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