Teaching mathematical modelling
using a research based approach
Greg Foley
School of Biotechnology
Dublin City University
BSc in Biotechnology, DCU
Biology
Bioprocess Engineering
Mathematics
Other
Context
• Third year students with no formal training in
computer programming (or any form of
computing!)
• Often mathematically ‘un-practiced’
• ‘Exciting’ biology versus ‘mundane’
engineering
As a chemical engineer, How can
I engage these students in a
mathematical / quantitative
approach to science ?
Mathematical Models
• Key tool of bioprocess engineering
– Typically involve understanding, mathematical skill
and judgement and creativity
• Model formulation – possibly too challenging
for Biotechnology students
– Emphasis on simulation and investigation of
model predictions
Requirements
• User friendly software for solving ODEs
• Modelling problems that will stimulate
student engagement
– Avoid using models to confirm what is already
known!
– Try to discover something by modelling
– Instructor doesn’t have the answer!
Solution!
• Berkeley Madonna
(www.berkeleymadonna.com)
• Topical research problem
Berkeley Madonna
Research Problem
(Interaction of Teaching and Research!)
Jaffrin M Y and Charrier J Ph. Optimization of ultrafiltration and
diafiltration processes for albumin production. Journal of
Membrane Science 1994, 97: 71-81.
Tekić MN, Zavargo ZZ, Krstić DM and Djurić MS. Mathematical model of
variable volume diafiltration. Hungarian Journal of Industrial
Chemistry 2000 30: 211-214.
Krstić DM, Tekić MN, Zavargo ZZ, Djurić MS and Ćirić GM. Saving water
in a volume-decreasing diafiltration process. Desalination 2004,
165: 283-288.
G. Foley (2006) Water usage in variable volume diafiltration:
comparison with ultrafiltration and constant volume diafiltration.
Desalination 196, 160-163.
G. Foley (2006) Ultrafiltration with variable volume diafiltration: a
novel approach to water saving in diafiltration processes.
Desalination 196, 220-221.
Variable Volume Diafiltration
Qp
Qp
Permeate
Added Water
Retentate tank
Class Project
• Optimisation of a novel type of variable
volume diafiltration (UFVVD)
• Unsolved problem
• Non-obvious answers revealed by modelling
Organisation
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6 groups of three students
Different aspect of problem for each group
Inter-group communication via email
Collation of all results
Examination based on collated results
Inter-Group Communication
Group C
Group E
Group F
Instructor
Group A
Group B
Group D
Experience
• Moderate level of engagement by students
• A little consumed with technicalities of
programming (Attention to detail!)
• Problem chosen possibly a little obscure
• Administration not prohibitive for small class
sizes
Future
• Prior instruction in using Berkeley Madonna
• Better, less ‘obscure’ problem