Lecture Notes 1 - H-SC
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Lecture Notes 1 What is Computational Science? What is Computational Science? Introduction to Computational Science , Fall 2010 Marcus Pendergrass Hampden-Sydney College
Transcript of Lecture Notes 1 - H-SC
Lecture Notes 1
What is Computational Science?What is Computational Science?Introduction to Computational Science , Fall 2010
Marcus PendergrassHampden-Sydney College
Lecture Notes 1
Dr. Pendergrass
Basics
The ModelingProcess
Types of Models
Outline
1 Basics
2 The Modeling Process
3 Types of Models
Dr. Pendergrass (H-SC) Lecture Notes 1 Fall 2010 2 / 16
Lecture Notes 1
Dr. Pendergrass
Basics
The ModelingProcess
Types of Models
Computational Science
Definition
Computational science is the theory and practice of using modelingand simulation to solve problems.
ComputationalScience
ModelingSimulation
Problem Domain
Dr. Pendergrass (H-SC) Lecture Notes 1 Fall 2010 3 / 16
Lecture Notes 1
Dr. Pendergrass
Basics
The ModelingProcess
Types of Models
Problem Domains
Definition
The problem domain is the field of study that the problem comesfrom.
Some important problem domains:
I biologyepidemiology, genomics, ecology, ...
I meteorologyweather prediction, climate modeling
I engineeringaircraft design, integrated circuit design, ...
I physicsgalaxy formation, stellar dynamics, ...
I many more...
Dr. Pendergrass (H-SC) Lecture Notes 1 Fall 2010 4 / 16
Lecture Notes 1
Dr. Pendergrass
Basics
The ModelingProcess
Types of Models
Problem Domains
Definition
The problem domain is the field of study that the problem comesfrom.
Some important problem domains:
I biologyepidemiology, genomics, ecology, ...
I meteorologyweather prediction, climate modeling
I engineeringaircraft design, integrated circuit design, ...
I physicsgalaxy formation, stellar dynamics, ...
I many more...
Dr. Pendergrass (H-SC) Lecture Notes 1 Fall 2010 4 / 16
Lecture Notes 1
Dr. Pendergrass
Basics
The ModelingProcess
Types of Models
Models
Definition
A model is a description of a system that reflects importantproperties of the system. A mathematical model is a model framed inthe language of mathematics.
Example
I System: a population whose rate of growth is proportional tothe size of the population.
I Mathematical model: dPdt = kP .
Dr. Pendergrass (H-SC) Lecture Notes 1 Fall 2010 5 / 16
Lecture Notes 1
Dr. Pendergrass
Basics
The ModelingProcess
Types of Models
Models
Definition
A model is a description of a system that reflects importantproperties of the system. A mathematical model is a model framed inthe language of mathematics.
Example
I System: a population whose rate of growth is proportional tothe size of the population.
I Mathematical model: dPdt = kP .
Dr. Pendergrass (H-SC) Lecture Notes 1 Fall 2010 5 / 16
Lecture Notes 1
Dr. Pendergrass
Basics
The ModelingProcess
Types of Models
Simulations
Definition
A simulation is physical system that mimics important properties ofsome other system. A computer simulation a simulation that isimplemented as a computer program.
Example
I System: a population whose rate of growth is proportional tothe size of the population.
I Mathematical model: dPdt = kP .
I Computer simulation: a Matlab program to solve themathematical model.
note:
Matlab is a computational environment for carrying out simulations.
Dr. Pendergrass (H-SC) Lecture Notes 1 Fall 2010 6 / 16
Lecture Notes 1
Dr. Pendergrass
Basics
The ModelingProcess
Types of Models
Simulations
Definition
A simulation is physical system that mimics important properties ofsome other system. A computer simulation a simulation that isimplemented as a computer program.
Example
I System: a population whose rate of growth is proportional tothe size of the population.
I Mathematical model: dPdt = kP .
I Computer simulation: a Matlab program to solve themathematical model.
note:
Matlab is a computational environment for carrying out simulations.
Dr. Pendergrass (H-SC) Lecture Notes 1 Fall 2010 6 / 16
Lecture Notes 1
Dr. Pendergrass
Basics
The ModelingProcess
Types of Models
Simulations
Definition
A simulation is physical system that mimics important properties ofsome other system. A computer simulation a simulation that isimplemented as a computer program.
Example
I System: a population whose rate of growth is proportional tothe size of the population.
I Mathematical model: dPdt = kP .
I Computer simulation: a Matlab program to solve themathematical model.
note:
Matlab is a computational environment for carrying out simulations.
Dr. Pendergrass (H-SC) Lecture Notes 1 Fall 2010 6 / 16
Lecture Notes 1
Dr. Pendergrass
Basics
The ModelingProcess
Types of Models
Computational Environment
A computational environment is a computer program that facilitatescalculations. Computational environments may be fairly simple (e.g.graphing calculators), or very sophisticated. Examples ofcomputational environments include
I CalculatorsI calculator app on iPhone, TI-8x graphing calculators, etc.
I SpreadsheetsI Microsoft Excel, Apple Numbers, Open Office Calc
I Numerical environmentsI Matlab, Octave
I Computer algebra systemsI Maple, Mathematica, Sage
Dr. Pendergrass (H-SC) Lecture Notes 1 Fall 2010 7 / 16
Lecture Notes 1
Dr. Pendergrass
Basics
The ModelingProcess
Types of Models
The Practice Of Computational Science
Interdisciplinary
Collaboration across disciplines is typical of computational science.
Teamwork
Teams usually include mathematicians, computer scientists, andexperts in the problem domain area (e.g. scientists, engineers).
Reporting
Results of computational science research and practice must becommunicated to a wider community in order to have an impact.
