes matrices, computers and differentiation. 

Our Weapons are the best in the War against Terror, 

But a missile hit our base due to a truncation error.   


We learn to eliminate with the method of Gaussian, 

I don’t understand this subject, to me it sounds like Russian. 

Distances, velocities, time, and accelerations, 

I can solve for all of them using Simultaneous Linear Equations     



Computational Methods is all about manipulation 

When analyzing a problem you might run into a regression 

You can spend some time by using Gaussian Elimination 

Other ways to solve include direct interpolation   


Finding roots of equations involve derivations 

To find distance from a velocity equation you will use integration 

When describing acceleration from a velocity equation use differentiation 

If you know what you’re doing you’ll have no hesitation.   



Simultaneous equations

Pivoting all the rows 

LU Decomposition 

Ideal for my woes. 


Naive Gauss Elimination 

Errors in the round   

I. switch my information 

No doubt by the sound. 

The types of solving methods 

Everyone is just fine 

Relative to the challenge 

Problem solved with Spline.   



Computational Methods burns my brain 

Sometimes I think I’m going insane 

I thought I was good at math 

But those days are far in the past   


Although on the first test I earned a D 

That will not be the end for me 

I will do better on the next test 

I will score higher than the rest!   



There was a boy who lived in the school 

With Numerical methods he didnt know what to do   

He studied and studied just to get C's 

Gonna study some more and get me a B   


Matrices and Interpolation and solving equations 

workin hard but its a lot of information   

I had the studyin good and goin 

but had to stop to write this poem.   


Numerical Methods is so fun 

We’ll come to class until it’s done 

Dr. Kaw shows us real world problems 

Then shows us how matrices can help solve them.   


By the time this class is through 

We’ll be able to show you too 

Some may think it’s all a bore 

But numerical methods we’ll use for sure.   



You add here and subtract there; 

That is the basics for numerical methods idea; 

Well… not so quick my dear; 

Don’t forget the algebra and calculus ideas.   


Problems??? Engineering is no exception; 

And with numerical methods there is no fear for deception; 

Just put your mathematics into good application; 

And now you’re ready to face, any engineering complication.   



(A) Math is greatest off all 

(A) Especially numerical methods in the fall 

(B) Learning it's fun, learning it's great 

(B) You have to study off your buns, until it is late.   

(C) Numerical methods isn’t easy  

(C) But more interesting than listening to Weezy 

(D) This class is no ordinary task  

(D) Through and through it is applicable until the last


Calculus has given me a fight 

But I have a goal in my sight 

To multiply my knowledge 

In this equation we call college.   


I'm in this divided road  

Learning how to carry my load 

Every problem has a solution  

So I'll carry on in this fine institution.   



As I walked to the classroom I thought of spline, 

I can feel a shiver running down my spine. 

LU method? " oh, the terror!" 

I hope I don’t get a large error.   


Do not extrapolate was what I affirmed, 

the absolute relative true error I must confirm. 

Simultaneous linear equations - "oh, the abuse!" 

Gaussian's method I must use.   



Using Numerical Methods can be a significant chore.  

You must approximate correctly to converge a high score.  

The matrix is not just a TV show. 

It will allow mathematical models to flow.    


As we regress into the classroom after a test 

We find that only a few have done their best. 

It's a good thing that our professor tells lots of jokes. 

That keeps the classroom filled with happy folks.



Numerical methods can be used to solve 

Any type of problem that can evolve. 

We use integration and interpolate too 

To find the numbers that we can use.   


Numerical methods can be fun I say, 

If you joke and laugh I’ll show you the way! 

Just remember to show all of your work, 

Or else confusion and head scratches can soon lurk!   



Here or anywhere around the World  

Inequality among us causes a war 

Whether Im rich or poor  

This differentiation makes us ignore the value of life 


Let’s not pretend this does not exist 

But instead, let’s work together with a common goal 

To see if can measure the length of that pandemic 

Then we will be able to define peace.    



Numerical methods is cool 

I like to learn it in school 

Quadratic equations are neat 

When I get the right answer it’s sweet.   


Solving linear equations can be hard 

It leaves my eyes starred 

But I better get done with my math 

Or I will receive my wife’s wrath.     



Alpha, Delta and Beta are supplying  

Simultaneous equations we are applying  

Solving by integration and differentiation  

We are understanding this wonderful creation   


From solving problems to life’s mysteries 

It’s been here through all of history 

Whether designing trunnions, turbines, or toys  

There’s always a Numerical Method to employ        



Love and respect are functions of time 

Your variables push me to tequila with lime 

Whether it’s love or hate you’re needed by all means 

When I think of you, I SUM in my jeans!   


