Learning Outcomes:

On completion of this module students should be able to:

1. Continuous time: First-Order Differential Equations
- understand geometry of flows direction fields, phase lines, equilibrium, stability
- identify bifurcation points.
- classify and describe different types of bifurcations.

2. Second-order differential equations: constant coefficient equations.
- construct fundamental solutions

3. Discrete time: First-Order Difference Equations

- understand dynamic stability to stability
- use graphical approach, phase plane, phase line.
- identify bifurcations

4. Discrete time: Second-Order Difference Equations
- solve constant coefficient equations

5. Systems of Differential and Difference Equations
- solve simultaneous dynamical equations
- construct two-variable phase diagrams
- carry out a stability analysis

Indicative Module Content:

Topics will be taken from the list below:

1. Continuous time: First-Order Differential Equations

a. first-order linear differential equations with constant coefficients.
- application: Dynamics of market price
- geometry of flows direction fields, phase lines, equilibrium, stability.
b. variable coefficient first order differential equations
- method of integrating factors.
c. nonlinear differential equations eg Bernoulli equation.
- application: Solow growth model, linear Cobb-Douglas function
d. elementary bifurcations – dependence on parameters.
- pitchfork, transcritical, saddle-node.
- application: population growth models

2. Second-order differential equations: constant coefficient equations.

a. fundamental solutions
b. applications: market model with price expectations, interaction of inflation and unemployment

3. Discrete time: First-Order Difference Equations

a. solving a first-order difference equation
b. dynamic stability to stability
c. cobweb models
d. application: market model with inventory
e. nonlinear difference equations – graphical approach, phase plane, phase line.
f. [application: market model with ceiling price]
g. bifurcations and chaos: dependence on parameters
h. application: logistic equation for population dynamics

4. Discrete time: Second-Order Difference Equations

a. constant coefficient equations
b. application: interaction models, inflation and unemployment

5. Systems of Differential and Difference Equations

a. solving simultaneous dynamical equations
b. application: input-output models, inflation-unemployment model
c. two-variable phase diagrams
d. linearisation of a nonlinear dynamical system
e. stability analysis

Student Effort Type	Hours
Lectures	36
Tutorial	12
Specified Learning Activities	32
Autonomous Student Learning	32
Total	112

Not applicable to this module.

Required:
BDIC1034J - College English 1, BDIC1035J - College English 2, BDIC1036J - College English 3, BDIC1037J - College English 4, BDIC1047J - English for Uni Studies BDIC, BDIC1048J - English Gen Acad Purposes BDIC, BDIC2007J - English for Spec Acad Purposes, BDIC2015J - Acad Wrt & Comm Skills


 

Assessment Strategy  

Description	Timing		Component Scale		% of Final Grade
Examination: End of Trimester Exam	Unspecified	No	Alternative linear conversion grade scale 40%	No	70
Continuous Assessment: In-class tests and assignments	Varies over the Trimester	n/a	Alternative linear conversion grade scale 40%	No	30

 

Remediation Type	Remediation Timing
In-Module Resit	Prior to relevant Programme Exam Board

• Feedback individually to students, post-assessment

Not yet recorded.

Name	Role
Dr Cornelia Roessing	Lecturer / Co-Lecturer
Dr Daniele Casazza	Tutor
Dr Cornelia Roessing	Tutor