Here we provide a selection of homework assignments templates and examples for school, college and university use. These often include a question and answer section already set out, along with space for the student name, course title, date and any other required information. Teachers and lecturers may also find these templates useful for preparing material for their classes.
The proof of the Dual State Lemma in Chapter 2.3 of Gilbert and Porter's Knots and Surfaces has some problems with the exposition and a critical typo. This document reworks the proof to make it more correct and comprehensible. (This material starts on page 33.)
We will study some aspects of the damped driven pendulum. We will see that the trajectory of damped driven pendulum is unpredictable under certain ranges of parameters.
Under some conditions, the trajectory behaves like random. A perturbation of initial condition will lead to different result. Several mathematical tools will be introduced in this study.