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1-3 Mathematical Modeling

Discussion of different types of scientific models, with an emphasis on mathematical modeling.
by

Kelli Warble

on 1 October 2015

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Transcript of 1-3 Mathematical Modeling

1-3 Mathematical Models
By
The
Way,
Here in 20012 AD,
The World
IS ENDING
Katelyn Barnett
So the Council of Elders and Global Elder Harvi-San,
Decided to send out teams to the past,
to change the future
And thu
And thus was born our Mission!
h
phase five
grow old and die
heros
Fall 2013
Agenda:
Discuss/Turn in HW
Types of Models
Developing a Math Model
Introduction to Logger Pro or Graphical Analysis from Vernier (easy graphing software)
Turn in HW:
Thursday, 8/29/2013
Any questions?
Models instead of "Truth"
Create interpretations of natural phenomena to organize experience.
Examine experience for additional data to support or contradict the interpretations.
Use the interpretation, or alter it as necessary when data doesn't fit.
MODEL DEVELOPMENT:
MODEL TESTING:
MODEL DEPLOYMENT and RE-MODEL:
Key scientific ideas which will permeate Unit 1:
2. Measurement
4. Graphs & Variables
3. Evidence Based Conclusions
Unit 1: Scientific Thinking & Measurement
1. What is science?
Announcements:
Lab #1 is split into two parts.
Part A will be due 1 week from today, Tues 9/3/2013.
Part B will be due on Mon 9/9/2013.
When you turn in Part A, be sure to keep data from Part B; we will discuss how to analyze it next week so you know what to include in Part B's report.
Types of Models:
Mathematical Models:
can provide successful quantitative predictions
e.g. finding a linear equation to fit some data
NOT an exact reproduction of what is really happening
extremely useful, but always remember its LIMITATIONS
Working Models:
simplified mental images for physical systems
e.g. the sphere model for the earth
...the particle model for the solar system
=
structural complexities are neglected
always simplified or idealized
Does this mean these working models are not useful?
Limitations of Working Models:
Analogue Models:
make an
analogy
between something already known and something new
e.g. the human circulatory system may be
analogous
to your homes' hot water heating system
~
the analogous system is more familiar than the new system
Are systems and their analogue models
equivalent?
Advantage of Analogue Models:
Does this mean analogue models should not be used?
The graph pictured shows some data about the growth of Ms. Warble’s son Jaen. When Jaen’s weight and age were plotted, it made a fairly straight line. Ms. Warble drew a “best fit” line through the data. Use it to answer the questions:
Example2:
Example 1 (cont):
d. Calculate baby weight at an age of 20 weeks.
Model Deployment:
e. Calculate when the baby will weigh 60 lbs.
f. Calculate baby weight at an age of 20 YEARS.
Example 1 (cont):
a. How many pounds does the baby gain each week?
b. How much did the baby weigh at birth?
c. Write an equation that matches the baby’s graph.
Model Development/Test:
Re-modeling:
h. Is a LINEAR model good for the entire baby's life? What might be a better model? Explain.
g. How would this equation change if Jaen actually lost weight each week? What about if he was born at a different weight? Explain.
Example 1 (cont):
Independent vs. Dependent Variable
Use the description to identify the variables and discuss what needs to be controlled for a "fair test":
A science class puts wide wheels onto a small cart and lets it roll down an inclined ramp and then across the floor. They measure the distance the cart travels. The investigation is repeated using the same cart but this time fitted with narrow wheels. The angle of the incline of the ramp remains constant. The mass of the cart is kept constant.
Example 1:
Graphing Data to get a Mathematical Model
Traditionally, the independent variable goes on the horizontal axis.
wheel width
distance
Lab Report Format
This will be the format for Lab #1B Circle lab.
Purpose
Apparatus/Procedure
Raw Data
Evaluation of Data
Conclusion
See more details on blackboard under "Course Information" tab in Lab Information folder.
Find the mathematical model.
Interpret the graph and equation.
"Analysis of Data" section of Lab Report.
Make an appropriate graph.
Apps on "my asu"
Look for My Apps
Log in again
Look for Graphical Analysis
See if you can make it run and let me know!
Graphing Technology:
Vernier Software
Graphical Analysis
Logger Pro
Available anywhere from an APP on my asu
Free download link available on blackboard under Course Information tab
Now finish Classwork 1-3. For the back, you may want to access graphing technology.
Homework:
Lab 1A due Tuesday.
HW 1-3 will be posted on blackboard with due date-will consist of graphing practice
Full transcript