The chain rule applied to generalized functions for use in teaching electric circuits. Issue 3 (July 2017)

• Record Type: Journal Article
• Authors: Cipparrone, Flavio AM; Consonni, Denise
• Is Part Of: International journal of electrical engineering education. Volume 54:Issue 3(2017)
• Page Start: 236
• Page End: 246
• Publication Date: 2017-07
• Subjects: Generalized functions -- chain rule -- electric circuits -- Heaviside function -- Dirac function; Electrical engineering -- Study and teaching (Higher) -- Periodicals; Electrical engineering -- Periodicals; 621.30711
• DOI: 10.1177/0020720916678641
• Languages: English
• ISSNs: 0020-7209

Abstract

Generalized functions, in particular the Heaviside unit step H ( t ) and the Dirac delta impulse δ ( t ), are valuable teaching tools in many contexts of electric circuits. However, engineering undergraduate courses and textbooks normally cover only an introduction to these functions along with their basic properties, without tackling the rigorous mathematical framework of the theory of distributions. In this work, the Heaviside function is used to represent a square wave signal f ( t ), and the Dirac function appears when the derivative is calculated. The steps for obtaining f ′( t ) compare a graphical method with analytical procedures that employ the chain rule. The topic is further extended with the presentation of a theorem and a proposed corollary related to the study of the chain rule applied to general functions involving H ( t ) and δ ( t ). Thus, the work provides an appropriate mathematical support for the intuitive graphical method of analysis, which is very familiar in engineering practice.