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ACM30220

Academic Year 2026/2027

Partial Differential Equations (ACM30220)

Subject:
Applied & Computational Maths
College:
Science
School:
Mathematics & Statistics
Level:
3 (Degree)
Credits:
5
Module Coordinator:
Dr Colm Clancy
Trimester:
Autumn
Mode of Delivery:
On Campus
Internship Module:
No
How will I be graded?
Letter grades

Curricular information is subject to change.

This course provides a thorough introduction to the mathematical theory of partial differential equations, and the techniques for solving them. Topics include first- and second-order equations, characteristics, classification (hyperbolic, parabolic, elliptic problems), initial and boundary value problems, separation of variables, Fourier methods, integral transform methods and Green’s functions. Examples discussed will include classical analysis of wave motion and heat flow, along with more modern applications such as option pricing with the Black-Scholes model.

About this Module

Learning Outcomes:

Upon successful completion of this module the student will have mastered the basic principles and methods for the analysis of partial differential equations and should be able to:
- Characterise PDEs as linear, nonlinear, quasi-linear etc and discuss different types of boundary conditions and problem domains (e.g. semi-infinite)
- Solve first-order PDEs using the method of characteristics
- Classify a second-order PDE by type (hyperbolic, parabolic, elliptic), and transform to canonical form
- Use the method of separation of variables to solve equations of various types
- Apply appropriate classical solution methods to analyse a range of problems, such the wave motion, diffusion, Laplace’s equation, and the Black-Scholes equation, and interpret the solutions generated

The United Nations identified seventeen Sustainable Development Goals (SDGs) as core to the 2030 Agenda for Sustainable Development, and UCD contributes in general to SDG 4 Quality Education. Further SDGs explored within this module if relevant are listed below. A scale of 1 - 5 indicates the extent to which the SDG is covered.


 

Student Effort Hours:
Student Effort Type Hours
Specified Learning Activities

24
Autonomous Student Learning

60
Lectures

36
Total

120

Approaches to Teaching and Learning:
Lectures, tutorials, enquiry, and problem-based learning.

AI use permitted as a learning tool: students may use AI tools as part of their learning in this module (e.g., summarising material, practice questions, or as a study aid). However, students remain fully responsible for the accuracy and reliability of their learning. Any use of AI must be cited appropriately.

Requirements, Exclusions and Recommendations
Learning Recommendations:

ACM20150 Vector and Integral Calculus


Module Requisites and Incompatibles
Incompatibles:
ACM30080 - PDEs in Financial Maths, ACM30120 - PDEs for Fin. Maths (online)


 

Assessment Strategy
Description Timing Component Scale Must Pass Component % of Final Grade Component repeat (in-module) Offered
Assignment(Including Essay): Assignments Week 1, Week 2, Week 3, Week 4, Week 5, Week 6, Week 7, Week 8, Week 9, Week 10, Week 11, Week 12 Standard conversion grade scale 40% No
20
 No
Exam (In-person): Final examination End of trimester
Duration:
2 hr(s)
 Standard conversion grade scale 40% No
60
 No
Exam (In-person): Midterm test Week 1, Week 2, Week 3, Week 4, Week 5, Week 6, Week 7, Week 8, Week 9, Week 10, Week 11, Week 12 Standard conversion grade scale 40% No
20
 No

As part of UCD's student support, under the Additional Consideration policy, extensions may be available for the following assessments in the module: Assignment (including essay/poster), Portfolio, Reflective Assignment, Report(s), and Individual Project.


Carry forward of passed components
No
 

Resit In Terminal Exam
Spring Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 

Feedback Strategy/Strategies

• Group/class feedback, post-assessment

How will my Feedback be Delivered?

Not yet recorded.

Timetabling information is displayed only for guidance purposes, relates to the current Academic Year only and is subject to change.
Autumn Lecture Offering 1 Week(s) - Autumn: All Weeks Fri 13:00 - 13:50
Autumn Lecture Offering 1 Week(s) - Autumn: All Weeks Thurs 11:00 - 11:50
Autumn Tutorial Offering 1 Week(s) - Autumn: All Weeks Wed 12:00 - 12:50
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