Exam Flashcards
Is open ended and explanatory, specially at the beginning.
Inductive model
A model that treats objects as discrete, such as the particles in a molecular model. A clock is an example of discrete model because the clock skips to the next event start time as the simulation proceeds.
DISCRETE MODEL
Emerged as a powerful, indispensable tool for studying a variety of problems in scientific research, product and process development and manufacturing.
Importance of Mathematical Modelling
Some areas where mathematical models are highly used are : Climate modeling, Aerospace Science, Space Technology, Manufacturing and Design, Seismology, Environment, Economics, Material Research, Water Resource, Drug Design, Populations Dynamics, Combat and War related problems, Medicine, Biology etc.
Uses of Mathematical Modelling
Is a system where all necessary information is available.
WHITE BOX MODEL
Types of Empirical Models
- Experiments
- Observations
A model that represents the objects in a continuous manner, such as the velocity field of fluid in pipe or channels, temperatures and electric field.
CONTINUOUS MODEL
It is basically a conceptual model that display visually of the important components of an ecosystem and linkages between them. It is a simplification of a complex system. The humans are good at common sense with qualitative reasoning.
QUALITATIVE MODEL
Models are mathematically focused and many times are based on complex formulas. In addition quantitative models generally through an input-output matrix. A model and simulation give precise numerical answers.
QUANTITATIVE MODEL
Representation of real-world problem in mathematical form with some simplified assumptions which helps to understand in fundamental and quantitative way.
Mathematical Modelling
Is a logical structure based on theory. A single conditional statement is made and a hypothesis (P) is stated. The conclusion (Q) is then deduced from the statement and hypothesis. (What this model represents ?)
DEDUCTIVE MODEL
Is a “Top-down” approach (Quantitative). It focus on existing theory and usually begins with hypothesis.
INDUCTIVE MODEL
It is used to complement theory and experiments and often to integrate them.
Mathematical Modelling
Is one in which every set of variable states is uniquely determined by parameters in the model and by sets of previous states of these variables. Model that describe behavior on the basis of some physical law.
DETERMINISTIC MODEL
All the operators in a mathematical model exhibit linearity, the resulting mathematical model. The model uses parameters that are constant and do not vary throughout a simulation.
LINEAR MODEL
Flow chart of Inductive Model
see ppt
Improves the quality of work and reduced changes, errors and rework
Importance of Mathematical Modelling
A model accounts for time-dependent changes in the state of the system. Are typically represented by differential equations.
DYNAMIC MODEL
To perform experiments and to solve real world problems which may be risky and expensive or time consuming.
Importance of Mathematical Modelling
Has a widespread applications in all branches of Science and Engineering & Technology, Medicine and several other interdisciplinary areas.
Mathematical Modelling
Solves real-world problems and has become widespread due to increasing computation power and computing methods.
Uses of Mathematical Modelling
Two type of real world problems’ models
BLACK BOX MODEL
WHITE BOX MODEL
Calculate the state of a system at a time using the past time from the state of the system at the current time.
EXPLICIT MODEL
Solution is obtained by solving an equation involving both the current state of the system and the later one which require extra computation and could be harder to solve.
IMPLICIT MODEL
A model calculates the system in equilibrium, and thus is time-invariant. A model cannot be changed, and one cannot enter edit mode when static model is open for detail view.
STATIC MODEL
Types of Theoretical Models
- statistical
- mathematical
- computational
Is a system of which there is no prior information available.
BLACK BOX MODEL
A model that is one where exact prediction is not possible and randomness is present, and variable states are not described by unique values, but rather by probability distributions.
PROBABILISTIC (STOCHASTIC) MODEL
Facilitated to handle large scale and complicated problems.
Uses of Mathematical Modelling
A model introduces dependent parameters that are allowed to vary throughout the course of a simulation run, and its use becomes necessary where interdependencies between parameters cannot be considered.
NONLINEAR MODEL
Types of Mathematical Models
STATIC OR DYNAMIC
DISCRETE OR CONTINUOUS
DETERMINISTIC OR PROBABILISTIC
LINEAR OR NONLINEAR
EXPLICIT OR IMPLICIT
QUALITATIVE AND QUANTITATIVE
Types of Mathematical Modelling
- Empirical
- Theoretical
