UE M5-B - Mathematics I

Level of knowledge:

N1: beginner
N2: intermediate
N3: confirmed
N4: expert

Knowledge expected at the end of the course


Knowledge of calculating the derivative of a function in finite or nonfinite dimension(C1,N3)


Knowledge of methods for calculating free and bound extrema (Lagrange multipliers): (C1,N2)


Knowledge of Poincaré's theorem on closed differential forms and its applications in vector analysis (C1,N2)


Vector analysis in different coordinate systems (approach via differential forms) (C1,N2)


Knowledge of Stokes' theorem (C1,N1)


Knowledge of Cauchy-Lipshitz theorem (C1, N1)


Knowledge of the definition of flow and its properties.


Know the various definitions of stability for solutions of an ODE (C1, N2)


Understand the principle of discretization of an ODE (C1, N2)


Know various methods of discretization of ordinary differential equations (C1, N2)


Know the definitions of order, A-stability and 0-stability (C1, N2)


Know the Dahlquist Barriers



Learning outcomes in terms of abilities, skills and attitudes expected at the end of the course


Know how to solve an autonomous ODE (C1,N2)


Know how to apply Grönwall's lemma (C1,N2)


Know how to apply the method of variation of the constant (C1,N2)


Know how to analyze the stability of the solutions of an ODE by studying the spectrum of the linearized (C1,N2)


Know how to analyze the stability of the solutions of an ODE by employing Lyapunov functions (C1,N2)


Know how to calculate the order of a Runge-Kutta method with trees (C1, N3)


Know how to calculate the order of a linear multi-step method (C1, N3)


Know how to analyze the A-stability of a one-step method (C1, N3)


Know how to analyze the A or 0-stability of a linear multi-step method (C1, N3)


Know how to choose the appropriate method for calculating a numerical solution (C1,N3)