Mathematical Models

Modelling in Mathematics and Other Aspects of Life

Introduction

• Is mathematics related to the real world?

• How is mathematics useful?

• Why do we have to do “Word Problems” or Story Problems?

ModelingWhat is a model (or a mathematical model)?

– Mathematics is the language of change

– The use of mathematics to describe a system’s behavior.

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

Features in ModelingWhat are the features of a mathematical

model?

– Has variables, constants, and exponents– Equations– Inequations

This is the most basic description.

Process of Mathematical Modeling

REAL WORLD MODEL

RESULT

System: Example (1)

System: Example (2)

Examples of Models

Architectural Chemical molecules

Kepler‘s Law

Feedbacks

How to Model?1. Assume and Formulate

2. Do the Maths

3. Interpret and Evaluate

4. Improve the Model

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.

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.

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.

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

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?