Abstract: Analysis of continuous-time piecewise linear systems based on piecewise quadratic (PWQ) Lyapunov functions typically requires continuity of these functions. Several conditions for ...

The pursuit of differentiability in functions is a cornerstone of calculus, demanding a delicate balance of smoothness and continuity. When tasked with finding specific parameters that ensure a ...

A piecewise relation, at its core, is a relation that is defined by multiple sub-relations, each applying to a certain interval of the domain. These sub-relations are essentially different equations ...

Physics and Python stuff. Most of the videos here are either adapted from class lectures or solving physics problems. I really like to use numerical calculations without all the fancy programming ...

The original version of this story appeared in Quanta Magazine. Calculus is a powerful mathematical tool. But for hundreds of years after its invention in the 17th century, it stood on a shaky ...

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In the late 19th century, Karl Weierstrass invented a fractal-like function that was decried as nothing less than a “deplorable evil.” In time, it would transform the foundations of mathematics.

I just noticed that the textbook lacks an example relevant to this exercise group, which is a type of problem we frequently assess: Given a piecewise-defined function, we want to know if it is ...

Ryan Rogers earned his Ph.D. in mathematics from the University of Kentucky in May 2024. His interests lie primarily in undergraduate mathematics education and especially in undergraduate students’ ...

Research Center of Dynamical Systems and Control, Suzhou University, Suzhou, Anhui 234000, P. R. China School of Earth and Space Sciences, University of Science and Technology of China, Hefei, Anhui ...