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Teaching mathematical modelling using a research based approach
Greg FoleySchool of Biotechnology
Dublin City University
BSc in Biotechnology, DCU
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
Retentate tank
Added WaterPermeate
Class Project
• Optimisation of a novel type of variable volume diafiltration (UFVVD)
• Unsolved problem
• Non-obvious answers revealed by modelling
Organisation
• 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
Group C
Group F
Group E
Group A
Group D
Group B
Instructor
Inter-Group Communication
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