- #1

matqkks

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Also would like to bring in some history of differential equations.

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- Thread starter matqkks
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- #1

matqkks

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Also would like to bring in some history of differential equations.

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- #2

Philip Koeck

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Charging and discharging of a capacitor comes to mind.matqkks said:

Also would like to bring in some history of differential equations.

Also chemical kinetics and radioactive decay.

See also https://www.researchgate.net/publication/333479286_Differential_equations_for_thermal_processes

for examples involving heat transport and gas pressure.

- #3

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https://www.physicsforums.com/insights/differential-equation-systems-and-nature/

Lotka-Volterra is the standard example because it is non-trivial and can be drawn. Maybe you like some of the many references I attached.

- #4

Will Flannery

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- #5

gmax137

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In my experience, modeling is synonymous with simulation, and was always real world applications, solved numerically.

This goes way beyond simple analytically tractible scenarios like tank concentration etc.

- #6

Haborix

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I don't interpret modeling to be synonymous with simulation. I was always annoyed with teachers who added numerical schemes into core courses. Felt like a waste of my time and their expertise.

Some highly recommended textbooks include "Differential Equations and Their Applications" by Martin Braun, "Nonlinear Dynamics and Chaos" by Steven Strogatz, and "Ordinary Differential Equations" by Vladimir Arnold. These books provide a solid foundation in both the theoretical and practical aspects of differential equations.

Yes, several online platforms offer excellent courses on differential equations. Websites like Coursera, edX, and Khan Academy provide courses ranging from beginner to advanced levels. MIT OpenCourseWare also offers free courses that include lecture notes, assignments, and exams.

Common software tools include MATLAB, Mathematica, and Maple. Python libraries such as SciPy and SymPy are also widely used for solving and visualizing differential equations. These tools offer a range of functionalities to handle both simple and complex differential equation models.

For advanced research, journals like the "Journal of Differential Equations," "SIAM Journal on Applied Dynamical Systems," and "Nonlinear Dynamics" are highly regarded. These journals publish cutting-edge research and reviews in the field of differential equations and their applications.

Yes, there are several online communities and forums where you can discuss differential equation modeling. Websites like Stack Exchange (especially the Mathematics and Computational Science sections), ResearchGate, and Reddit’s r/math and r/learnmath are good places to ask questions, share knowledge, and collaborate with other enthusiasts and experts in the field.

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