This textbook offers an introduction to the mathematical modeling of complex living systems. The authors guide undergraduate students in modeling ecological and biomedical problems using differential equations, dynamical systems, and data-driven methods. The modeling process—including assumption formulation, model construction, numerical simulation, sensitivity analysis, prediction, and biological interpretation—is presented step by step. Through hands-on projects and case studies, students learn to apply mathematical techniques and numerical simulations to study glucose–insulin regulation in diabetes, tumor–immune interactions in cancer therapy, and multi-species dynamics in Chesapeake Bay ecosystem. Together, these projects link mathematical theory to meaningful practice, helping students develop technical skills while fostering an appreciation of mathematics as a powerful tool for discovery and decision-making. Accompanied by student exercises and supported by MATLAB® code, the book also provides instruction on fitting models to real data and performing parameter sensitivity analysis. The book is well-suited for upper-undergraduate coursework or independent study and serves as a valuable resource for those aspiring to be researchers and practitioners in the life sciences.