You are important to all and hold a place in my brain 

But not in my love matrix; you’re more of a pain 

When you test me, it makes me squirm 

“Numerical Methods,” you’re great, but not during this term       



I can be used to approximate, differentiate, and interpolate. 

However, some of my techniques students do not fully appreciate. 

With me practice makes perfect so be prepared to spend some time, 

Because taking shortcuts is most definitely a crime.   


Be cautious of chopping which may lead to a large error, 

Because after such you may be cursing like a sailor. 

I command attention to detail and must be respected, 

Because I am.. numerical methods.



Dark corners of LIF 272...   

Lost in a world full of gauss and decomposition 

haunted dreams and matrix superstition 

absolute relative approximate error will make you cry for mother 


just as we begin the interpretive regression mystery....    

hold that thought, break for five 

when we return, a clicker quiz to see who stays alive 

gasp for breath, check your messages or run for cover 

if only i hadn't changed my major from chemistry     



Why is it so hard for me to rhyme, 

About numerical methods and functions of time, 

Too busy interpolating to find the shortest path, 

Studying forward elimination to avoid professor wrath.


Linear, quadratic, and cubic splines, 

My mind is full of so many lines, 

Like an infinite loop trying to reach a conclusion, 

An engineer must keep on learning to find a solution.



In the land of mathematics 

The engineers were problematic, 

With problems, numbers so erratic, 

Their work became completely static.


Numerical Methods came and said “Wait! 

There is a way to put them straight. 

Find the error and integrate, 

Regress a line or interpolate.”   



I am writing a poem for computation 

i didn't realize what time it was now IM in a bad situation 

i wish i had done this sooner  

hey look on TV threes a guy sailing a scooner   


Comp methods has some problems 

with enough work i hope i can solve them 

i hope this class goes smooth 

but i feel it will be as tough as pulling a tooth



I like Numerical Methods and I cannot lie 

You other Engineers can't deny 

That when a matrix walks in 4x4 deep 

The methods for solving the inverse can be very, very steep.   


But don't worry, it's a breeze 

Just step back from the Naive. 

Substitute your mind forward to 4.07 and cram it in your head 

To make sense of the LU Decomposition Method.    



With Newton Rhapson 

You will need only one 

To care for Bisection 

Take two for your selection.   


With Gaussian Elimation 

You will go forward and back 

If you forget this 

Your answer will be whack.   



Numerical methods is sweeping our nation, 

as a better way to solve math equations.  

Errors caused by chopping or rounding, 

now so small no longer astounding!   


Its possibilities are like dividing by zero, 

making it our mathematical hero. 

All in all, at the end of the day, 

numerical methods is paving the way!   



In learning the nuances to this method of numerical solution 

This Stegner did not make a straight path to failure as a resolution 

the practices taught and many hours of study would not fail 

Yet verily the outcome told an empirical tail   


Old lessons learned and new ones taught 

the mind needs to integrate the data without fraught 

as the masses reveal the skills they learned 

A happy graduation to those sojourned



Numerical Methods, what is your sign? 

Your path to solutions is simply divine. 

I'm trying to learn all your magical ways, 

or at least enough, for a passing grade.   


Numerical Methods requires some thought. 

Sometimes I get it, sometimes, not... 

I'll learn what I can, no matter the cost. 

From the quote of a rap song, "Like a Boss"   


In computational methods 

true errors are welcome 

therefore breaks are need it 

youtube videos are for the weekend     


If I ever lost  my comp methods book 

I could still remember  how to find a root   

formulate my alternatives to  solve my troubles 

interpret my thoughts will  implement my teachings   



Comp Methods, the class is fun. 

Comp Methods, the class is fine. 

Comp Methods makes me want to run. 

Comp Methods makes me want to dine.   


Interpolation, oh I can not wait. 

Interpolation, oh I can not decline. 

Interpolation, it must be fate. 

Interpolation, it must be divine.   



We try to intimidate you with our symbols and big words; 

Engineers are smart (some cocky) you can be assured; 

This class they call Comp Methods, it's not all that bad; 

Furthest thing from a bore, unlike some classes we've had;   


Integration, Regression, Gaussian Elimination..not to mention T-pain; 

We cover it all, even talk about Luke “dancing in the rain”;  

And when programming in MATLAB, we can locate the glitch; 

Cuz if we keep all this up, one day we'll be RICH! : )     



Computational methods is our glorious mission 

Solving equations using LU decomposition 

Numerical values and their propagation of errors 

Make this living nightmare quite a terror   


Focus and concentration are the integral of success 

Moving forward-elimination can help clear the mess 

Then take a step back-substitution and see 

That the answer lies just a few computations from thee     



Numerical methods is the newest sensation... 

