Dynamic Systems

Wat kun je straks?

On completion of this module, you should be able to:

• (LO1) set up a differential equation using a description of a system;
• (LO2) solve a 2nd order ODE with constant coefficients using the classical method. Show that the differences between the solution types are understood;
• (LO3) solve a 2nd order ODE through Laplace methods;
• (LO4) use the Laplace methods or convolution to solve a transfer problem or an input/output problem of a CT or DT system. Understand, recognize, interpret or formulate important conclusions about input/output systems by using the Laplace;
• (LO5) solve a CT or DT system problem in state space and apply linear algebra for this purpose;
• (LO6) understand, recognize, interpret or formulate conclusions about statespace systems;
• (LO7) understand, recognize or interpret a problem related to simulating ODEs (using Taylor expansion or other methods from class);
• (LO8) implement and/or simulate a system model by using software tools, e.g. Python (or MATLAB/Simulink), applied to a description of a system;
• (LO9) compartmental modeling methods: recognize, define, postulate, interpret, classify, connect. Postulate equations from a diagram or draw a diagram from equations. Select the correct conclusion, statement, fact or relationship;
• (L10) compartmental modeling methods: use, formulate, conclude. Solve a system's equations analytically. Draw conclusions/statements from analytic solutions;
• (LO11) compartmental model analysis: recognize, define, postulate, interpret, classify, connect. Graphical analysis of model observability. Find or prove distinguishability and/or reducibility conditions through analysis.

Inhoud

The Dynamic Systems course, is a partial-semester course (period 2) but in tandem with the Applied Mathematics course (period 1) which brings the fundamental mathematical methods within the programmatic master course. The course includes both high-stakes and low-stakes moments, ether for testing yourself, as well as for testing for the final grade. Entrant students are expected to be familiar with Calculus and/or Differential Equations. A low-stake moment has been the test of Applied Mathematics in the program, at an undergraduate level as well as the basics in Algebra from their previous study. A Signals & Systems course -followed previously in any form- can be helpful, however it is not required. Some extra materials in this area is provided for those interested.

This module reviews a number of important topics in Calculus, Fourier analysis and linear algebra that you need with the tools and pre-knowledge, needed for the quantum core of the Master program. Calculus, Fourier analysis, and linear algebra are essential mathematical tools for studying quantum, because they provide the necessary framework to describe, analyse, and understand the behaviour of quantum systems. These mathematical foundations allow physicists and researchers to formulate and solve the equations that govern quantum phenomena, making these tools indispensable in the field of quantum physics. This specific course will be indispensable to quantum topics such as (calculus) differential equations, wavefunctions, probability distributions, (Fourier analysis) wave-particle duality, uncertainty principle, energy spectra, (linear algebra) state representation, operators, eigenvalues and eigenvectors.

Afronding

Students are assessed by means of a written exam in week 10.

Praktische informatie

Questions? Contact Tjeerd Bollmann at [email protected].

Toelating en aanmelden

Students are expected to have successfully completed the Applied Mathematics course, as the mathematical methods used in this course are assumed to be known.