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Differential Equations Lectures

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This is the complete course of differential equations by Professor Leonard.

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• 2 months later...

Hello, what an insightful post. The lectures are easy to interpret and understand for all ages. Students from their teen ages must be motivated to learn the basics of such things so that it can be helpful for them in the future.
In the mathematical modeling of physical systems, differential equations are extremely significant. Differential equations may be used to express many fundamental rules of physics and chemistry. Differential equations are used to predict the behavior of complex systems in biology and economics. Differential equations are equations including one or more terms involving derivatives of one variable (dependent variable) with respect to another variable (independent variable), or equations involving derivatives of a function or functions. They have a unique capacity to foresee the future. They're used to describe exponential growth and decay, species population growth, investment return changes over time, bank interest, and even solving radioactive decay problems, continuous compound interest problems, flow problems, cooling and heating problems, orthogonal trajectories, and investigating problems involving fluid mechanics, circuit design, heat transfer, population or conservation biology, and seismic waves.

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1 hour ago, buttocksboss said:

Hello, what an insightful post. The lectures are easy to interpret and understand for all ages. Students from their teen ages must be motivated to learn the basics of such things so that it can be helpful for them in the future.
In the mathematical modeling of physical systems, differential equations are extremely significant. Differential equations may be used to express many fundamental rules of physics and chemistry. Differential equations are used to predict the behavior of complex systems in biology and economics. Differential equations are equations including one or more terms involving derivatives of one variable (dependent variable) with respect to another variable (independent variable), or equations involving derivatives of a function or functions. They have a unique capacity to foresee the future. They're used to describe exponential growth and decay, species population growth, investment return changes over time, bank interest, and even solving radioactive decay problems, continuous compound interest problems, flow problems, cooling and heating problems, orthogonal trajectories, and investigating problems involving fluid mechanics, circuit design, heat transfer, population or conservation biology, and seismic waves.

I totally agree with everything you wrote, and I still regret very much that this forum does not have the LaTex package, and we cannot display mathematical operations, such as differential equations, except as an image copied from elsewhere and pasted. We had many threads before where DEs were used, including some that I participated in, and using DEs to make a point is not only interesting, but a lot of fun. Not long ago I was quite proficient in Differential and Integral calculus, but I am losing some ability simply through none use.

I also used to work out and had a decent pair of biceps, but not quite as impressive as professor Leonard. That is another thing you lose through none use! Good for him to stay in great physical shape as well as a having a sharp mathematical mind. I usually don’t like spending a lot of time on YouTube, but I will give these lectures a look, time permitting.

NOAA is getting into the very busy season now, with excursions already underway. The good ship Okeanos Explorer is currently at sea engaged in the 2022 North Puerto Rico Mapping and Deep-Sea Camera Demonstration. While I am still at home due to some medical issues. But I can enjoy the telepresence, watching the livestream cameras, and you can do the same. I hope you enjoy it as much as I do!

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