# Why does the professor derive the equation?

## Main Question or Discussion Point

"why does the professor derive the equation?"

I often hear people of other majors (engineering) ask me why the professor derives the equation to be used in some situation (like a continuous charge distribution electric field from coulomb's law divided by the test charge) instead of just giving them the bottom line formula.

This question infuriates me because I don't know how to answer it. I learn how to derive all my equations because I like to. I understand the formula better and can modify it to a situation better because I know how it is formed.

I just feel like the question sounds like they don't want to do ANYTHING, I mean anyone can plug numbers into an equation.

What's worse is when I help someone solve some intensive problem and end up with some simple expression at the very end like "x = 2q^2" and they are like "cool, thanks" and they write down that last little expression that was derived based on the specific circumstances of the problem. Then they memorize that in hopes that that very same question will be on an exam (with different values.)

How do you respond to that question?

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That person is very trustworthy and isn't thinking like a scientist should.
Ask him if he believes EVERYTHING his professor says, when (not if) he says no tell 'em "That's why we derive things"

Many engineering problems can be really complicated even when you have all the "bottom line formulas". I found deriving equations waste of time or a leisure activity that you can do if only it pleases you and you have lots of time on yours hands.

Astronuc
Staff Emeritus

I often hear people of other majors (engineering) ask me why the professor derives the equation to be used in some situation (like a continuous charge distribution electric field from coulomb's law divided by the test charge) instead of just giving them the bottom line formula.

This question infuriates me because I don't know how to answer it. I learn how to derive all my equations because I like to. I understand the formula better and can modify it to a situation better because I know how it is formed.

I just feel like the question sounds like they don't want to do ANYTHING, I mean anyone can plug numbers into an equation.

What's worse is when I help someone solve some intensive problem and end up with some simple expression at the very end like "x = 2q^2" and they are like "cool, thanks" and they write down that last little expression that was derived based on the specific circumstances of the problem. Then they memorize that in hopes that that very same question will be on an exam (with different values.)

How do you respond to that question?
It's important to know how to derive the equations in order to understand the limitations and exceptions, and in the future, derive better models. In my engineering classes, in neutron transport and reactor physics, and in fluid mechanics and heat transfer, we derived the fundamental differential equations and we were expected to know how to do that with a piece of chalk and blackboard. When one develops computer models, one has to know the significance of each term of a PDE or kernel. Each kernel is a piece of physics. To program correctly and integrate the various kernels, one has to have a fundamental knowledge of the equations and physics.

Not everyone wants to put in that kind of effort.

Staff Emeritus
2019 Award

As said before, there are several reasons for this. One is so you know the approximations and assumptions that went in. Another is so you can have a chance of deriving something similar for a different set of assumptions - or to spot an error in someone else's derivation.

In any event "when am I gonna need this?" is so junior high.

In any event "when am I gonna need this?" is so junior high.

Generally in engineering undergrad, professor will walk you through the derivations but wouldn't expect you to know them. Focus is primarily on the application. It can be too time consuming when you want to understand the fundamentals as well the applications in limited time you have and heavy engineering classes workload. Besides that, engineering math doesn't go deep. So you wouldn't have strong enough math foundation to understand the derivations.

It's physics and math where you would focus on derivations.

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dlgoff
Gold Member

One is so you know the approximations and assumptions that went in. Another is so you can have a chance of deriving something similar for a different set of assumptions - or to spot an error in someone else's derivation.
And another, as stated by my Electro-Magnetic Theory professor on the first day of class, "Those who can not derive Maxwells Equations on the final exam will receive an F in the course".

Pythagorean
Gold Member

For me, it's all about knowing how to model the world with mathematics, and knowing how to change and adapt your models for particular cases. To do that, you have to know the motivation for every expression and term in the model. Knowing the derivation gives you an intuition for the motivation of each part of an equation.

I've found a good "shut the hell up" (or something with similar meaning but more colorful language) works wonders.

BobG
Homework Helper

What astronuc said.

People don't like to do an enormous amount of work. As a result, it's very useful to reduce two or three calculations into a single, simple formula that may use a few clever shortcuts along the way.

