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Mathematics LibreTexts

1: First Order ODEs

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"The profound study of nature is the most fertile source of mathematical discoveries." - Joseph Fourier (1768-1830)

  • 1.1: Free Fall
    In this chapter we will study some common differential equations that appear in physics. We will begin with the simplest types of equations and standard techniques for solving them We will end this part of the discussion by returning to the problem of free fall with air resistance. We will then turn to the study of oscillations, which are modeled by second order differential equations.
  • 1.2: First Order Differential Equations
    BEFORE MOVING ON, WE FIRST DEFINE an n -th order ordinary equation. It is an equation for an unknown function y(x) a relationship between the unknown function and its first n derivatives.
  • 1.3: Applications
    IN THIS SECTION WE WILL LOOK AT SOME simple applications which are modeled with first order differential equations. We will begin with simple exponential models of growth and decay.
  • 1.4: Other First Order Equations
    There are several nonlinear first order equations whose solution can be obtained using special techniques. We conclude this chapter by looking at a few of these equations named after famous mathematicians of the 17−18th century inspired by various applications
  • 1.5: Problems


This page titled 1: First Order ODEs is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by Russell Herman via source content that was edited to the style and standards of the LibreTexts platform.

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