Differential Equations - Modeling

In summary: I'm thinking of but I'm not sure if it's the right one. It's called "Mathematical Models of Real-World Systems" and it was written by Michael S. Behe. I'll have to check if it's available at the library.In summary, HeLiXe thinks that if a student has taken differential equations before, they should have learned more about modeling. He recommends a workshop class over a theoretical class. Google will provide applicable hits for differential equation modeling. There is only one resource HeLiXe knows of for modeling, Mathematical Models of Real-World Systems, which he recommends checking out at the library.
  • #1
HeLiXe
440
1
I'm not sure if this should go in this section or the learning materials section, so please feel free to move this thread to the appropriate location.

This semester I am taking differential equations. I have a totally awesome professor :) So far we have been working on linear algebra and solving first order ODE's but I noticed that the very first part of the book was about modeling and we did not cover that. The book also does not go into great detail which leads me to wonder if this is something I should have learned in Calc I or II. So my questions:
1) Should I have learned more about modeling prior to this class? If so, which class should it have been covered in? (I will go back and reference materials)
2) Are there any good resources you can recommend that covers modeling?

I appreciate your help with this!
 
Physics news on Phys.org
  • #2
Hi HeLiXe! :smile:

Modeling is about applying what you know from mathematics to real-life situations.
I do not believe there are theoretical courses in it.

What I had, was a workshop class, where we were given (simple) hypothetical real-life problems and asked to create mathematical models for them.
The challenge is to keep the models simple but meaningful.
It's very easy to make your model so complex that you can't do anything useful with it anymore!
 
  • #3
Hi I like Serena :biggrin:
Your answer actually helps me A LOT. I read the modeling section of my textbook like 10 times and I was wondering if I am thinking of it correctly or if it is a little more exotic than what I am idealising. Thanks a zillion!

Edit:
Was there a book for your workshop class? I'm looking for resources for practice. Thanks!
 
Last edited:
  • #4
Sorry, no book. :(
They just gave us 3 problems, 1 at a time.
We had to solve those in teams at home.
Then we had a class wide discussion.
For our grade, each team had to hand in a report for each problem.

Btw, I do see that Google will give you applicable hits.And if you have questions about your textbook, perhaps I can help with that... :smile:

For practice, you'll only need to select an appropriate problem and start a thread!
Actually, I think such a thread would be cool! :cool:
 
Last edited:
  • #5
I like Serena said:
Sorry, no book. :(
They just gave us 3 problems, 1 at a time.
We had to solve those in teams at home.
Then we had a class wide discussion.
For our grade, each team had to hand in a report for each problem.

Btw, I do see that Google will give you applicable hits.And if you have questions about your textbook, perhaps I can help with that... :smile:

For practice, you'll only need to select an appropriate problem and start a thread!
Actually, I think such a thread would be cool! :cool:

Great idea about starting the thread! There is a cool problem here about rhinoceros so I will work on it and start a thread about it in the DE section :D We are using Differential Equations 4th ed. by Blanchard, Devaney, and Hall. It covers modeling in section 1.1 and there are a few problems after it is explained.

google "differential equations modeling"? I will look through the hits again-- I see explanations but not many practice problems/ exercises.
 
  • #6
So the trick is to not look at the explanations yet (if you can! :wink:).
Just put the bare problem out.
Try to think up a simple model for it and put it out there on PF!
You can refine the model as the thread evolves.

And you do get hits with google, although they're not neatly organized for your purpose.
To get a practice problem, you'd have to be a bit creative and lift it out yourself.

For some reason most scientists always want to work everything out, making sure there's nothing to criticize, before publishing a nice and interesting problem. It really is a shame! :biggrin:
 
  • #7
Good topic. I'm in DE at the moment, also, and I recently had this conversation with my professor. I said the hardest problem I had with the class was modeling the real-world problems we were given.
He told me to just do many, many exercises and you would eventually get the hang of constructing your own models. Easier said than done, though, when all of my time is spent trying to keep up with newer material we're getting. :)
I like the idea of a separate workshop to help you out with modeling. I can definitely see the benefits to that.
 
  • #8
I like Serena said:
So the trick is to not look at the explanations yet (if you can! :wink:).
Just put the bare problem out.
Try to think up a simple model for it and put it out there on PF!
You can refine the model as the thread evolves.
OK will do! I already read the modeling section 10 times :biggrin: There is no specific explanation for the rhinoceros problem, however.

Latecomer said:
Good topic. I'm in DE at the moment, also, and I recently had this conversation with my professor. I said the hardest problem I had with the class was modeling the real-world problems we were given.
He told me to just do many, many exercises and you would eventually get the hang of constructing your own models. Easier said than done, though, when all of my time is spent trying to keep up with newer material we're getting. :)
I like the idea of a separate workshop to help you out with modeling. I can definitely see the benefits to that.
Hi latecomer :)
We are not doing any modeling in our class, just working on problem solving methods for existing problems (separation of variables, bifurcations, linear systems and matrices etc etc). Well... we had one lab with a population model, but that was sort of easy as it relied on the exponential growth model and Euler's method. I would also LOVE a modeling workshop :) I will put the link to the thread I start here and you can post some of your own practice problems there too :biggrin:
 
  • #9
OK ILS I started it raw lol and got stuck. It is a simple one I'm sure, but I have never modeled before -_-
 
  • #10
So, put it out there!
Create a thread in the homework section (Calculus & beyond) and explain what it's for! :smile:
 
  • #11
Oh ok there ...lol I was thinking of putting it in DE so others could add their models, but I guess it would be less confusing to just put it in calc&beyond.
 

Related to Differential Equations - Modeling

1. What are differential equations and why are they important in modeling?

Differential equations are mathematical equations that describe the relationship between a function and its derivatives. They are important in modeling because they allow us to understand the behavior of complex systems and make predictions based on mathematical principles.

2. What types of systems can be modeled using differential equations?

Differential equations can be used to model a wide range of systems, including physical phenomena such as motion, electricity, and heat transfer, as well as biological, ecological, and economic systems.

3. How do you solve a differential equation?

The method for solving a differential equation depends on its type and complexity. Some differential equations can be solved analytically using mathematical techniques, while others require numerical methods such as Euler's method or Runge-Kutta methods.

4. What is the difference between ordinary and partial differential equations?

Ordinary differential equations involve functions of a single variable, while partial differential equations involve functions of multiple variables. Ordinary differential equations describe the behavior of a single variable over time, while partial differential equations describe the relationships between multiple variables in a system.

5. How are differential equations used in real-world applications?

Differential equations are used in a wide range of real-world applications, including engineering, physics, biology, economics, and finance. They are essential for understanding the behavior of complex systems and making predictions based on mathematical principles.

Similar threads

  • STEM Academic Advising
Replies
4
Views
1K
Replies
19
Views
1K
Replies
8
Views
277
  • STEM Academic Advising
Replies
16
Views
2K
  • STEM Academic Advising
Replies
8
Views
831
  • STEM Academic Advising
Replies
2
Views
1K
  • STEM Academic Advising
Replies
6
Views
1K
  • STEM Academic Advising
Replies
7
Views
1K
  • STEM Academic Advising
Replies
5
Views
2K
Replies
5
Views
1K
Back
Top