Mathematical Foundations of Engineering Systems provides a comprehensive introduction to the mathematical concepts essential for understanding and analysing engineering systems. The book covers key topics such as calculus, differential equations, linear algebra, numerical methods, probability, statistics, and mathematical modelling. With an emphasis on engineering applications, it connects theoretical principles with practical problem-solving and system analysis. Designed for engineering students, researchers, and professionals, this book develops mathematical reasoning and analytical skills required to address complex engineering challenges and understand modern technological systems.