Differential equations and infinite series | Ole Christensen

The book is written for the course Advanced Engineering Mathematics 2 at the Technical University of Denmark. Longer proofs are placed in an Appendix, so the book can be used as well in a practically oriented course as in a more theoretically oriented course. The presentation requires a solid knowledge of calculus, linear algebra, and differential equations of first- and second order. 
The main topics are:• Differential equations of nth order; • Systems of differential equations of first order; • Transfer functions; • Stability; • Nonlinear differential equations; • Infinite series with constant terms; • Infinite series with variable terms; • Power series; • Fourier series; • Solution of differential equations using power series; • Solution of differential equations using Fourier series; • The Fourier transform.  
The book also contains a large collection of exercises and an appendix with Maple commands.