Mathematics and Physics for Nanotechnology Technical Tools and Modelling

Nanobiotechnology is a new interdisciplinary science with revolutionary perspectives arising from the fact that at nanosize the behaviour and characteristics of matter change with respect to ordinary macroscopic dimensions. Nanotechnology is a new way for producing and getting materials, structures and devices with greatly improved or completely new properties and functionalities. This book provides an introductory overview of the nanobiotechnology world along with a general technical framework about mathematical modelling through which we today study the phenomena of charge transport at the nanometer level. Although it is not a purely mathematics or physics book, it introduces the basic mathematical and physical notions that are important and necessary for theory and applications in nanobiotechnology. Therefore, it can be considered an extended formulary of basic and advanced concepts. It can be the starting point for discussions and insights and can be used for further developments in mathematical–physical modelling linked to the nanobiotechnology world. The book is dedicated to all those who follow their ideas in life and pursue their choices with determination and firmness, in a free and independent way.

1. Introduction 2. Vector Analysis 3. Vector Differentiation 4. Coordinates systems and important theorems 5. Ordinary differential equations 6. Fourier series and integrals 7. Functions of one complex variable 8. Complex integration 9. Partial differential equations 10. Numerical methods 11. Quantum Basics for Nanotechnology 12. Schrödinger equation and nanotechnology 13. Mathematical modelling for nanotechnology 14. Plasmonics and modelling 15. Nanodiffusion in graphene

Paolo Di Sia is adjunct professor at the University of Padova, Italy. He holds a bachelor’s degree in metaphysics, master’s in theoretical physics and PhD in mathematical modelling applied to nanotechnology. His research interests include quantum–relativistic nanophysics, theoretical physics, mathematics, history and philosophy of science and science education. He has authored 260 publications and is a reviewer of several international journals. He has received 15 international awards and nominations and is a member of many scientific societies and international advisory and editorial boards.