【摘要】 希尔伯特空间中的元素—向量,可以代表矢量、函数和相量,它们满足希尔伯特空间的共有性质。将函数和相量类比作矢量,可建立起函数空间和相量空间的几何直观性。基于希尔伯特空间理论,采用类比方法,电路课程中的重点、难点问题能得到清晰的数学解释。希尔伯特空间理论既能丰富教师教学手段,又能开拓学生视野,提高其数学能力。更多还原

【Abstract】 Elements of the Hilbert space, which represent vectors, functions, and phasor, satisfy the common properties of Hilbert space. Comparing functions and phasor to vectors, the geometric intuition of function space and phasor space is established. Based on Hilbert space theory and analogy method, the key and difficult problems in the circuit course are explained in mathematics. Hilbert space theory can not only enrich teaching means, but also broaden students’ horizons and improve their mathematical ability.更多还原