A Course of Mathematics for Engineers and Scientists, Volume 4 delves into advanced mathematical techniques crucial for physics and engineering. Divided into five chapters, it commences with vector analysis, followed by Chapter II's exploration of ordinary and partial differential equations. Chapter III investigates properties of Bessel, Legendre, Laguerre, and Hermite functions. The final two chapters detail differential equations of field lines, level surfaces, and matrices. This text is invaluable for undergraduate students seeking to understand and apply advanced mathematical methods in physics and engineering.