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The study of differential equations is a wide field in pure and applied mathematics, physics, and engineering. All of these disciplines are concerned with the properties of differential equations of various types. Pure mathematics focuses on the existence and uniqueness of solutions, while applied mathematics emphasizes the rigorous justification of the methods for approximating solutions. Differential equations play an important role in modeling virtually every physical, technical, or biological process, from celestial motion, to bridge design, to interactions between neurons. Differential equations such as those used to solve real-life problems may not necessarily be directly solvable, i.e. do not have closed form solutions. Instead, solutions can be approximated using numerical methods.
The study of differential equations is a wide field in pure and applied mathematics, physics, and engineering. All of these disciplines are concerned with the properties of differential equations of various types. Pure mathematics focuses on the existence and uniqueness of solutions, while applied mathematics emphasizes the rigorous justification of the methods for approximating solutions. Differential equations play an important role in modeling virtually every physical, technical, or biological process, from celestial motion, to bridge design, to interactions between neurons. Differential equations such as those used to solve real-life problems may not necessarily be directly solvable, i.e. do not have closed form solutions. Instead, solutions can be approximated using numerical methods.
微分方程的研究涉及很多领域，例如理论数学，应用数学，物理和工程。所有这些学科都与各种类型的微分方程的性质有关。纯数学关注解的存在性和唯一性，而应用数学则强调解的逼近方法的严格性。从天体运动到桥梁设计，再到神经元之间的相互作用，微分方程在几乎所有物理、技术或生物过程的建模中都扮演着重要的角色。那些用来解决实际问题的微分方程，可能不一定是直接可解的，比如它们没有封闭形式的解。但取而代之的是，我们可以用数值方法来近似方程的解。