MATH 2270 Lecture Notes - Mechanical Resonance, Brie, Integral Curve
21 Dec 2013
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Document Summary
A di erential equation or de is an equation that contains derivatives. Typi- cally, a de provides a relationship between a function and its derivatives with respect to one or more variables. Y2 = u d2x dt2 + 3 dx dt. Equation 1. 1, we call y = y(x) the dependent variable because the quantity y literally depends on x. (if you want, think y is a function of x though the relationship may not necessarily be that of a function. ) Similarly, equation 1. 2 has an independent variable of u and independent variables. Equation 1. 3 has an independent variable of x and an independent variable of t. sometimes, the relationship is explicitly written as in 1. 1. To quickly determine which variable is independent, look at the variable being di erentiated ; those variables that are being di erentiated with respect to are the independent variables. Di erential equations are very useful for modelling real-world problems over a wide range of disciplines.
