Stability and Control I: Fundamentals

Chapters 2 and 3 of Reference [1] contain detailed review. In our course, we just highlight the absolutely necessary to be able to follow the calculations. In fact, looking at the list of terms below and following the links to the corresponding articles on Wikipedia may be sufficient to get you started. If you find the wealth of information too confusing, our course has been designed to cut through the clutter and succinctly distill the required essence out of the resources.

• Linear Algebra: vectors, matrices, matrix multiplication, matrix inversion, linear maps, groups, rings, fields, modules, vector spaces, vector space isomorphisms, bases and basis transformations, spatial rotations and rotation matrices. We only treat the necessary basics of linear algebra without any higher theorems, however, we do recast the basics in the basis-independent formalism of abstract algebra.
• Differential Calculus: we review the total and partial derivative with the corresponding notation, chain rule, product rule. Integral calculus will only be touched upon.
• Differential Equations: definition and absolute basics, just to get the idea.
• Geometry: Spatial rotations, Euler angles, body rates.