Module description
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.
Prerequisites:
Students are advised to have taken 4CCM111A Calculus I and 4CCM113A Linear Algebra and Geometry I
Assessment details
Written examination or alternative assessment.
Exercises or quizzes will be set each week to be handed in the following week. These problems will be discussed in the tutorials and solutions will be available.
Educational aims & objectives
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
Three hours of lectures and one hour of tutorial per week throughout the term
Suggested reading list
Suggested reading/resources (link to My Reading Lists)