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Curricular information is subject to change
Upon completion of this module the student should be able to:
identify an ordinary differential equation and classify it by order or linearity.
determine whether or not a unique solution to a firstorder initialvalue problem exists.
understand differences between solutions of linear and nonlinear firstorder differential equations.
recognize and solve linear, separable and exact firstorder differential equations.
use substitutions to solve various firstorder differential equations.
recognize and solve autonomous firstorder differential equations, analyze trajectories, and comment on the stability of critical points.
model and solve application problems using linear and nonlinear firstorder differential equations, including, but not limited to, topics such as: Dynamics of market price, Solow growth model.
determine whether or not a set of solutions to a differential equation are linearly dependent or independent using the Wronskian
use reduction of order to find a second solution from a known solution
solve homogeneous linear equations with constant coefficients
use the method of undetermined coefficients to solve nonhomogeneous linear differential equations for which the nonhomogeneous term can be annihilated
solve nonhomogeneous linear differential equations using variation of parameters
model, solve and analyze problems involving secondorder linear differential equations with application t inflation and unemployment models.
find trajectories associated with, determine critical points of, and perform phase plane analyses for simple autonomous linear and nonlinear systems of equations.
solve first order difference equations and analyse stability of equilibria.
model and solve application problems using difference equations including market models with inventory
First Order Ordinary Differential Equations:
Introduction to first order linear ordinary differential equations with constant coefficients.
First order linear differential equations with variable coefficients.
Nonlinear ordinary differential equations of first order.
Solution of first order linear and nonlinear ordinary differential equations by separable variables method.
Exact linear and nonlinear ordinary differential equations, Integrating factor.
Solution of first order linear ordinary differential equations by integrating factor method,
Equation reducible to linear form: Bernoulli’s equation.
Economic applications: Dynamics of market price, Solow growth model.
Second Order Ordinary Differential Equation
Second order linear ordinary differential equations with constant coefficients.
Applications: A market model with price expectations, The interaction of inflation and unemployment.
Second order linear ordinary differential equations with variable coefficients. Variation of constants and undetermined coefficient techniques to construct solutions
First Order Difference Equations:
Discrete time,
Differences and difference equations.
Solving a first order linear difference equation.
Conditions for dynamic stability of equilibrium. The Cobweb model. Market Model with Inventory.
FirstOrder Systems of two Ordinary Differential Equations
Solving simultaneous dynamical equations.
Phase plane analysis.
Inflation  Unemployment models.
Student Effort Type  Hours 

Lectures  36 
Tutorial  12 
Specified Learning Activities  36 
Autonomous Student Learning  36 
Total  120 
Not applicable to this module.
Description  Timing  Component Scale  % of Final Grade  

Exam (Inperson): 2 Hour Final Exam  n/a  Standard conversion grade scale 40%  No  70 

Assignment(Including Essay): Ten Exercise Sheet Problems to be Submitted Weekly During Tutorials  n/a  Standard conversion grade scale 40%  No  10 

Exam (Inperson): 1 Hour InClass Midterm Exam  n/a  Standard conversion grade scale 40%  No  20 
Resit In  Terminal Exam 

Autumn  Yes  2 Hour 
• Feedback individually to students, postassessment
• Group/class feedback, postassessment
Homeworks and in class tests will be graded and returned to students. Grading will indicate how marks were awarded.
Name  Role 

Jakob Neef  Tutor 
Mr Brian Skelly  Tutor 