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- W2480309503 abstract "Differential equations constitute one of the most powerful mathematical tools to understand and predict the behavior of dynamical systems in nature, engineering, and society. A dynamical system is some system with some state, usually expressed by a set of variables, that evolves in time. For example, an oscillating pendulum, the spreading of a disease, and the weather are examples of dynamical systems. We can use basic laws of physics, or plain intuition, to express mathematical rules that govern the evolution of the system in time. These rules take the form of differential equations. You are probably well experienced with equations, at least equations like (ax+b=0) or (ax^{2}+bx+c=0). Such equations are known as algebraic equations, and the unknown is a number. The unknown in a differential equation is a function, and a differential equation will almost always involve this function and one or more derivatives of the function. For example, (f^{prime}(x)=f(x)) is a simple differential equation (asking if there is any function f such that it equals its derivative – you might remember that e x is a candidate)." @default.
- W2480309503 created "2016-08-23" @default.
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- W2480309503 date "2016-01-01" @default.
- W2480309503 modified "2023-09-24" @default.
- W2480309503 title "Solving Ordinary Differential Equations" @default.
- W2480309503 doi "https://doi.org/10.1007/978-3-319-32428-9_4" @default.
- W2480309503 hasPublicationYear "2016" @default.
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