It'll help you with your math, especially interpolation. 

You'll have to add, subtract, multiply and divide, 

And if you follow these rules, you'll know how to get by   


The first two steps are formulate and solve, 

Once you're done with that you must interpret it all. 

After interpretation, comes the implementation, 

And that numerical methods! The newest sensation!   



It starts of as one divided by three

Then there was mathematical error exists

Here we learn how to calculate

We know computational methods are the best.


There was an area under the curve

It was challenging how to discover

We use computational method to be precise

Forward, Backward and Central Divide


Learn numerical methods so you can formulate a model right on the first try,  

if you don’t you have no chance of ever being as successful as T.I.   

Time and money lost by round-off or truncation errors will make your boss as mad as can be,  

And don’t even try to blame the poor interns and say “it wasn’t me!”   


Because I’m a pro at calculating true and approximate errors and if they turn out to be too high 

I’ll show the boss you should’ve used a polynomial regression model, you’ll be embarrassed and start to cry.   

Soon I’ll be in charge using Taylor series, Gaussian elimination and spline interpolation just fine,  

And you will be chillin’ in the unemployment line.     



Numerical Methods is just for me, 

Using my TI-30Xa with glee. 

Interpolating and approximating is up to ye, 

Studying you must if you wish to flee.   


Class is a blast and you must jive, 

Laughing and learning is how things drive. 

No matter how hard you strive, 

The answer is always five!!   



Approximating mathematical processes 

Finding the error your answer possesses 

The tolerance is pre-specified 

Does your approximation fit inside   


Differentiation integration 

Simultaneous linear equations 

Interpolation and ODE's 

Solved with numerical M-E-T-HOD's   



So I’m taking comp methods right now 

And this is class is omg wow 

I have this huge test with interpolation 

Let me show you a demonstration   


Not enough time, I’m only kidding  

Just like this course, it can be misleading 

But if I can understand partial pivoting, 

Passing this course will be riveting    



The method of Gaussian Elimination I learned, 

In turn, many erasers I have burned. 

My calculator is of no value anymore 

As such, simultaneous equations I adore   


My errors are true and absolute, 

With Matlab in my arsenal there's nothing I cannot shoot. 

Differential equations were once my enemies 

Now I can solve them in my undies.   



Naïve Gaussian? 

Or maybe just shy? 

Oh, you’re innocent 

Come here let me see why   


Partial pivoting  

That’s the secret I share 

Let me switch those 

Two rows In your matrix right there.     



Some may feel like not going to class 

because during the weekend they lost gray mass. 

The teacher makes you feel you are on a excursion 

only when you get comfortable with backward substitution.   


Going to class feels like a family reunion 

discussing how we're going to fit the freaking trunnion. 

After checking the calculations we felt the terror 

it was a false alarm caused by the absolute error.   



Comp Methods is an interesting class 

Mr. Miyagi says practice and you will pass 

While some problems cause great hesitation 

I hope that they are easy to solve like Gaussian Elimination.   

With great advice  

All we have to do is make the right choice 

Using quadratic interpolation to find a specific point 

To the left pass that joint.   



As I sit here studying for my test, 

I am wondering how I can do my best. 

Spline Interpolation I understand the least, 

Floating Point Representation, I can tear up like a beast!   


Without repetition, I will fail this class, 

But I must use a Ti-30Xa if I want to pass. 

Life is like a set of Simultaneous Linear Equations, 

I don't have enough variables which gives me many frustrations!   



Hurry to the car 

Its not that far 

So need not fear 

Lets get in gear   


Here it comes 

Its getting closer 

Excitement grows 

Computational Methods will end my woes!   



Cook book is like a calculus book 

A soup of things to do 

A chain of rules   

The ingredients... 


Three quarts of integration 

And one cup of calculation 

that's the soup named

computational methods   


I walk into Numerical Methods; my day, a blur,

I spend my days searching for the answer,

Only to learn there is more than one end,

To this quadratic equation I must tend,


Thinking numerically outside the bun,

Holistically makes me want some fun,

Raphson, Gauss, Euler and Newton,

Are nothing compared to the great Clayton.


Copyrights: UnCreative Commons Licenseiversity of South Florida, 4202 E Fowler Ave, Tampa, FL 33620-5350. All Rights Reserved. Questions, suggestions or comments, contact  This material is based upon work supported by the National Science Foundation under Grant# 0126793, 0341468, 0717624,  0836981.  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  Other sponsors include Maple, MathCAD, USF, FAMU and MSOE.  Numerical Methods for Undergraduates by  is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License.  Based on a work at