Functions in Calculus textbook do not reflect behavior in Nature

In summary, the person is looking for a book or resource that can help them develop their skills in modeling real world data mathematically. However, the expert explains that this is a difficult task and there is no general algorithm for creating models that accurately represent the world. The process involves taking data, making assumptions, and using math to make predictions. Finding a function that fits the data is just the first step, and being able to use it to make predictions is a completely different challenge.
  • #1
neg_ion13
30
0
Hopefully this isn't a foolish question but, I am up to CalcII and am anxious to apply what I've learned but have found nature fails to provide functions for it's behaviour like textbooks do. Is there a book or something I can read to develop this skill?
 
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  • #2
Electricity & Magnetism; upper division and some lower division Physics courses.
 
  • #3
I'm an electrical engineering student so I don't think that will be a problem. I am looking for a general approach to modeling. IE what to do after you have collected data. I don't want to just plug things into equations I want to be able to take anything I come across and try to model it mathematically
 
  • #4
this is much more difficult problem than you think. there is no general algorithm that tells you how to devise a model that approximates the world. there are many books that tell you how to model things that have already been figured out though.
 
  • #5
Is that to say it is diffucult to find a function that represents collected real world data and it's not just that I have missed something?
 
  • #6
neg_ion13 said:
Is that to say it is diffucult to find a function that represents collected real world data and it's not just that I have missed something?

you're basically talking about theoretical physics here where people take a bunch of data, think about the phenomena they represent, make a couple of assumptions, make up some math that is closely in accord with that data and then make predictions using that math. if their predictions come true then their model is good.

so finding a function that represents a bunch of data maybe difficult or easy but whether you can use that function to make predictions is a completely different game.

for example take two data points. i can always find a line that contains those two data points. will other data points from that process also lie on that line?
 

1. How can functions in a calculus textbook not reflect behavior in nature?

Functions in a calculus textbook are often simplified and idealized versions of real-world phenomena. They may not take into account all the complexities and variables that exist in nature.

2. Why is it important to consider the limitations of functions in calculus when studying natural phenomena?

By understanding the limitations of functions in calculus, we can better interpret and analyze real-world data and make more accurate predictions about natural phenomena.

3. Can functions in calculus still be useful for studying natural systems?

Yes, functions in calculus can still provide valuable insights and help us understand the behavior of natural systems. They serve as a useful tool for making predictions and analyzing trends.

4. How can we bridge the gap between functions in calculus and real-world behaviors?

We can use more complex and realistic mathematical models, as well as incorporate data from real-world observations, to create a more accurate representation of natural phenomena in calculus.

5. Are there any cases where functions in calculus accurately reflect behavior in nature?

Yes, there are some simple natural phenomena that can be accurately described by functions in calculus, such as basic motion and growth patterns. However, in more complex systems, the behavior may not be fully captured by these simplified functions.

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