Agenda, Semester Week 12

Differential Equations and Systems hereof

This week will concern differential equations, one of the most important mathematical concepts for engineering purposes. In particular, linear, first-order differential equations and system of them will be treated. Such differential equations describe many physical systems and phenomena such as natural cooling/heating processes, changes in concentration of chemical solutions etc. It turns out that eigenvectors and eigenvalues as well as the complex exponential function are useful for finding, describing, and interpreting their solutions. Of that reason we will see all of the tools and topics covered this far coming together this and the next week, tying a knot on the whole semester.

Key Terms

Differential equations of order 1. Systems of 1st-order differential equations. Linearity. Homogeneity vs. inhomogeneity. Initial conditions. A particular solution vs the general solution.

Preparation and Syllabys

This week will cover Sections 13.1 and 13.2 from Chapter 13 in [the textbook].

Opgaver

Exercises for Long Day. A Jypyter Notebook for the fourth and final Python module will be released on Long Day at 15:30 on DTU Learn.

Exercises for Short Day.