Notes on Differential Equations

Welcome to the world of differential equations! They describe many processes in the world around you, but of course we’ll have to convince you of that. Today we are going to give an example, and find out what it means to read a differential equation.

• The Banker’s Equation, A Gallery of Differential Equations
• The Transport Equation, The Logistic Population Model
• Existence and Uniqueness and Software, Newton’s Law of Cooling
• Exact equations for Air and Steam, Euler’s Numerical Method
• Spring-mass oscillations, Applications of Complex Numbers
• Three masses oscillate, Boundary Value Problems
• The Conduction of Heat
• Initial Boundary Value Problems for the Heat Equation
• The Wave Equation, Application of Power Series: a Drum model
• The Euler equation for Fluid Flow, and Acoustic Waves
• The Laplace Equation, Application to the weather?

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