The title of this book is solved examples on Advanced Engineering Mathematics. It consists of several topics from Advanced Engineering Mathematics. In it, we collect a lot of examples with their solutions. Our goal in this book how to learn, not only to solve, in that sense in each problem, we discuss more than one method, but in solving, it is sufficient to use one of them. These topics are Linear Dependence and independence, second order differential equations, Fourier series, Fourier integrals, Laplace transforms, Special functions (gamma and Beta functions), Partial differential equations and solution of differential equations in series. The book can be of use to readers of various professions dealing with applications of mathematics in their current work. The subject matter is presented in a very systematic and logical manner.