Advanced Engineering Mathematics 2

• Determine the solutions to nth order homogeneous differential equations
• Determine the solutions to linear homogeneous systems of differential equations
• Master the transfer function and apply it to solution of inhomogeneous differential equations
• Determine and argue for the stability of linear systems of differential equations
• Know the differences between various types of convergence (absolute, conditional, point-wise, uniform) of infinite series and identify them
• Estimate the number of terms which is needed in order to obtain a desired approximation of an infinite series
• Find the Fourier series for simple periodic functions, clarify their convergence properties, and approximation-theoretic properties
• Apply Fourier series, power series and various other types of infinite series to solution of differential equations

Solution of homogeneous/inhomogeneous differential equations and systems of differential equations. Transfer functions. Infinite series, power series, Fourier series. Applications of infinite series and power series for solving differential equations. Stability. Short introduction to related topics (Fourier transform and nonlinear differential equations). Solutions via computer software.

01002/01004/01005/01006/01015/01920, Knowledge of complex numbers, matrix calculations, eigenvalues and eigenvectors for matrices, systems of linear first order differential equations and linear differential equations of first and second order.

Lectures and exercises. Projects in selected weeks.

Information regarding re-exam: The homework can only be re-used for the first coming re-exam.