Module description
Aims
The module aims to introduce you to the analysis of simple dynamical systems described in terms of first or second order differential equations, emphasising concepts such as phase flow, fixed points, and stability of fixed points. The ideas introduced have applications in biology and economics, as well as in Newtonian mechanics. Newtonian mechanics is taught with emphasis on motion in one spatial dimension, and in that case furnishes examples of so-called second order dynamical systems. Elements of the Hamiltonian approach to Newtonian mechanics are also introduced.
Syllabus
Differential equations; first-order dynamical systems, autonomous systems, phase flow and fixed points; second-order dynamical systems, phase flow, classification of fixed points; kinematics of particle motion, Newton's laws; conservation of energy, conservative forces, motion on a straight line; Hamiltonian systems; elements of Hamiltonian mechanics.
Teaching arrangements
Three hours of lectures each week. In addition, a one hour small group tutorial each week and one hour of large group problem classes.
Prerequisites
Normally 4CCM111a Calculus I and 4CCM113A Linear Algebra and Geometry I
Formative assessment
Exercise sheets will be given out. Solutions handed in will be marked and difficulties discussed during tutorials and in class. Assignments are regarded as an essential element of the course as they provide the necessary opportunity for active training and for sharpening ideas about the material presented in the course
Required reading/resources : None
Suggested reading/resources (link to My Reading Lists)
Assessment details
Written examination and class tests or alternative assessment.
Educational aims & objectives
Aims
The module aims to introduce you to the analysis of simple dynamical systems described in terms of first or second order differential equations, emphasising concepts such as phase flow, fixed points, and stability of fixed points. The ideas introduced have applications in biology and economics, as well as in Newtonian mechanics. Newtonian mechanics is taught with emphasis on motion in one spatial dimension, and in that case furnishes examples of so-called second order dynamical systems. Elements of the Hamiltonian approach to Newtonian mechanics are also introduced.
Teaching pattern
Teaching arrangements
Three hours of lectures each week. In addition, a one hour small group tutorial each week and one hour of large group problem classes.
Suggested reading list
Suggested reading/resources (link to My Reading Lists)