This book provides a comprehensive introduction to the finite-difference time-domain (FDTD) method, a widely used numerical technique for simulating wave propagation and related physical phenomena. The book equips readers with theoretical foundations and practical tools to develop their own transparent, modular simulation codes. Covering electromagnetic, acoustic, quantum, and mechanical systems, as well as coupled multiphysics processes, the book progresses from fundamental principles to advanced applications, offering ready-to-use algorithms and examples executable on modest hardware. The book serves as both a reference and a practical guide for those seeking to understand and extend FDTD methods in research and development contexts. The code used throughout the book includes C, FORTRAN, Pascal and MATLAB. All code listings are written in Python. 

• Offers a multiphysics FDTD framework, integrating electromagnetic, acoustic, quantum, magnetic and mechanical phenomena
• Explores unconventional applications in multiphysics FDTD, featuring original case studies and examples
• Features computational tools and practical computer codes optimized to run efficiently on standard desktop or laptop

Ivan Maksymov began his academic journey at the renowned Kharkov Physics School, founded by Nobel Laureate Lev Landau, and continued his work at one of Europe’s leading optics and photonics research centres. He held the prestigious Australian Research Council Future Fellowship, cementing his reputation as one of Australia’s foremost scientists and earning a place on Stanford University’s list of the World’s Top 2% Researchers. In his most recent role, he has led research in quantum neural networks, human cognition, and machine learning, merging physics and AI in ways that push the boundaries of both technological innovation and our understanding of the human mind. His academic publications have also inspired popular science articles for general audiences (see links on p. 2 of the attached CV document). He received the 2020 Ig Nobel Prize in Physics and was featured with a personal exhibition at the National Museum of Emerging Science and Innovation in Tokyo.