Advanced Engineering Mathematics 2 (Summer University)

• Determine the solutions to n’th 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 and various other types of infinite series to solution of differential equations
• Determine the Fourier transform of simple functions
• Apply Maple to calculations and control of the results

Solution of homogeneous/inhomogeneous differential equations and systems of differential equations. Transfer functions. Infinite series, power series, Fourier series. Applications of infinite series for solving differential equations, the exponential matrix. Stability. Introduction to the Fourier transform. Solutions via MAPLE.

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.

Two hour lectures and two hour exercises per day in 13 days. Projects and other teaching activities in two selected days.