When Artech House authors write their books, we ask them what they want their readers to get out of the project. In this series, we show you what our authors, in their own words, wish to impart upon readers. Karl Warnick, author of Problem Solving in Electromagnetics, Microwave Circuit, and Antenna Design for Communications Engineering, describes what his book is about:
I receive regular inquiries from students of electromagnetic field theory and mathematical physics about the calculus of differential forms. Differential forms is a framework for dealing with vector fields and partial differential equations that is similar to vector calculus. Differential forms offers a complementary viewpoint on field quantities. My PhD advisor, David Arnold, years ago described vectors as the “force picture” for electromagnetic fields and differential forms as the “energy picture.”
One of the most difficult concepts in electromagnetic theory is the physical meaning of the differential curl operator. When expressed using differential forms, the curl operation has a very intuitive graphical visualization. I expanded on this at length in my PhD dissertation and in one of my early papers, “Teaching electromagnetic field theory using differential forms,” IEEE Transactions on Education, vol. 40, no. 1, pp. 53-68, 1997.
Since that time, the use of differential forms has expanded into numerical methods, the theory of Green’s functions, electromagnetic materials, and other advanced topics. The book by Warnick and Russer, Problem Solving in Electromagnetics, Microwave Circuit, and Antenna Design for Communications Engineering, Artech House, 2006 is a collection of concrete, real-world problems in electromagnetics and applications using the differential forms notation. This book provides a great resource for those interested in a new way of looking at and understanding the principles and mathematics of electromagnetic theory and its applications.
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