电路理论的数学和工程背景

在电路教课书中 ,常常会强调各种计算方法和分析的技巧 ,而忽略了数学和工程的背景 ,为解决此问题 ,文章从数学处理和工程应用的角度 ,讨论了电路理论中建模的基本规则和各种分析方法产生的背景。指出由于数学求解和物理量可比性的限制 ,模型一般都采用线性化建模 ,通常分为代数模型和常微分模型。在具体的分析过程中 ,考虑到数学处理的简化和物理概念的清晰 ,引进了减少方程数目和简化电路模型的思路 ,并且为了避免常微分方程的求解 ,引入了相量法和拉氏变换 ,变微分方程为代数方程 ,从而形成了电路理论较完整的体系

Circuit Theory and Its Mathematics and Engineering Background

In the process of circuit teaching, people always emphasize the methods and skills and put the background of mathematics and engineering aside, which makes students feel difficult to understand theory in full scale. This paper discusses the basic rule of modeling and the background of analyzing methods from the aspects of mathematics and work apply, and points out that the model should be linearized for the limitation of mathematics solved and physics compared. It usually uses algebraic model or constant differential model. In the actual process of analysis, the thought of reducing equation and sampling physics model is introduced to ease mathematics transaction and focus on physics concept. The method of phasor and Laplace transform is used to change differential equations into algebraic equations for avoiding solving differential equations. All of these form the integrate system of circuit theory.