This book demonstrates how to use functions of a complex variable to solve engineering problems that obey the 2D Laplace equation (and in some cases the 2D Poisson equation). The book is written with the engineer/physicist in mind and the majority of the book focuses on electrostatics.
This book demonstrates how to use functions of a complex variable to solve engineering problems that obey the 2D Laplace equation (and in some cases the 2D Poisson equation). The book was written with the engineer/physicist in mind and the majority of the book focuses on electrostatics. A key benefit of the complex variable approach to electrostatics is the visualization of field lines through the use of field maps. With todays powerful computers and mathematical software programs, field maps are easily generated once the complex potential has been determined. Additionally, problems that would have been considered out of scope previously are now easily solved with these mathematical software programs. For example, solutions requiring the use of non-elementary functions such as elliptic and hypergeometric functions would have been viewed as not practical in the past due to the tedious use of look up tables for evaluation. Now, elliptic and hypergeometric functions are built-in functions for most mathematical software programs making their evaluation as easy as a trigonometric function. Key highlights in the book include
- 2D electrostatics completely formulated in terms of complex variables
- More than 60 electrostatic field maps
- Comprehensive treatment for obtaining Greens functions with conformal mapping
- Fully worked Schwarz-Christoffel transformations to more than usual number of problems
- A full chapter devoted to solving practical problems at an advanced level
- Detailed solutions to all end of chapter problems available on books website
Although the text is primarily self-contained, the reader is assumed to have taken differential and integral calculus and introductory courses in complex variables and electromagnetics.
1. Functions of a Complex Variable.
2. Electrostatics.
3. Line Charges.
4. Conformal Mapping I.
5. Conformal Mapping II.
6. Case Studies with
Conformal Mapping.
7. Other Fields of Physics. Appendix A. Differentiating an
Integral. Appendix B. Dirac -Function. Appendix C. Elliptic Integrals.
Appendix D. Jacobis Elliptic Functions. Appendix E. Gamma and Beta
Functions. Appendix F. Gausss Hypergeometric Function. Appendix G.
Dilogarithm and Trilogarithm Functions.
Robert L. Coffie is the Founder and President of RLC Solutions, a semiconductor/microelectronics consulting company. He has designed, developed and matured AlGaN/GaN high electron mobility transistor (HEMT) technologies for RF applications from L-band to Q-band at Northrop Grumman and TriQuint Semiconductor (now Qorvo). He also developed the first JEDEC qualified AlGaN/GaN HEMTs for 600 V power switching applications at Transphorm where he served as Director of Device Engineering.
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