SM-722: Dynamic Modelling
Credits: 4 (3-1-0)
COURSE OBJECTIVE
This course exposes the students in mathematical tools for exploring and studying real world
problems. The overall objective of this course is to provide an introduction to the process of
mathematical modelling while giving students an opportunity to



develop and construct appropriate models for various problem situations,
analyze given models to uncover underlying assumptions, and
investigate particular problems to find out what has already been done toward developing
solutions.
COURSE DESCRIPTION:
Unit -I:
System modelling, classification of models, validation and verification. Systems, reservoirs,
processes, converters, interrelationships. Uses of systems models. A systems approach: systems
thinking, feedback-positive, negative.
Basic modelling concepts, building blocks, modelling of growth or decay-linear, exponential, logistic,
overshoot or collapse, oscillation. Strategies for analysing and using systems models. Analysing a
model, applying the strategy-problem definition, model validation, exploratory analysis, case
analysis.
Unit-II:
Modelling predator-prey systems-problem definition, background information, difference equations,
steady state solution. Modelling the dynamic deer-wolf system. Modelling surface water
contamination-problem definition, background information, difference equations, steady state
solution. Modelling the dynamic DO system.
Unit-III:
Modelling matter cycling in ecosystems-problem definition, background information, difference
equations, steady state solution. Modelling the dynamic phosphorus system. Modelling mobile
source air pollution inventories-problem definition, background information, difference equations,
steady state solution. Modelling the dynamic mobile source emissions system.
Unit-IV:
Modelling greenhouse gases and global warming-problem definition, background information,
difference equations, steady state solution. Modelling the dynamic greenhouse gas system.
Modelling atmospheric chemistry and pollution transport-problem definition, background
information, difference equations, steady state solution. Modelling the dynamic acid deposition
system.
TEXTBOOKS
Deaton Michael L., Winebrake James J.: Dynamic Modelling of Environmental Systems. Springer.
Brian Albright: Mathematical Modelling with excel
Meerschaert, M., Mathematical Modeling, Academic Press, Fourth Edition
COURSE PLAN:
Week
Unit
1
I
2
I
3
I
4
I
5
II
6
7
II
II
8
9
II
III
10
11
III
III
12
III
13
IV
14
15
IV
IV
16
IV
TOTAL
Topics
Hours
Lecture Tutorial
System modelling, classification of models, validation
3
1
and verification. Systems, reservoirs, processes,
converters, interrelationships. Uses of systems
models.
A systems approach: systems thinking, feedback3
1
positive, negative.
Basic modelling concepts, building blocks, modelling
3
1
of growth or decay-linear, exponential, logistic,
overshoot or collapse, oscillation.
Strategies for analysing and using systems models.
3
1
Analysing a model, applying the strategy-problem
definition, model validation, exploratory analysis,
case analysis.
Modelling
predator-prey
systems-problem
3
1
definition, background information, difference
equations, steady state solution.
Modelling the dynamic deer-wolf system.
3
1
Modelling surface water contamination-problem
3
1
definition, background information, difference
equations, steady state solution.
Modelling the dynamic DO system.
3
1
Modelling matter cycling in ecosystems-problem
3
1
definition, background information, difference
equations, steady state solution.
Modelling the dynamic phosphorus system.
3
1
Modelling mobile source air pollution inventories3
1
problem definition, background information,
difference equations, steady state solution.
Modelling the dynamic mobile source emissions
3
1
system.
Modelling greenhouse gases and global warming3
1
problem definition, background information,
difference equations, steady state solution.
Modelling the dynamic greenhouse gas system.
3
1
Modelling atmospheric chemistry and pollution
3
1
transport-problem
definition,
background
information, difference equations, steady state
solution.
Modelling the dynamic acid deposition system.
3
1
48
16
Practical
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0