Electric Circuit Theory and the 

 Operational Calculus 



By JOHN R. CARSON 



Note: This is the first of thrrt- iiisl.illinonts l)y Mr. Cirson whii h will 

 i'iiiIkkIv material piven by him in a course of lectures at the Moore School 

 of Klectrical Kngmeering, I'niversity of IVnnsylvania, May, l')25. No 

 effort has l)ccn spared l)y the author to make his treatment clear and as 

 simple as the suliject matter will permit. The methfxi of presentation is 

 distinctively pedaKoi;ic. To electrical engineers and to engineering in- 

 structors, this ex|>osilion of the fundamentals of electric circuit theory and 

 the operational calculus should be of great value. — KuiTOk. 



Foreword 



THE following pages embody, substantially as dcli\crecl, a course 

 of fifteen lectures given during the Spring of 1!)25 at the Moore 

 School of Klectrical Kngineering of the l'ni\ersity of PennsyK'ania. 



After a brief introduction to the subject of electric circuit theory, 

 the first chapters are devoted to a systematic and fairly complete 

 e.xposition and critic|ue of the Heaviside Operational Calculus, a 

 remarkably direct and powerful method for the solution of the diflfer- 

 ential ecjuations of electric circuit theory. 



The name of Oliver Heaviside is known to engineers the world over: 

 his operational calculus, however, is known to, and employed by, 

 only a relatively few specialists, and this notwithstanding its remark- 

 able properties and wide applicability not only to electric circuit 

 theor%' but also to the differential equations of mathematical physics. 

 In the writer's opinion this neglect is due less to the intrinsic dififi- 

 ciilties of the subject than to unfortunate obscurities in Heaviside's 

 own exposition. In the present work the operational calculus is 

 made to depend on an integral equation from which the Heaviside 

 Rules and Formulas are simply but rigorously deducible. It is the 

 hope of the writer that this inode of approach and exposition will be 

 of service in securing a wider use of the operational calculus by en- 

 gineers and physicists, and a fuller and more just appreciation of 

 its unique ad\antages. 



The second part of the present work deals with adxanced problems of 

 electric circuit theorv', and in particular with the theory of the propaga- 

 tion of current and voltage in electrical transmission systems. It is 

 hoped that this part will be of interest to electrical engineers gener- 

 ally because, while only a few of the results are original with the 

 present work, most of the transmission theory dealt with is to be 

 found only in scattered memoirs, and there accompanied by formid- 

 able mathematical difficulties. 



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