Am I supposed to understand everything in a formula?

[Tsunnnami]

When studying equations, formulas, laws - am I supposed to understand each bit of information ?

For example, let's take Fick's law:

So I can memorize the law and I can tell with words what is "t", what is "x", what is "D", and so on, but I don't truly understand why is one divided with the other, why is there an exponential function, and what does the product represent, why is there a product instead of an addition, and so on.

Or another thing, when there are given abstract things, such as Avogadro's constant - I don't know what that means, I can tell you the definition of it, but yet I can't truly grasp the meaning of it. How to imagine it ?

We've just finished nuclear radiations and it seems like a something utterly complex and detailed and hard to grasp again. There is for example Bethe's formula - I don't even understand half of that, although I'm trying, but I'm not even sure that when I think that I understand it, I actually understand it - how can I be sure that I'm right in my understanding ?

Our professor in Premed doesn't help us. He says that it's not his duty to teach students and I guess he's right, but how can I check myself then when I want to know if I'm understanding a concept or not ?

 

[ZapperZ]

When studying equations, formulas, laws - am I supposed to understand each bit of information ?

For example, let's take Fick's law:

So I can memorize the law and I can tell with words what is "t", what is "x", what is "D", and so on, but I don't truly understand why is one divided with the other, why is there an exponential function, and what does the product represent, why is there a product instead of an addition, and so on.

There's a potential for a serious problem here. It appears that you are not aware that those "...one divided with the other..." are derivatives. Is this true? Because if it is, and you are in such a class that uses this, there's an issue with students having the proper mathematical prerequisites for this class.

Zz.

 

[berkeman]

For example, let's take Fick's law:

So I can memorize the law and I can tell with words what is "t", what is "x", what is "D", and so on, but I don't truly understand why is one divided with the other, why is there an exponential function, and what does the product represent, why is there a product instead of an addition, and so on.

For me, I usually like to try to understand what is going on intuitively with equations. That helps me to remember them, and to visualize what is going on -- this helps me to work on problems, and to help me see when I'm making mistakes (like the picture in my head no longer makes sense -- some quantity is too big or too small, etc.).

On the diffusion equation you posted, there are lots of tutorials and animations that help you to understand it intuitively. Like this Khan Academy learning resource:

https://www.khanacademy.org/science...tem/gas-exchange-jv/v/fick-s-law-of-diffusion

There are certainly times when intuition will be hard to come by (like with some QM equations and concepts), but often visualization is a very valuable thing to try to develop when working with equations and concepts, IMO.

 

[berkeman]

Our professor in Premed doesn't help us. He says that it's not his duty to teach students

That's a pretty strange thing to say, if they really did say it...

 

[Tsunnnami]

There's a potential for a serious problem here. It appears that you are not aware that those "...one divided with the other..." are derivatives. Is this true? Because if it is, and you are in such a class that uses this, there's an issue with students having the proper mathematical prerequisites for this class.

Zz.

I know what a derivation is , but what I meant is that I don't understand why is it the way it is.
Like for example, if I try to understand how Fick came up with that law, I couldn't put it together, I couldn't explain how he got that law, therefore I don't fully understand the law itself.

It's like I have difficulty translating the mathematical language so that I can understand the phenomenon.

 

[berkeman]

I know what a derivation is

Hopefully that is just a typo or a translation issue. Did you mean to say that you know what a derivative is?

It's like I have difficulty translating the mathematical language so that I can understand the phenomenon.

Maybe try watching the Khan Academy info on the diffusion equation, to see if that helps with your intuition and understanding of how it was derived and why it has that form? For me, the diffusion equation is one of the more visually intuitive equations...

 

[Tsunnnami]

I understand the diffusion. That's simple, I guess.
What I mean is that I understand it like at least I can visualize it and somehow the elements of the equation make sense, but I still don't fully get how that law is constructed. Like how did Fick know that it has to be a derivative ? And why it is a derivative anyway, like what should be the intuitive approach here ?

When it comes to more abstract things, such as nuclear radiations, that's when even bigger problems arise.

PS:yes, I'm not an English speaking student, I make grammatical mistakes.

 

[Mark44]

When studying equations, formulas, laws - am I supposed to understand each bit of information ?

For example, let's take Fick's law:

This is actually Fick's Second Law. There is a discussion of how Fick's First and Second Laws are derived here - https://en.wikipedia.org/wiki/Fick's_laws_of_diffusion.

