Abstract
We derive first order ODE modeling the temperature of a cooling incandescent light bulb, the voltage across a capacitor discharging through a resistor, the position of a sprinter during a 100 m dash, and the variation of atmospheric pressure with altitude. Although in all cases the ODE are nonlinear, they can be linearized. As a consequence, all aforementioned quantities can be approximately described with exponential laws; with the exception of atmospheric pressure, the exponential fits are very good. Linearization brings out unexpected similarity between convective cooling and RC-circuits which is called the electro-thermal analogy. More importantly, it justifies our narrow focus on linear ODE with constant coefficients.
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Beltukov, A. (2025). Linearized ODE and Exponential Laws. In: Differential Equations and Data Analysis. Synthesis Lectures on Mathematics & Statistics. Springer, Cham. https://doi.org/10.1007/978-3-031-62257-1_3
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DOI: https://doi.org/10.1007/978-3-031-62257-1_3
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