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.
