Advanced Engineering Mathematics 2

• Master the general solution method for linear, nth order, differential equations with constant coefficients
• Master the general solution method for linear homogeneous systems of differential equations with constant coefficients
• Apply different solution techniques, including transfer functions, for obtaining particular solutions to inhomogeneous differential equations
• Determine and argue for the stability of linear systems of differential equations
• Understand the differences between various types of convergence (absolute, conditional, point-wise, uniform) of infinite series and determine the convergence type in concrete cases
• Estimate the number of terms needed in order to obtain a desired accuracy in the approximation of an infinite series
• Find the Fourier series for simple periodic functions, determine their convergence properties, and approximation-theoretic properties
• Apply Fourier series and power series methods to the solution of differential equations
• Master convergence tests (including Leibniz’s test, ratio test, comparison test, equivalence test, integral test, n term test) for series of complex numbers
• Be able to recognize both homogeneous and inhomogeneous linear differential equations and distinguish the cases corresponding to constant and nonconstant coefficients

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.

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