The formula works great, is easy to use and gets you your results, but is now completely opaque. It's virtually turned into a PFM box where something goes in and magically comes out looking like what you want.

The only way to understand what's happening in the process (which also means understanding the limitations, boundaries, etc) is to break that formula out into the step by step process that built the formula in the first place.

Of course, some people's obsession for not doing an enormous amount of work is excessive and they start to ask themselves why they need to understand anything at all. They just want the formula, assume they'll input data perfectly every time, and accept the results at face value no matter how absurd the results look - because how could they possibly know whether the results are absurd or not since they never bothered to learn what the formula actually does? Those people are data entry operators; not engineers or physicists or whatever. Of course, they're kind of wasting their money if they're taking college classes to be a data entry operator since most high school graduates should be able to do that job.

We derive things, so that we won't need to remember too many 'assumptions'.
For eg, by assuming columb's Law of Force between two charges to be true, we could derive and the Voltage, Charge and Capacitance relation C = q/v.
Of course someone could Take C = q/v as well as the columbs law as something that is valid and verified by experiment; I find it rewarding to understand that, one law follows from the other and that I ain't assuming too many things.

Just my 2 cents.

What astronuc said.

People don't like to do an enormous amount of work. As a result, it's very useful to reduce two or three calculations into a single, simple formula that may use a few clever shortcuts along the way.

The formula works great, is easy to use and gets you your results, but is now completely opaque. It's virtually turned into a PFM box where something goes in and magically comes out looking like what you want.

The only way to understand what's happening in the process (which also means understanding the limitations, boundaries, etc) is to break that formula out into the step by step process that built the formula in the first place.

Of course, some people's obsession for not doing an enormous amount of work is excessive and they start to ask themselves why they need to understand anything at all. They just want the formula, assume they'll input data perfectly every time, and accept the results at face value no matter how absurd the results look - because how could they possibly know whether the results are absurd or not since they never bothered to learn what the formula actually does? Those people are data entry operators; not engineers or physicists or whatever. Of course, they're kind of wasting their money if they're taking college classes to be a data entry operator since most high school graduates should be able to do that job.
Many thermodynamics problems are quite complicated involve partial differentiations, finite element method techniques. One simply cannot put them down on a paper. Sure, you can do a simple derivation on paper but nothing beyond. And, many models are not even analytical so there's no derivation to be done.

I agree that conceptual understanding of models is important but you don't have to derive the formulas to understand the concepts. For instance, our control course mainly relied on qualitative discussion of the models. You could come up with really absurd conclusions relying only on the math that can only be rejected if you know the concepts not simply how to derive the final formula.

The only way to understand what's happening in the process (which also means understanding the limitations, boundaries, etc) is to break that formula out into the step by step process that built the formula in the first place.
Many processes are very complicated and involve lots of fields. One person simply cannot break and understand every step in the process. Only reason we have multiple fields (Mathematics, Physics, Mechanical Eng, Electrical Eng) is that you don't have to know everything in the process to build the process.

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Staff Emeritus
2019 Award

In any event "when am I gonna need this?" is so junior high.
I stand by Junior High. The fact that an increasing fraction of undergrads think this is a separate sad thing.

Astronuc
Staff Emeritus

Many thermodynamics problems are quite complicated involve partial differentiations, finite element method techniques. One simply cannot put them down on a paper. Sure, you can do a simple derivation on paper but nothing beyond. And, many models are not even analytical so there's no derivation to be done.

Many processes are very complicated and involve lots of fields. One person simply cannot break and understand every step in the process. Only reason we have multiple fields (Mathematics, Physics, Mechanical Eng, Electrical Eng) is that you don't have to know everything in the process to build the process.
Fortunately, I started in physics, and took a lot of math and applied math. I did partial differential equations and QM my second year at university, as well as classical mechanics/dynamics. I then migrated into nuclear engineering, and the math and physics background had given me great preparation.

In upper level classes and grad school, we derived equations from the ground up. We also learned numerical methods with which to apply the various equations.

I work with some folks who developed some of the fundamental methods in structural mechanics (or mechanics of materials), and now we have the opportunity to apply them with advanced methods.

There are users (those who use the computational methods and tools) and developers (those who develop the computational methods and tools). I prefer to be a user/developer, and that requires the ability to understand the theory and apply it, and when necessary, improve it.

