INSTRUCTOR: Associate Prof Wang Jian-Sheng, TA: Zeng Nan (g0306095@.nus.edu.sg)
LECTURES: Monday 2:00-4:00pm LT20, Lab/tutorial slots: Tue 2:00-- and Wed 4:00-- (lab last for 2 hrs, tutorial 1 hr, tutorials are on week 3,5,8,9,11,13, lab on week 2,4,6,8,10). Week 1 starts 5 Jan 2004. Final exam 15 Apr 04, 1:00pm, at S9A-02-01.
TEXTBOOK: Mathematical Modeling for Industry and Engineering, by Thomas Svobodny, Prentice Hall (1998). Additional reference: "Mathematics for Dynamic Modeling", by E. Beltrami, 2nd ed, Academic Press (1998).
SYLLABUS: Methods for developing models that represent physical, biological, and social systems, including use of dimensional analysis, empirical data, approximation level of models, and model validation. Emphasis will be on eventual development of computational models and on the use of prototyping software environments. Use of visualization software and techniques will be an integrated, interactive part of the modeling process. The course will include modeling case studies: e.g.: biological pattern formation, wave propagation, traffic modeling, and financial modeling.
Week 1. 5 Jan , introduction
Week 2. 12 Jan , examples of modeling process, lab 1and answers
Week 3. 19 Jan , least-squares and planetary motion, tutorial/homework 1
Week 4. 26 Jan , stability and bifurcation, lab 2 and answers (Mathematica notebook format) and processed moon data.
Week 5. 2 Feb , (no class), tutorial/homework 2
Week 6. 9 Feb , dimensional analysis, lab 3
Week 7. 16 Feb , Buckingham Pi theorem, tutorial/homework 3,
Week 8. 23 Feb , growth and logistic equation (50min midterm test, answers), lab 4,
Week 9. 1 Mar , rate equations, ecological models, vibrations tutorial/homework 4
Week 10. 8 Mar , further examples of ODE, lab 5
Week 11. 15 Mar , probabilities, tutorial/homework 5
Week 12. 22 Mar , random processes, Markov chain models
Week 13. 29 Mar , revision, summary, tutorial/homework 6