This updated edition of the book explores COMSOL 5 and MATLAB, essential modeling tools for engineers and scientists. It includes five new models and covers systems from 0D to 3D, introducing numerical analysis techniques in COMSOL 5.6 and MATLAB. Using examples from electromagnetic, electronic, optical, thermal physics, and biomedical models, the book provides fundamental concepts and step-by-step instructions for building each model. Companion files include all models and related animations. The course starts with modeling methodology and material properties, progressing through 0D electrical circuit interface, 1D, 2D, 2D axisymmetric, 2D simple and complex mixed mode, and 3D modeling. Advanced topics like Perfectly Matched Layer models and Bioheat models are also covered. Each chapter builds on the previous one, ensuring a comprehensive understanding of modeling techniques. Understanding these concepts is crucial for developing and analyzing engineering, science, and biomedical systems. This book transitions readers from basic to advanced modeling, combining theoretical knowledge with practical skills. Companion files enhance the learning experience, making this an essential resource for mastering COMSOL 5 and MATLAB.