Fortunately, I started in physics, and took a lot of math and applied math. I did partial differential equations and QM my second year at university, as well as classical mechanics/dynamics. I then migrated into nuclear engineering, and the math and physics background had given me great preparation.
In Electrical Engineering, we never went much into anything that's non-linear or needs solving partial differentiations. Professors formulated problems (equations) for us, then linearized the models and provided us the qualitative description of the models. I recall in our thermodynamics course, professor provided us final analytical formulas and some empirical formulas. However, he did provided us the qualitative description and formulated problems for us so that those who know the math can go ahead can solve the equations as a leisure activity. And in our power systems course, the professor didn't want to go into teaching us all the optimization so provided us final formulas. As for our control course, it was completely qualitative and relied on matlab or other lab software to carry out the assignments. We never had to solve more than a linear system equation and interpreting graphs by hands.

Our courses were mostly focused on learning how to use the software rather than implementing models. Many of my friends got jobs just for knowing how to use few softwares. And people like me who are going to graduate schools are taking more math courses. My supervisor recommended me to take few courses on non-linear/optimization/numerical methods etc.

Future students might even learn less math in their undergraduate education than us. Right now, high schools here are watering down the math they teach. I recall needing three math courses to get into universities but now you only need to take two.

Pythagorean
Gold Member
I stand by Junior High. The fact that an increasing fraction of undergrads think this is a separate sad thing.
Until they utilize the material to out-earn you in the financial sector while you're busy intellectually wanking yourself. ;)

Hurkyl
Staff Emeritus
Gold Member

How do you respond to that question?
Frequently in mathematics classes -- and I assume this is true in engineering classes -- a derivation of a formula or a proof of the theorem is an example: a demonstration of the knowledge and expertise you're supposed to be learning, and how to apply that knowledge and expertise to a situation of interest.

The hard part is to get them to realize they're supposed to be learning, e.g., kinematics and not merely $x = (1/2)at^2 + vt + x_0$.

PAllen
2019 Award

"why does the professor derive the equation?"

to get to the other side of the blackboard.

Astronuc
Staff Emeritus

Our courses were mostly focused on learning how to use the software rather than implementing models. Many of my friends got jobs just for knowing how to use few softwares.
I've heard concerns regarding that. Most engineering and technology companies want problem solvers, not just data entry technicians.

Future students might even learn less math in their undergraduate education than us. Right now, high schools here are watering down the math they teach. I recall needing three math courses to get into universities but now you only need to take two.
That's rather disturbing.

Borek
Mentor

I understand the formula better and can modify it to a situation better because I know how it is formed.
Why do I have a feeling you have answered your own question? :tongue:

jtbell
Mentor

"why does the professor derive the equation?"

to get to the other side of the blackboard.
:rofl:

In the process, he has to take care not to get run over by a mob of chickens, er, students.

lisab
Staff Emeritus
Gold Member

I just started Structural Analysis, an upper-division civil engineering class.

We're given an equation approximating the pressure on a building caused by a constant wind - without even a hand-waving attempt at a derivation! In this equation, there are 3 "factors" that we look up in a table . But...this is inexcusable...there are NO UNITS on these "factors"!

For crying out loud.

I'm taking the class as a distance learner (from several states away), asking questions might be tough. Could be a long semester.

Borek
Mentor

We're given an equation approximating the pressure on a building caused by a constant wind - without even a hand-waving attempt at a derivation! In this equation, there are 3 "factors" that we look up in a table . But...this is inexcusable...there are NO UNITS on these "factors"!
Discussion not for this thread, but perhaps these factors are unitless? I recall being shown a method from dimensional analysis during my chemical technology course. Say you expect something to be a function of some parameters: x=f(a,b,c,d,...). You combine parameters b,c,d... to make the dimensionless expressions (say A=a2/c, B=d*b/c3/2 and so on - each of A,B... is unitless, parameters can be used more than once) and then you express x as k*Ag*Bh... - and you fit values of k,g,h... (these are not necessarily integers - but it doesn't matter, as we know A,B... to be unitless) to known experimental values of x. These values are then tabularized - and for obvious reasons they are unitless.