signalvorti.blogg.se - Application linear differential equation systems population

#APPLICATION LINEAR DIFFERENTIAL EQUATION SYSTEMS POPULATION HOW TO#
#APPLICATION LINEAR DIFFERENTIAL EQUATION SYSTEMS POPULATION PROFESSIONAL#

Generalising the Euler-Lagrange equation to the case of several dependent variables.

Special-case solutions of the Euler-Lagrange equation: geodesics, Fermat's principle, Principle of Least Action.

Derivation of the Euler-Lagrange equation.

Motivation: finding the shortest distance between two points, the shape of a hanging chain and other important problems.

Applications - including modelling interacting populations, models for epidemics.

Limit cycles, bifurcations in 2D systems, Hopf bifurcations.

Nonlinear systems and linearisation, the Hartman-Grobman theorem.

Analysis of linear systems in two dimensions, the phase plane.

Matlab ODE solvers and non-linear IVPs.ĭeveloping and analysing ordinary differential equation models.

Numerical solution of ordinary differential equations

#APPLICATION LINEAR DIFFERENTIAL EQUATION SYSTEMS POPULATION HOW TO#

Modelling examples, different types of questions (and how to answer them), necessity for theory and computation.Graduates are self-aware and reflective they are flexible and resilient and have the capacity to accept and give constructive feedback they act with integrity and take responsibility for their actions.

#APPLICATION LINEAR DIFFERENTIAL EQUATION SYSTEMS POPULATION PROFESSIONAL#

Graduates engage in professional behaviour and have the potential to be entrepreneurial and take leadership roles in their chosen occupations or careers and communities.Īttribute 8: Self-awareness and emotional intelligence Graduates convey ideas and information effectively to a range of audiences for a variety of purposes and contribute in a positive and collaborative manner to achieving common goals.Īttribute 4: Professionalism and leadership readiness Graduates are effective problems-solvers, able to apply critical, creative and evidence-based thinking to conceive innovative responses to future challenges.Īttribute 3: Teamwork and communication skills Graduates have comprehensive knowledge and understanding of their subject area, the ability to engage with different traditions of thought, and the ability to apply their knowledge in practice including in multi-disciplinary or multi-professional contexts.Īttribute 2: Creative and critical thinking, and problem solving This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below: University Graduate AttributeĪttribute 1: Deep discipline knowledge and intellectual breadth Modelling with Ordinary Differential Equations Hon Topics covered are: analytical methods for systems of ODEs, including vector fields, fixed points, phase-plane analysis, linearisation of nonlinear systems, bifurcations general theory on existence and approximation of ODE solutions biological modelling explicit and implicit numerical methods for ODE initial value problems, computational error, consistency, convergence, stability of a numerical method, ill-conditioned and stiff problems.

A key aim of the course is building practical skills that can be applied in a wide range of scientific, business and research settings. A range of important biological problems, from areas such as resource management, population dynamics, and public health, drives the study of analytical and numerical techniques for systems of nonlinear ODEs. This course focuses on ordinary differential equations (ODEs) and develops students' skills in the formulation, solution, understanding and interpretation of coupled ODE models. Differential equation models describe a wide range of complex problems in biology, engineering, physical sciences, economics and finance.