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Many of the natural laws of the world involve the rates at which things happen. When translated into mathematical models, these relationships become equations which contain derivatives. The study of these differential equations is critical to understanding the behavior of the world around us. We will begin our study with first order differential equations, including linear, separable, exact, and homogeneous equations. Our discussion of higher order differential equations will focus on constant coefficients, undetermined coefficients, and the variation of parameters. In addition, we will consider series solutions to differential equations as well as the Laplace transform. | |||||||