mathematical models modelling in mathematics and other aspects of life
TRANSCRIPT
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Mathematical Models
Modelling in Mathematics and Other Aspects of Life
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Introduction
• Is mathematics related to the real world?
• How is mathematics useful?
• Why do we have to do “Word Problems” or Story Problems?
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ModelingWhat is a model (or a mathematical model)?
– Mathematics is the language of change
– The use of mathematics to describe a system’s behavior.
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Why ModelingWhy do we need them and what purpose do
they serve?– To analyze a system to be controlled or
optimized– To hypothesize about how a system works– To make predictions at parameter values
and/or scales that are difficult to test
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Features in ModelingWhat are the features of a mathematical
model?
– Has variables, constants, and exponents– Equations– Inequations
This is the most basic description.
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Process of Mathematical Modeling
REAL WORLD MODEL
RESULT
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System: Example (1)
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System: Example (2)
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Examples of Models
Architectural Chemical molecules
Kepler‘s Law
Feedbacks
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How to Model?1. Assume and Formulate
2. Do the Maths
3. Interpret and Evaluate
4. Improve the Model
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Models
• Models are used to express the characteristics of reality which are considered important and to neglect those which seem secondary.
• By these simplifications, good models allow us to obtain an easily understandable, mathematically calculable image of the real world
• If a model is formulated with the aid of mathematical relations, we speak of mathematical models.
This lecture deals with construction and use of mathematical models in natural sciences.
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Models
• Models are used to express the characteristics of reality which are considered important and to neglect those which seem secondary.
• By these simplifications, good models allow us to obtain an easily understandable, mathematically calculable image of the real world.
• If a model is formulated with the aid of mathematical relations, we speak of mathematical models.
This lecture deals with construction and use of mathematical models in natural sciences.
![Page 13: Mathematical Models Modelling in Mathematics and Other Aspects of Life](https://reader035.vdocuments.net/reader035/viewer/2022070401/56649f1d5503460f94c33500/html5/thumbnails/13.jpg)
Models
• Models are used to express the characteristics of reality which are considered important and to neglect those which seem secondary.
• By these simplifications, good models allow us to obtain an easily understandable, mathematically calculable image of the real world
• If a model is formulated with the aid of mathematical relations, we speak of mathematical models.
![Page 14: Mathematical Models Modelling in Mathematics and Other Aspects of Life](https://reader035.vdocuments.net/reader035/viewer/2022070401/56649f1d5503460f94c33500/html5/thumbnails/14.jpg)
Walking Rates
• Kecepatan = Jarak/Waktu = … m/s
Karena itu, jarak yang ditempuh adalah• Jarak = Kecepatan (m/s) . Waktu (s)
= … mContoh:
Marti memiliki kecepatan: 1,2 m/s
Berarti dalam 1 detik, Marti menempuh jarak =
1,2 m/s . 1 s = 1,2m
Dalam 60 detik, Marti menempuh jarak =
1,2 m/s . 60 s = 72 m
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Walking Rates .. Cont’d
• Bagaimana persamaan model dari Perjalanan Marti?
d = 1,2 . t
Dengan d = distance, t = waktu tempuh. Jenis persamaan apakah ini?
Berapakah waktu yang dibutuhkan Marti untuk menempuh 10 km?