Dr. Pendergrass (H-SC) Lecture Notes 1 Fall 2010 8 / 16
Lecture Notes 1
Dr. Pendergrass
Basics
The ModelingProcess
Types of Models
The Practice Of Computational Science
Interdisciplinary
Collaboration across disciplines is typical of computational science.
Teamwork
Teams usually include mathematicians, computer scientists, andexperts in the problem domain area (e.g. scientists, engineers).
Reporting
Results of computational science research and practice must becommunicated to a wider community in order to have an impact.
Dr. Pendergrass (H-SC) Lecture Notes 1 Fall 2010 8 / 16
Lecture Notes 1
Dr. Pendergrass
Basics
The ModelingProcess
Types of Models
The Practice Of Computational Science
Interdisciplinary
Collaboration across disciplines is typical of computational science.
Teamwork
Teams usually include mathematicians, computer scientists, andexperts in the problem domain area (e.g. scientists, engineers).
Reporting
Results of computational science research and practice must becommunicated to a wider community in order to have an impact.
Dr. Pendergrass (H-SC) Lecture Notes 1 Fall 2010 8 / 16
Lecture Notes 1
Dr. Pendergrass
Basics
The ModelingProcess
Types of Models
Outline
1 Basics
2 The Modeling Process
3 Types of Models
Dr. Pendergrass (H-SC) Lecture Notes 1 Fall 2010 9 / 16
Lecture Notes 1
Dr. Pendergrass
Basics
The ModelingProcess
Types of Models
The Modeling Process
The basic modeling process
Dr. Pendergrass (H-SC) Lecture Notes 1 Fall 2010 10 / 16
Lecture Notes 1
Dr. Pendergrass
Basics
The ModelingProcess
Types of Models
The Modeling Process
The basic modeling process
I Problems with verification and interpretation may cause you togo back to previous steps in the process.
Dr. Pendergrass (H-SC) Lecture Notes 1 Fall 2010 11 / 16
Lecture Notes 1
Dr. Pendergrass
Basics
The ModelingProcess
Types of Models
The Modeling Process
The basic modeling process
I Problems with verification and interpretation may cause you togo back to previous steps in the process.
I Maintaining the model may also require you to revisit earliersteps.
Dr. Pendergrass (H-SC) Lecture Notes 1 Fall 2010 12 / 16
Lecture Notes 1
Dr. Pendergrass
Basics
The ModelingProcess
Types of Models
Outline
1 Basics
2 The Modeling Process
3 Types of Models
Dr. Pendergrass (H-SC) Lecture Notes 1 Fall 2010 13 / 16
Lecture Notes 1
Dr. Pendergrass
Basics
The ModelingProcess
Types of Models
Types Of Models
Deterministic and Stochastic Models
A probabilistic or stochastic model exhibits random effects. Adeterministic model does not. Many models are combinations of thetwo.
Static and Dynamic Models
A static model does not consider time, while a dynamic modelchanges with time.
Continuous and Discrete Models
A continuous-time model treats time as a continuous variable, able totake on any value. A discrete-time model treats time as a discretevariable, only able to take on certain pre-defined values.
Dr. Pendergrass (H-SC) Lecture Notes 1 Fall 2010 14 / 16
Lecture Notes 1
Dr. Pendergrass
Basics
The ModelingProcess
Types of Models
Types Of Models
Deterministic and Stochastic Models
A probabilistic or stochastic model exhibits random effects. Adeterministic model does not. Many models are combinations of thetwo.
Static and Dynamic Models
A static model does not consider time, while a dynamic modelchanges with time.
Continuous and Discrete Models
A continuous-time model treats time as a continuous variable, able totake on any value. A discrete-time model treats time as a discretevariable, only able to take on certain pre-defined values.
Dr. Pendergrass (H-SC) Lecture Notes 1 Fall 2010 14 / 16
Lecture Notes 1
Dr. Pendergrass
Basics
The ModelingProcess
Types of Models
Types Of Models
Deterministic and Stochastic Models
A probabilistic or stochastic model exhibits random effects. Adeterministic model does not. Many models are combinations of thetwo.
Static and Dynamic Models
A static model does not consider time, while a dynamic modelchanges with time.
Continuous and Discrete Models
A continuous-time model treats time as a continuous variable, able totake on any value. A discrete-time model treats time as a discretevariable, only able to take on certain pre-defined values.
Dr. Pendergrass (H-SC) Lecture Notes 1 Fall 2010 14 / 16
Lecture Notes 1
Dr. Pendergrass
Basics
The ModelingProcess
Types of Models
Practice
Practice 1.1
What is the difference between a model and a simulation? Whichcomes first in the basic modeling process?
Practice 1.2
Suppose we want to model the angle of the minute hand of a clock(measured from the 12 o’clock position, say). If θ is the angle indegrees, and t is the time in minutes past the hour, find an equationthat models the relationship between θ and t.
Practice 1.3
Suppose I have a spreadsheet that tells me how much I have left topay on my mortgage at the end of each month. Does this represent adiscrete-time model or a continuous-time model?
Dr. Pendergrass (H-SC) Lecture Notes 1 Fall 2010 15 / 16
Lecture Notes 1
Dr. Pendergrass
Basics
The ModelingProcess
Types of Models
Practice
Practice 1.4
Give an example of a system for which a probabilistic model would beappropriate. Give another example in which a probabilistic modelwould not be appropriate.
Practice 1.5
Write an essay describing an example of computational science inaction in industry, government, or academia. Carefully delineate theproblem that was addressed, and the computational science approachthat was used to solve the problem. Reference all sources used inyour report.
Dr. Pendergrass (H-SC) Lecture Notes 1 Fall 2010 16 / 16
