Single-Course Dansk 5 ECTS

Advanced Engineering Mathematics 2

Overall Course Objectives

To provide participants with tools, e.g., infinite series, to solve differential equations and systems of differential equations.

See course description in Danish

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 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 for solving differential equations. Stability. Short introduction to related topics (Fourier transform and nonlinear ODEs). 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.