So I can memorize the law and I can tell with words what is "t", what is "x", what is "D", and so on, but I don't truly understand why is one divided with the other, why is there an exponential function, and what does the product represent, why is there a product instead of an addition, and so on.

As already mentioned, $\frac{\partial \phi}{\partial t}$ and $\frac{\partial^2 \phi}{\partial x^2}$ shouldn't be thought of as fractions, with something divided by something else. They are partial derivatives, with $\frac{\partial \phi}{\partial t}$ being the rate of change of concentration $\phi$ with respect to time t, and with $\frac{\partial^2 \phi}{\partial x^2}$ being the second partial of $\phi$ with respect to position x. Here $\phi$, the concentration, is a function of both time and position, so any rates of change (derivatives) are necessarily partial derivatives.

Our professor in Premed doesn't help us. He says that it's not his duty to teach students and I guess he's right

I'm guessing that this class is not a math class, and he's probably saying that it's not his job to teach students mathematics.

 

[ZapperZ]

I know what a derivation is , but what I meant is that I don't understand why is it the way it is.
Like for example, if I try to understand how Fick came up with that law, I couldn't put it together, I couldn't explain how he got that law, therefore I don't fully understand the law itself.

It's like I have difficulty translating the mathematical language so that I can understand the phenomenon.

You are all over the place here.

First of all, you need to clearly and unambiguously declare if you know calculus. Period. With your difficulty in English, it is still unclear if you mean "derivative" or "derivation", or if you are confusing the two. So clearly state that you know calculus, or not.

Secondly, there is a difference between knowing how something is derived versus knowing how to use it! Just because you know how something is derived does not automatically mean that you know how to use it. I can derive the basic intro-physics kinematical equations and teach my students how to do that, but I can guarantee you 100% that they will STILL not be able to use it correctly if I don't spend time showing them how to apply them.

So the question here is, do you want to know the derivation (which Mark44 has given the link to), or do you want to understand how to use the equation, which is a different issue. Do NOT be fooled into thinking that if you know how it is derived that you have understood how to use such equation.

BTW, most pre-meds take physics courses that do not require calculus. Do you not have a choice in enrolling in such a class? This equation not only requires that you know basic calculus, but also 2nd order ordinary differential equation. Based on your posts, I have a sneaking suspicion that this is not something that you know about.

Zz.

 

[russ_watters]

When studying equations, formulas, laws - am I supposed to understand each bit of information ?

...

So I can memorize the law and I can tell with words what is "t", what is "x", what is "D", and so on, but I don't truly understand why is one divided with the other, why is there an exponential function, and what does the product represent, why is there a product instead of an addition, and so on.

Or another thing, when there are given abstract things, such as Avogadro's constant - I don't know what that means, I can tell you the definition of it, but yet I can't truly grasp the meaning of it. How to imagine it ?

Differential equations aside, the answer is yes: you should understand how math relates to reality so intuitively that you don't need to remember equations for every situation; most of the time you can just build them when you need them (or derive them from a few simple laws). If you don't know/understand (for example) that driving 60 kph for an hour to go 60 km is multiplication, that's a serious problem.

For Avogadro's number, now that I think about it, I'm not sure I was ever taught the why/how, just that it's the number of atoms in a mole. But like a lot of funny looking numbers, it is just an arbitrary unit conversion factor to convert atoms into grams. If Avogadro had been British, it would be a different number.

 

[Mark44]

If Avogadro had been British, it would be a different number.

Like the number of atoms or molecules in a dram.

 

[mpresic3]

You mention your professor in Premed. Apparently your professor is teaching this course at a level appropriate with pre-meds. I have confidence in my doctor in medical matters, and I grant that Fick's law (on some level), can model the transport of blood in capillaries, veins, and arteries. Nevertheless, I would be surprised if my doctor can solve or work with a partial differential equation, such as Fick's law.

If you were a physics or engineering grad student, I would encourage you to learn to solve this equation (for some simple systems like flow in a pipe (cylinder)), by separation of variables, and to learn characteristics of the solution. The fact is many professional engineers I have worked with, have never solved a partial diffferential equation.

You may need to consult your professor to ask what salient features of Fick's law are important going forward. I expect your professor has reasonable requirements for his students and can provide his/her expectations.