Hilbert’s Nullstellensatz
Monday, May 23rd, 2005
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Discussion of (affine) Varieties, ideals and examples of how they relate. Statement and proof of the Nullstellensatz.
Archive for May, 2005
Lyapunov stability
Saturday, May 21st, 2005
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Lyapunov (Liapunoff) stability is the standard notion of stability and a vital notion in the study of dynamical systems (including applications such as Mathematical Biology). It appears on the syllabus of many courses at Bath. This writeup covers the defintion (with plain-english interpretation), describes the direct method, and proves the Lyapunov stability theorem. Lyapunov functions and asymptotic stability are briefly mentioned.
Brachistochrone
Friday, May 20th, 2005
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Describes the physical interpretation of the brachistochrone, a motivating example of the calculus of variations. Identification of a special case of that method, and its application to the problem.
