分部积分法与换元积分法的统一、格林定理与常微分方程的唯一性
Integration by parts and by substitution unified, Green's Theorem and uniqueness for ODEs
摘要：
我们提出了一个相当未知的版本的非自治函数的变量变量变换公式。我们将证明，这个公式是等价于格林定理的区域的平面所界定的两个连续可微函数的图形。此外，该公式在常微分方程解的唯一性方面也有有趣的应用。
英文摘要：
We present a rather unknown version of the change of variables formula for non-autonomous functions. We will show that this formula is equivalent to Green's Theorem for regions of the plane bounded by the graphs of two continuously differentiable functions. Besides, the formula has interesting applications in the uniqueness of solution of ordinary differential equations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
