<p>This book provides a comprehensive approach to engineering mathematics, concentrating on advanced topics. The book is the second of two complementary textbooks. Volume 2 covers analytical, approximate (semi-analytical), and numerical solution of differential equations, finite element and optimization methods. Within the context of numerical solution of differential equations, explicit and implicit methods are extensively covered. Distinct from similar books, unique sections are covered in each chapter, for example, differential quadrature method is uniquely included in the numerical solution of differential equations. In optimization section, both classical and modern optimization methods are covered in sufficient detail. To deepen conceptual understanding and improve overall learning, example problems are solved in each chapter illustrating both theory and software-based methods. MATLAB programs developed by the author are additionally provided in appendices to implement the methods and show the examples of program development for engineering applications.</p>