Contribution of the theory of complex numbers to the field of electrical engineering education and practice.

摘要

Despite the importance of complex numbers in electrical engineering, their history has been little studied by engineering students, and no comprehensive history of the contributions of complex numbers to electrical engineering is available for use by instructors and students. Nowadays, most textbooks on alternating current theory either begin with an introductory chapter on the algebra of complex numbers or provide the theory in an appendix. As late as 1911, however, as discussed in Chapter 3 of this thesis, American mathematicians, engineers, and educators were still arguing about whether or not undergraduate mathematical instruction should include the study of complex numbers. Chapter 3 also discusses the emancipation of complex numbers in electrical engineering education.; The present study begins with a chronological review of the theory of complex numbers in mathematics and electrical engineering spanning five different eras. The material presented in Chapter 4 provides real life applications that illustrate the direct connection between complex numbers and topics considered in the undergraduate electrical engineering curriculum. Because many of the electrical terms used in this thesis might be unfamiliar to undergraduate teachers of mathematics, a glossary of terms and concepts is presented in Appendix H.; In Chapter 5, through a review of the most popular textbooks on circuit analysis, the study shows that the phasor concept, a method developed by Charles P. Steinmetz in 1893 to use the theory of complex numbers to simplify the analysis of alternating current theory, is typically introduced to students without historical background. The study concludes with a discussion of its implications for the teaching of the phasor concept to electrical engineering students. Recommendations on how the material of this study can best benefit electrical engineering teachers are also presented. In sum, this study illuminates for teachers of electrical engineering and secondary school mathematics the interplay between various branches of undergraduate mathematical science, the history of mathematics, and concepts encountered in the study of alternating current.