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Mastering Differential Equations: Applications and Solutions

Explore Ordinary Differential Equations (ODEs) through real-life problems like mixture and mass-spring systems. Learn how to solve governing equations for population growth, fluid motion, and convection-diffusion phenomena. Ideal for math enthusiasts and students.

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Mastering Differential Equations: Applications and Solutions

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  1. MATH 3331—Ordinary Differential Equations Weijiu Liu Department of Mathematics University of Central Arkansas

  2. Why ODEs?

  3. Mixture Problems Governing equation: where x denotes the amount of salt in the tank and c is the concentration of the salt in the inflow.

  4. Mass-spring Systems Governing equation: m: the mass of the object. k: the stiffness of the spring. f: the external force acting on the object.

  5. Population growth Logistic population model Where p denotes the population at time t and a, b Are positive constants.

  6. Motion of Fluid Particles Velocity: Governing equations:

  7. Coffee in Water Convection-diffusion equation: coffee water

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