Edo Priyo Utomo Putro Mujiono
5002201017
Pemodelan matematika B
Resume kuliah tamu mathematical modelling
Mathematical modelling is the process of describing a real world problem in mathematical terms,
usually in the form of equations, and then using these equations both to help understand the original
problem, and also to discover new features about the problem.
Models provide a framework for conceptualizing our ideas about the behaviour of a particular
system.Models allow us to find structure in complex systems and to investigate howdifferent factors
interact
Models can play an important role in informing policies:By providing understanding of underlying causes
for a complex phenomenonBy predicting the future By predicting the impact of interventions.
Mathematical modelling can be used for various different reasons. Developing scientific or systematic
understanding through quantitative expression of the known quantity of the system. Test the effect of
changes in a system, Aid decision making, including tactical decisions by managers strategic decisions by
planners.How well any particular objective is achieved depends on both the state of knowledge about a
system and how well the modelling is done.
--Use of mathematical modelling,
Solves the real world problems and gas become wide spread due to increasing computation power and
computing methods, facilitated to handle large scale and complicated problems, and some areas where
mathematical models used are: climate modelling, aerospace etc,
--Type od mathematical modelling,
Emprical models: experiments, observations
Theoretorical: staticistical, mathematical, and computational
Real world problem simplify working model represent mathematical model translate computational
model and the simulate result/conclusions
There are many different types of mathematical models. Classifying them into broad categories can tell
you much about their purpose and scope and often require different mathematical techniques.
1) Empirical vs mechanistic
Empirical Models (Statistical Models):
Data driven modelling approach, starting point: data obtained from empirical studies
Mechanistic Models (Process Based Models):
Hypothesis driven modelling approach, starting point: specific phenomena of interest – observed from
data
2) Deterministic vs stochastic
Deterministic models:
Assume that the outcome is precisely determined by the model inputs and
relationships, Ignore all random variation.
Stochastic models:
Incorporate inherent randomness, Use a range of values for the model variables in form of probability
distributions
3)Static vs dynamic
Static Models:
In static systems, time does not play any part, the variables and relationships describing the system are
time-independent.
Dynamic Models:
In dynamic systems, time plays a very important role with the variables and/or relationships describing
the system changing with time.
4)Linear vs non-linear
Linear models:
Observation data has a linear relation among variables (linear regression), the rate of change is in a
linear relation (linear differential equations).
Non-linear models:
When the data shows a curvy relationship that is not a straight line applying a nonlinear model gives the
accurate output, The rate of change is in a nonlinear relation (nonlinear differential equations)
5)Discrete vs continuous
Discrete models:
The state variables change only at a countable number of points in time.
Continuous models:
the state variables change in a continuous way, and not abruptly from one state to another (infinite
number of states).