First-Order Differential Equations
First-order differential equations provide a rich example of differential equations of many forms, most of which we can solve easily in the formal sense, and many of which we can solve and actually get answers. From calculus, we need the rules of differentiation, both the formulas (for sums, products, quotients, chain rule, and so on) and the derivatives of the standard Mathematica functions (x n , trigonometric functions, logarithms, exponentials, hyperbolic functions, and the like), and techniques of integration. We will likely see an example of most of the kinds of integrals that you ever attempted. If this sounds like bad news, the good news is that Mathematica can do these integrations for you. You will serve as the mastermind, and Mathematica will do the labor. Your responsibility is to ensure the correctness of the work that you are having Mathematica do, but Mathematica will do these correctness and consistency checks for you. You control what is being done; Mathematica does the hard work. It is important that you manually do some examples of problems of each type. The reason for this is that if you have no idea how to do a problem yourself, then it is not too likely that you will know how to guide Mathematica through the solution process.
KeywordsDifferential Equation Vector Field Linear Differential Equation Differential Inclusion Constant Solution
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