9: Applications of First Order Equations

Differential Equations and Linear Algebra · LibreTexts

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    From LibreTexts, under CC BY-NC-SA 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    In this chapter, we consider applications of first order differential equations.

    • 9.1: Growth and Decay
      This section begins with a discussion of exponential growth and decay, which you have probably already seen in calculus. We consider applications to radioactive decay, carbon dating, and compound interest. We also consider more complicated problems where the rate of change of a quantity is in part proportional to the magnitude of the quantity, but is also influenced by other other factors for example, a radioactive susbstance is manufactured at a certain rate, but decays at a rate proportional
    • 9.2: Cooling and Mixing
      This section deals with applications of Newton's law of cooling and with mixing problems.
    • 9.3: Elementary Mechanics
      This section discusses applications to elementary mechanics involving Newton's second law of motion. The problems considered include motion under the influence of gravity in a resistive medium, and determining the initial velocity required to launch a satellite.

    Thumbnail: False color time-lapse video of E. coli colony growing on microscope slide. This growth can be model with first order logistic equation. Added approximate scale bar based on the approximate length of 2.0 μm of E. coli bacteria. (CC BY-SA 4.0 International; Stewart EJ, Madden R, Paul G, Taddei F).

    This page titled 9: Applications of First Order Equations was last modified on Mon, 09 Jan 2023 21:42:41 GMT and is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by William F. Trench via source content that was edited to the style and standards of the LibreTexts platform.