Program, 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. Homogeneous vs. inhomogeneous. Initial conditions. Particular solution and general solution.

SymPy Demos

For this week we have SymPy demo 6 about differential equations.

Preparation and Syllabys

This week will cover Sections 12.1 and 12.2 from Chapter [12 - Systems of linear ordinary differential equations of order one with constant coefficients].

Opgaver

Exercises for Long Day.

Exercises for Short Day.