Differential Equations Dynamical Systems and an Introduction to Chaos

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Studies mathematical theory of dynamical systems emphasizing both discrete-time dynamics and nonlinear systems of differential equations. Courses offer the chance to delve deeply into a particular topic and culminate in a certificate of completion for participants who earn passing marks.


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Basic knowledge of matrix theory will be assumed.

. It is the outer product of direct space and reciprocal space. 3 or 4 undergraduate hours. Mathematical and theoretical biology or biomathematics is a branch of biology which employs theoretical analysis mathematical models and abstractions of the living organisms to investigate the principles that govern the structure development and behavior of the systems as opposed to experimental biology which deals with the conduction of experiments to prove and validate the.

Chaos fractals attractors bifurcations with application to areas such as population biology fluid dynamics and classical physics. TAs are available to answer questions or provide clarifications. Courses are accompanied by un-graded quizzes for self-assessment as well as graded exams at the end of each module.

In dynamical system theory a phase space is a space in which all possible states of a system are represented with each possible state corresponding to one unique point in the phase space. For mechanical systems the phase space usually consists of all possible values of position and momentum variables.


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